User manual | theano Documentation

theano Documentation
Release 0.8.2
LISA lab, University of Montreal
April 21, 2017
CONTENTS
1
News
3
2
Download
5
3
Citing Theano
7
4
Documentation
9
5
Community
11
6
Help!
13
Python Module Index
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Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Theano features:
• tight integration with NumPy – Use numpy.ndarray in Theano-compiled functions.
• transparent use of a GPU – Perform data-intensive calculations up to 140x faster than with
CPU.(float32 only)
• efficient symbolic differentiation – Theano does your derivatives for function with one or many
inputs.
• speed and stability optimizations – Get the right answer for log(1+x) even when x is really tiny.
• dynamic C code generation – Evaluate expressions faster.
• extensive unit-testing and self-verification – Detect and diagnose many types of errors.
Theano has been powering large-scale computationally intensive scientific investigations since 2007. But it
is also approachable enough to be used in the classroom (University of Montreal’s deep learning/machine
learning classes).
CONTENTS
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CONTENTS
CHAPTER
ONE
NEWS
• 2016/05/09: New technical report on Theano: Theano: A Python framework for fast computation of
mathematical expressions. This is the new preferred reference.
• 2016/04/21: Release of Theano 0.8.2, adding support for CuDNN v5.
• 2016/03/29: Release of Theano 0.8.1, fixing a compilation issue on MacOS X with XCode 7.3.
• 2016/03/21: Release of Theano 0.8. Everybody is encouraged to update.
• Multi-GPU.
• We added support for CNMeM to speed up the GPU memory allocation.
• Theano 0.7 was released 26th March 2015. Everybody is encouraged to update.
• We support cuDNN if it is installed by the user.
• Open Machine Learning Workshop 2014 presentation.
• Colin Raffel tutorial on Theano.
• Ian Goodfellow did a 12h class with exercises on Theano.
• New technical report on Theano: Theano: new features and speed improvements.
• HPCS 2011 Tutorial. We included a few fixes discovered while doing the Tutorial.
You can watch a quick (20 minute) introduction to Theano given as a talk at SciPy 2010 via streaming (or
downloaded) video:
Transparent GPU Computing With Theano. James Bergstra, SciPy 2010, June 30, 2010.
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Chapter 1. News
CHAPTER
TWO
DOWNLOAD
Theano is now available on PyPI, and can be installed via easy_install Theano, pip install
Theano or by downloading and unpacking the tarball and typing python setup.py install.
Those interested in bleeding-edge features should obtain the latest development version, available via:
git clone git://github.com/Theano/Theano.git
You can then place the checkout directory on your $PYTHONPATH or use python setup.py
develop to install a .pth into your site-packages directory, so that when you pull updates via
Git, they will be automatically reflected the “installed” version. For more information about installation and
configuration, see installing Theano.
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Chapter 2. Download
CHAPTER
THREE
CITING THEANO
If you use Theano for academic research, you are highly encouraged (though not required) to cite the following, most recent paper:
• Theano Development Team. “Theano: A Python framework for fast computation of mathematical
expressions”. (short BibTeX, full BibTeX)
Theano is primarily developed by academics, and so citations matter a lot to us. As an added benefit, you
increase Theano’s exposure and potential user (and developer) base, which is to the benefit of all users of
Theano. Thanks in advance!
See our citation for details.
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Chapter 3. Citing Theano
CHAPTER
FOUR
DOCUMENTATION
Roughly in order of what you’ll want to check out:
• Installing Theano – How to install Theano.
• Theano at a Glance – What is Theano?
• Tutorial – Learn the basics.
• API Documentation – Theano’s functionality, module by module.
• faq – A set of commonly asked questions.
• Optimizations – Guide to Theano’s graph optimizations.
• Extending Theano – Learn to add a Type, Op, or graph optimization.
• Developer Start Guide – How to contribute code to Theano.
• developer – Primarily of interest to developers of Theano
• Internal Documentation – How to maintain Theano and more...
• Release – How our release should work.
• Acknowledgements – What we took from other projects.
• Related Projects – link to other projects that implement new functionalities on top of Theano
You can download the latest PDF documentation, rather than reading it online.
Check out how Theano can be used for Machine Learning: Deep Learning Tutorials.
Theano was featured at SciPy 2010.
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Chapter 4. Documentation
CHAPTER
FIVE
COMMUNITY
“Thank YOU for correcting it so quickly. I wish all packages I worked with would have such
an active maintenance - this is as good as it gets :-)”
(theano-users, Aug 2, 2010)
• Register to theano-announce if you want to be kept informed on important change on theano(low
volume).
• Register and post to theano-users if you want to talk to all Theano users.
• Register and post to theano-dev if you want to talk to the developers.
• Register to theano-github if you want to receive an email for all changes to the GitHub repository.
• Register to theano-buildbot if you want to receive our daily buildbot email.
• Ask/view questions/answers at StackOverflow
• We use Github tickets to keep track of issues (however, some old tickets can still be found on Assembla).
• Come visit us in Montreal! Most developers are students in the LISA group at the University of
Montreal.
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Chapter 5. Community
CHAPTER
SIX
HELP!
6.1 How to Seek Help
The appropriate venue for seeking help depends on the kind of question you have.
• How do I? – theano-users mailing list or StackOverflow
• I got this error, why? – theano-users mailing list or StackOverflow (please include the full error
message, even if it’s long)
• I got this error and I’m sure it’s a bug – Github ticket
• I have an idea/request – post the suggestion to theano-dev or, even better, implement the idea and
submit a GitHub pull request!
• Why do you? – theano-users mailing list (not appropriate for StackOverflow)
• When will you? – theano-dev mailing list (not appropriate for StackOverflow)
Please do take some time to search for similar questions that were asked and answered in the past. If you
find something similar that doesn’t fully answer your question, it can be helpful to say something like “I
found X but it doesn’t address facet Y” and link to the previous discussion.
When asking questions on StackOverflow, please use the theano tag, so your question can be found, and
follow StackOverflow’s guidance on asking questions. Consider also using the python and numpy tags,
especially if you are unsure which library your problem relates to.
It’s often helpful to include the following details with your question:
• If you have an error, the full error message, even if it’s long
• Which versions of Python and Theano you’re using
• Whether you’re using a CPU or GPU device
• Details of your Theano configuration settings (you can print this in Python via print theano.config)
Spending the time to create a minimal specific example of a problem is likely to get you to an answer quicker
than posting something quickly that has too much irrelevant detail or is too vague. A minimal example may
take you a bit more time to create but the first response is more likely to be the answer you need than, rather
than a frustrated request for clarification.
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6.2 How to provide help
If you see a question on the theano-users mailing list, or on StackOverflow, that you feel reasonably confident you know an answer to, please do support the community by helping others.
We were all newbies to Theano once and, as the community expands, there is a constant stream of new
Theano users looking for help. Perhaps you asked a question when you were first starting out? Now you
can pay it forward by helping others. It’s also a good way to reinforce your own Theano knowledge.
Often it’s easiest to answer a question directly but sometimes it may be better to refer people to a good
answer that was provided in the past. Pointing people to relevant sections in the documentation, or to a
Theano tutorial, can also be helpful.
When answering questions please be nice (as always!) and, on StackOverflow, follow their guidance for
answering questions.
6.2.1 Release Notes
Theano 0.8.2 (21th of April, 2016)
This is a point release with only the support for cudnn v5 convolution and minor fixes.
Highlights: - cuDNN v5 convolution support (cuDNN v3 isn’t supported anymore) - A few crash fixes
Theano 0.8.1 (29th of March, 2016)
This is a point release without any new feature.
It fixes compilation issues on MacOS X with the command line tools for XCode 7.3, which was released
shortly after Theano 0.8.0.
Theano 0.8 (21th of March, 2016)
We recommend that everybody update to this version.
Highlights:
• Python 2 and 3 support with the same code base
• Faster optimization
• Integration of cuDNN for better GPU performance
• Many Scan improvements (execution speed up, ...)
• optimizer=fast_compile moves computation to the GPU.
• Better convolution on CPU and GPU. (CorrMM, cuDNN, 3d conv, more parameter)
• Interactive visualization of graphs with d3viz
• cnmem (better memory management on GPU)
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• BreakpointOp
• Multi-GPU for data parallism via Platoon (https://github.com/mila-udem/platoon/)
• More pooling parameter supported
• Bilinear interpolation of images
• New GPU back-end:
– Float16 new back-end (need cuda 7.5)
– Multi dtypes
– Multi-GPU support in the same process
A total of 141 people contributed to this release, see the list at the bottom.
Installation:
• Better BLAS detection
• Fixes for more recent software and OS versions
• Support Anaconda on Windows
Bug fixes:
• GpuJoin now supports negative axis
• Fix GpuCumsum for negative axis
Interface Deprecation (a warning is printed):
• Deprecate Param class, use In instead
Interface Changes:
• Rename DownsampleFactorMax to Pool.
• tensor.stack now uses the same interface as numpy.stack
• optimizer=fast_compile moves computation to the GPU
• Raise the user stack trace more frequently.
• Change dev version numbering to follow the PEP 440
New Interface (reuses existing functionality):
• theano.tensor.nnet.relu
• theano.tensor.nnet.elu
• BatchNormalization.
• MaxAndArgmax support axis=None
• Add theano.tensor.compress (equivalent of numpy.compress)
• theano.tensor.signal.downsamples.max_pool_2d_same_size
• COp
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• __props__
New features
• tensor.unique
• map_variables
• erfcx
• mgrid, ogrid
• allclose
• BreakpointOp
• Make bincount work on GPU
• SolveOp on GPU
• Optional optimization remove_all_assert
• AllocEmpty
• LogSoftmax, for stability optimization when the crossentropy optimization does not apply.
• theano.tensor.repeat works on GPU
• BatchedDot on the GPU and faster on the CPU.
• Faster batched_tensordot and make it work on GPU.
• SoftmaxGrad grad
• 3d conv via CorrMM on the GPU
• CPU Max Pool support of padding and strides!=windows size
• theano.function() now accepts a dict for the outputs. When doing this, the function will return a
dict. Helpful to keep track of which output is what.
• Warn for unknown or misspelled theano config variables
• theano.tensor.tile update (accept symbolic reps, work on GPU)
• scan how have a strict flag. If set to True, this make scan building faster and could make execution faster.
• theano.tensor.signal.conv2d(2d,2d) output 2d answer
• More convolution parameter supported
• Bilinear interpolation of images
Speed-ups:
• Faster SetSubtensor on the GPU.
• Support more reduction pattern on the GPU.
• More graph optimization
• Faster graph optimization
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• GpuCrossentropySoftmaxArgmax1HotWithBias
Crash/no return fixes:
• Fix crash in the assert op grad
• Fix curand crash on Mac
• Multiple Fix scan crashes
• Finish to update all Op.grad() implementation to the new interface
Others:
• Support ARM processor.
• Better tests
• Code clean up.
• Doc updates
• doctest and sphinx test in travis
• More tests tagged as slow
• Better same_shape implementation
• More op with c code to lower overhead
• Custom pickler for SharedVariable theano.misc.pkl_utils.{dump,load}
• function_dump to help us reproduce user error during compilation
• assert_no_cpu_op
• pep8, flake8
• Better error messages
• On non-default modes, reduce the number of allocation when allow_gc=False
• Better lock
Committers for this dev version only:
• Frederic Bastien
• Arnaud Bergeron
• Pierre Luc Carrier
• Iban Harlouchet
• Pascal Lamblin
• Chienli Ma
• Tim Cooijmans
• Nicolas Ballas
• Amjad Almahairi
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• David Warde-Farley
• Christof Angermueller
• Ziye Fan
• Caglar
• Sina Honari
• Roy Xue
• hantek
• Mohammad Pezeshki
• Melanie Ducoffe
• Alexandre de Brebisson
• Harm de Vries
• Samira Shabanian
• Alex Lamb
• Ramana.S
• Francesco Visin
• Saizheng Zhang
• Ying Zhang
• Jan Schlüter
• Xavier Bouthillier
• Bart van Merrienboer
• Cesar Laurent
• Iulian Vlad Serban
• Li Yao
• Sigurd Spieckermann
• Dmitrii Serdiuk
• Kelvin Xu
• Sebastien Jean
• Thomas Mesnard
• Seon-Wook Park
• Vincent Michalski
• Dustin Webb
• Mikhail Korobov
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• Orhan Firat
• Olivier Mastropietro
• Daniel Renshaw
• Julien Rebetez
• Peng Liu
• Sean Lee
• TimSalimans
• Andre Holzner
• Gijs van Tulder
• Guillaume Alain
• Julien Demouth
• Markus Beissinger
• Mehdi Mirza
• Moslem Kazemi
• Saxenauts
• Søren Kaae Sønderby
• sentient07
• Anatoly Belikov
• Diogo Moitinho de Almeida
• Jakub Sygnowski
• Kashif Rasul
• Laurent Dinh
• Rémy Léone
• Taesup (TS) Kim
• gw0 [http://gw.tnode.com/]
• mronian
• vesis84
• Benni
• Chiheb Trabelsi
• JesseLivezey
• Marius Killinger
• Matt Graham
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• Matthew Willson
• Piotr Frankowski
• Stefan Krastanov
• vdumoulin
• Adithya Ganesh
• Anish Shah
• Balázs Hidasi
• Colin Raffel
• Cory Lorenz
• Doug
• Jesse Livezey
• John Salvatier
• John Zedlewski
• Jonathan Ho
• Kaixhin
• Liang-Chi Hsieh
• Lucas Beyer
• Luke Metz
• Marc-Alexandre Cote
• Martin Arjovsky
• Matthias Kümmerer
• Sirisha Rambhatla
• briancheung
• cai-lw
• ivdorelian
• jan-matthis
• jojolalpin
• joncrall
• peterjsadowski
• scottsievert
• Étienne Simon
•
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• AlOa
• Albert Zeyer
• Andrea
• Andy Jiang
• Balázs
• Ben Poole
• Brian Cheung
• Christophe Van Gysel
• Claude Coulombe
• Clay McLeod
• Dario Garcia
• Jakob Lombacher
• Joao Felipe Santos
• John Arevalo
• Jonas Degrave
• Martin Thoma
• Mathieu Germain
• Matthew Koichi Grimes
• Michael Eickenberg
• Michael Opitz
• Paul Hollensen
• Prayag Verma
• Saatvik Shah
• Sergei Lebedev
• Vik Kamath
• Wei Ouyang
• Wojciech Głogowski
• Yi-Lin Juang
• Yurii Shevchuk
• Zach Dwiel
• dan
• eulerreich
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• jotterbach
• rolf
• theaverageguy
• wuaalb
6.2.2 Theano at a Glance
Theano is a Python library that lets you to define, optimize, and evaluate mathematical expressions, especially ones with multi-dimensional arrays (numpy.ndarray). Using Theano it is possible to attain speeds
rivaling hand-crafted C implementations for problems involving large amounts of data. It can also surpass
C on a CPU by many orders of magnitude by taking advantage of recent GPUs.
Theano combines aspects of a computer algebra system (CAS) with aspects of an optimizing compiler. It
can also generate customized C code for many mathematical operations. This combination of CAS with
optimizing compilation is particularly useful for tasks in which complicated mathematical expressions are
evaluated repeatedly and evaluation speed is critical. For situations where many different expressions are
each evaluated once Theano can minimize the amount of compilation/analysis overhead, but still provide
symbolic features such as automatic differentiation.
Theano’s compiler applies many optimizations of varying complexity to these symbolic expressions. These
optimizations include, but are not limited to:
• use of GPU for computations
• constant folding
• merging of similar subgraphs, to avoid redundant calculation
• arithmetic simplification (e.g. x*y/x -> y, --x -> x)
• inserting efficient BLAS operations (e.g. GEMM) in a variety of contexts
• using memory aliasing to avoid calculation
• using inplace operations wherever it does not interfere with aliasing
• loop fusion for elementwise sub-expressions
∑︀
• improvements to numerical stability (e.g. log(1 + exp(𝑥)) and log( 𝑖 exp(𝑥[𝑖])))
• for a complete list, see Optimizations
Theano was written at the LISA lab to support rapid development of efficient machine learning algorithms.
Theano is named after the Greek mathematician, who may have been Pythagoras’ wife. Theano is released
under a BSD license (link).
Sneak peek
Here is an example of how to use Theano. It doesn’t show off many of Theano’s features, but it illustrates
concretely what Theano is.
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import theano
from theano import tensor
# declare two symbolic floating-point scalars
a = tensor.dscalar()
b = tensor.dscalar()
# create a simple expression
c = a + b
# convert the expression into a callable object that takes (a,b)
# values as input and computes a value for c
f = theano.function([a,b], c)
# bind 1.5 to 'a', 2.5 to 'b', and evaluate 'c'
assert 4.0 == f(1.5, 2.5)
Theano is not a programming language in the normal sense because you write a program in Python that
builds expressions for Theano. Still it is like a programming language in the sense that you have to
• declare variables (a,b) and give their types
• build expressions for how to put those variables together
• compile expression graphs to functions in order to use them for computation.
It is good to think of theano.function as the interface to a compiler which builds a callable object
from a purely symbolic graph. One of Theano’s most important features is that theano.function can
optimize a graph and even compile some or all of it into native machine instructions.
What does it do that they don’t?
Theano is a Python library and optimizing compiler for manipulating and evaluating expressions, especially
matrix-valued ones. Manipulation of matrices is typically done using the numpy package, so what does
Theano do that Python and numpy do not?
• execution speed optimizations: Theano can use g++ or nvcc to compile parts your expression graph
into CPU or GPU instructions, which run much faster than pure Python.
• symbolic differentiation: Theano can automatically build symbolic graphs for computing gradients.
• stability optimizations: Theano can recognize [some] numerically unstable expressions and compute
them with more stable algorithms.
The closest Python package to Theano is sympy. Theano focuses more on tensor expressions than Sympy,
and has more machinery for compilation. Sympy has more sophisticated algebra rules and can handle a
wider variety of mathematical operations (such as series, limits, and integrals).
If numpy is to be compared to MATLAB and sympy to Mathematica, Theano is a sort of hybrid of the two
which tries to combine the best of both worlds.
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Getting started
Installing Theano Instructions to download and install Theano on your system.
Tutorial Getting started with Theano’s basic features. Go here if you are new!
API Documentation Details of what Theano provides. It is recommended to go through the Tutorial first
though.
A PDF version of the online documentation may be found here.
Theano Vision
This is the vision we have for Theano. This is give people an idea of what to expect in the future of Theano,
but we can’t promise to implement all of it. This should also help you to understand where Theano fits in
relation to other computational tools.
• Support tensor and sparse operations
• Support linear algebra operations
• Graph Transformations
– Differentiation/higher order differentiation
– ‘R’ and ‘L’ differential operators
– Speed/memory optimizations
– Numerical stability optimizations
• Can use many compiled languages, instructions sets: C/C++, CUDA, OpenCL, PTX, CAL, AVX, ...
• Lazy evaluation
• Loop
• Parallel execution (SIMD, multi-core, multi-node on cluster, multi-node distributed)
• Support all NumPy/basic SciPy functionality
• Easy wrapping of library functions in Theano
Note: There is no short term plan to support multi-node computation.
Theano Vision State
Here is the state of that vision as of December 3th, 2013 (after Theano release 0.6):
• We support tensors using the numpy.ndarray object and we support many operations on them.
• We support sparse types by using the scipy.{csc,csr,bsr}_matrix object and support some operations
on them.
• We have started implementing/wrapping more advanced linear algebra operations.
• We have many graph transformations that cover the 4 categories listed above.
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• We can improve the graph transformation with better storage optimization and instruction selection.
– Similar to auto-tuning during the optimization phase, but this doesn’t apply to only 1 op.
– Example of use: Determine if we should move computation to the GPU or not depending on the
input size.
– Possible implementation note: allow Theano Variable in the fgraph to have more than 1 owner.
• We support Python 2 and Python 3.
• We have a CUDA backend for tensors of type float32 only.
• Efforts have begun towards a generic GPU ndarray (GPU tensor) (started in the libgpuarray project)
– Move GPU backend outside of Theano.
– Will provide better support for GPU on Windows and support an OpenCL backend on CPU.
• Loops work, but not all related optimizations are currently done.
• The cvm linker allows lazy evaluation. It is the current default linker.
– How to have DebugMode check it? Right now, DebugMode checks the computation non-lazily.
• SIMD parallelism on the CPU comes from the compiler.
• Multi-core parallelism support limited. If the external BLAS implementation supports it, many dot
are parallelized via gemm, gemv and ger. Also, element-wise operation are supported. See Multi
cores support in Theano.
• No multi-node support.
• Most, but not all NumPy functions/aliases are implemented. * https://github.com/Theano/Theano/
issues/1080
• Wrapping an existing Python function in easy and documented.
• We know how to separate the shared variable memory storage location from its object type (tensor,
sparse, dtype, broadcast flags), but we need to do it.
Contact us
Discussion about Theano takes place in the theano-dev and theano-users mailing lists. People interested in
development of Theano should check the former, while the latter is reserved for issues that concern the end
users.
Questions, comments, praise, criticism as well as bug reports should be submitted to these mailing lists.
We welcome all kinds of contributions. If you have any questions regarding how to extend Theano, please
feel free to ask on the theano-dev mailing list.
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6.2.3 Installing Theano
Warning: If you want to install the bleeding-edge or development version of Theano from GitHub,
please make sure you are reading the latest version of this page.
Requirements
In order to use Theano, the following libraries and software will need to be installed (MacOS and Windows
users should refer to platform-specific instructions below for detailed installation steps):
Linux, Mac OS X or Windows operating system We develop mainly on 64-bit Linux machines. other architectures are not well-tested.
Python 2 >= 2.6 or Python 3 >= 3.3 The development package (python-dev or
python-devel on most Linux distributions) is recommended (see just below).
Python 2.4 was supported up to and including the release 0.6. Python 3 is supported past
the 3.3 release.
g++ (Linux and Windows), clang (macOS), python-dev (All platforms) Not technically required but highly recommended, in order to compile generated C code. Theano
can fall back on a NumPy-based Python execution model, but a C compiler allows for
vastly faster execution. g++ >= 4.2 (for openmp that is currently always used) more
recent version recommended!
NumPy >= 1.7.1 Earlier versions could work, but we don’t test it.
SciPy >= 0.11 Only currently required for sparse matrix and special functions support, but
highly recommended. SciPy >=0.8 could work, but earlier versions have known bugs with
sparse matrices.
A BLAS installation (with Level 3 functionality) Including the development headers (-dev,
-devel, depending on your Linux distribution). Mac OS X comes with the Accelerate
framework built in, and various options exist for Windows (see below).
The following libraries and software are optional:
nose >= 1.3.0 and nose-parameterized >= 0.5.0 Recommended, to run Theano’s test-suite.
Sphinx >= 0.5.1, pygments For building the documentation. LaTeX and dvipng are also necessary for math to show up as images.
Git To download bleeding-edge versions of Theano.
graphiz and either pydot-ng or pydot To be able to make picture of Theano computation
graph. pydot-ng is a pydot compatible replacement that support newer Python.
NVIDIA CUDA drivers and SDK Required for GPU code generation/execution on NVIDIA
gpus
libgpuarray Required for GPU/CPU code generation on CUDA and OpenCL devices (see:
GpuArray Backend.)
note OpenCL support is still minimal for now.
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Linux
CentOS 6
install_centos6 provides instructions on how to install Theano on CentOS 6, written by the Theano developers. It covers how to install Theano (for CPU-based computation only) with the distribution-packaged
ATLAS, a free fast implementation of BLAS.
Ubuntu
install_ubuntu provides instructions on how to install Theano on Ubuntu. It covers how to install Theano
with the distribution-packaged OpenBlas or ATLAS. Both are free fast implementation of BLAS.
Alternative installation on Gentoo
Brian Vandenberg emailed installation instructions on Gentoo, focusing on how to install the appropriate
dependencies.
Nicolas Pinto provides ebuild scripts.
Alternative installation on Mandriva 2010.2
A contributor made rpm package for Mandriva 2010.2 of Theano 0.3.1.
AWS Marketplace with Bitfusion AMI
AWS EC2 AMI pre-installed with Nvidia drivers, CUDA, cuDNN, Theano, Keras, Lasagne, Python 2,
Python 3, PyCuda, Scikit-Learn, Pandas, Enum34, iPython, and Jupyter. Note, as always there is no charge
for Theano and other open software, however there is a charge for AWS hosting + Bitfusion.
Launch an instance from the AWS Marketplace.
Docker
Builds of Theano are available as Docker images: Theano Docker (CPU) or Theano Docker (CUDA). These
are updated on a weekly basis with bleeding-edge builds of Theano. Examples of running bash in a Docker
container are as follows:
sudo docker run -it kaixhin/theano
sudo nvidia-docker run -it kaixhin/cuda-theano:7.0
For a guide to Docker, see the official docs. CUDA support requires NVIDIA Docker. For more details on
how to use the Theano Docker images, consult the source project.
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Basic user install instructions
The easiest way to obtain the released version of Theano is from PyPI using pip (a replacement for
easy_install provided by setuptools/distribute) by typing
pip install Theano
This should work under Python 2 or Python 3. To test, run
nosetests theano
You may need to add sudo before the pip command to install into your system’s site-packages
directory. If you do not have administrator access to your machine, you can install Theano locally (to
~/.local) using
pip install Theano --user
Alternatively you can use virtualenv to create an isolated site-packages directory; see the virtualenv
documentation for details.
Note: Theano can be installed with easy_install, however we recommend pip. pip offers many benefits
over easy_install such as more intelligent dependency management, better error messages and a pip
uninstall command for easily removing packages.
If you do not have pip installed but do have easy_install, you can get pip by simply typing
easy_install pip.
Updating Theano
The following command will update only Theano:
sudo pip install --upgrade --no-deps theano
The following command will update Theano and Numpy/Scipy (warning bellow):
sudo pip install --upgrade theano
If you installed NumPy/SciPy with yum/apt-get, updating NumPy/SciPy with pip/easy_install is not always a good idea. This can make Theano crash due to problems with BLAS (but see below). The versions of NumPy/SciPy in the distribution are sometimes linked against faster versions of BLAS. Installing
NumPy/SciPy with yum/apt-get/pip/easy_install won’t install the development package needed to recompile it with the fast version. This mean that if you don’t install the development packages manually, when
you recompile the updated NumPy/SciPy, it will compile with the slower version. This results in a slower
Theano as well. To fix the crash, you can clear the Theano cache like this:
theano-cache clear
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Bleeding-edge install instructions
If you are a developer of Theano, then check out the Developer Start Guide.
If you want the bleeding-edge without developing the code you can use pip for this with the command line
below. Note that it will also try to install Theano’s dependencies (like NumPy and SciPy), but not upgrade
them. If you wish to upgrade them, remove the --no-deps switch to it, but go see a previous warning
before doing this.
pip install --upgrade --no-deps git+git://github.com/Theano/Theano.git
or (if you want to install it for the current user only):
pip install --upgrade --no-deps git+git://github.com/Theano/Theano.git --user
The following are general instructions that will set you up with the bleeding-edge version of Theano and
allow you to hack it. First, get the code using Git:
git clone git://github.com/Theano/Theano.git
From here, the easiest way to get started is (this requires setuptools or distribute to be installed):
cd Theano
python setup.py develop
This will install a .pth file in your site-packages directory that tells Python where to look for your
Theano installation (i.e. in the directory your just checked out of Github). Using develop mode is
preferable to install as any modifications you make in the checkout directory (or changes you pull
with Git) will be automatically reflected in the “installed” version without re-running python setup.py
install.
If you do not have permission to modify your site-packages directory you can specify an alternative
installation prefix using
python setup.py develop --prefix=~/.local
A common choice is ~/.local which is automatically searched for Python >= 2.6; for earlier
Python versions and other installation prefixes, the prefix specified must contain lib/pythonA.B/
site-packages, where A.B is e.g. 2.5, and this site-packages directory must be listed in
PYTHONPATH.
An alternative, perhaps simpler way of creating and using an isolated site-packages is to use virtualenv;
see the virtualenv documentation for details. If you find yourself using virtualenv frequently you may find
the virtualenvwrapper package useful for switching between them.
Configuring PYTHONPATH
If import theano does not work in Python, you may need modify the environment variable
PYTHONPATH accordingly. In bash, you may do this:
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export PYTHONPATH=<new location to add>:$PYTHONPATH
In csh:
setenv PYTHONPATH <new location to add>:$PYTHONPATH
To make this change stick you will usually need to add the above command to your shell’s startup script, i.e.
~/.bashrc or ~/.cshrc. Consult your shell’s documentation for details.
Updating
To update your library to the latest revision, change directory (cd) to your Theano folder and execute the
following command:
git pull
You should update frequently, bugs are fixed on a very regular basis.
Specific git commit
You can install a specific git commit by using the bleeding edge instruction and adding @COMMIT_ID to
the pip command like:
pip install --upgrade --no-deps git+git://github.com/Theano/Theano.
˓→[email protected]
Testing your installation
Once you have installed Theano, you should run the test suite. At a Python (or IPython) interpreter,
import theano
theano.test()
You can also run them in-place from the Git checkout directory by typing
theano-nose
You should be able to execute it if you followed the instructions above. If theano-nose is not found by
your shell, you will need to add Theano/bin to your PATH environment variable.
Note: In Theano versions <= 0.5, theano-nose was not included. If you are working with such a
version, you can call nosetests instead of theano-nose. In that case, some tests will fail by raising
the KnownFailureTest Exception, and will be considered as errors, but they are nothing to worry about.
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Note: The tests should be run with the configuration option device set to cpu (default). If you need to
change this value, you can do that by setting the THEANO_FLAGS environment variable, by prefixing the
theano-nose command with THEANO_FLAGS=device=cpu. If you have a GPU, it will automatically
be used to run GPU-related tests.
If you want GPU-related tests to run on a specific GPU device, and not the default one, you should use
init_gpu_device. For instance: THEANO_FLAGS=device=cpu,init_gpu_device=gpu1.
See config – Theano Configuration for more information on how to change these configuration options.
All tests should pass (skipped tests and known failures are normal). If some test fails on your machine, you
are encouraged to tell us what went wrong on the [email protected] mailing list.
Troubleshooting: Make sure you have a BLAS library
There are many ways to configure BLAS for Theano. This is done with the Theano flags blas.ldflags
(config – Theano Configuration). The default is to use the BLAS installation information in NumPy, accessible via numpy.distutils.__config__.show(). You can tell theano to use a different version
of BLAS, in case you did not compile NumPy with a fast BLAS or if NumPy was compiled with a static
library of BLAS (the latter is not supported in Theano).
The short way to configure the Theano flags blas.ldflags is by setting the environment
variable THEANO_FLAGS to blas.ldflags=XXX (in bash export THEANO_FLAGS=blas.
ldflags=XXX)
The ${HOME}/.theanorc file is the simplest way to set a relatively permanent option like this one. Add
a [blas] section with an ldflags entry like this:
# other stuff can go here
[blas]
ldflags = -lf77blas -latlas -lgfortran #put your flags here
# other stuff can go here
For more information on the formatting of ~/.theanorc and the configuration options that you can put
there, see config – Theano Configuration.
Here are some different way to configure BLAS:
0) Do nothing and use the default config, which is to link against the same BLAS against which NumPy was
built. This does not work in the case NumPy was compiled with a static library (e.g. ATLAS is compiled by
default only as a static library).
1) Disable the usage of BLAS and fall back on NumPy for dot products. To do this, set the value of blas.
ldflags as the empty string (ex: export THEANO_FLAGS=blas.ldflags=). Depending on the
kind of matrix operations your Theano code performs, this might slow some things down (vs. linking with
BLAS directly).
2) You can install the default (reference) version of BLAS if the NumPy version (against which Theano
links) does not work. If you have root or sudo access in fedora you can do sudo yum install
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blas blas-devel. Under Ubuntu/Debian sudo apt-get install libblas-dev. Then use
the Theano flags blas.ldflags=-lblas. Note that the default version of blas is not optimized. Using
an optimized version can give up to 10x speedups in the BLAS functions that we use.
3) Install the ATLAS library. ATLAS is an open source optimized version of BLAS. You can install a precompiled version on most OSes, but if you’re willing to invest the time, you can compile it to have a faster
version (we have seen speed-ups of up to 3x, especially on more recent computers, against the precompiled
one). On Fedora, sudo yum install atlas-devel. Under Ubuntu, sudo apt-get install
libatlas-base-dev libatlas-base or libatlas3gf-sse2 if your CPU supports SSE2 instructions. Then set the Theano flags blas.ldflags to -lf77blas -latlas -lgfortran. Note
that these flags are sometimes OS-dependent.
4) Use a faster version like MKL, GOTO, ... You are on your own to install it. See the doc of that
software and set the Theano flags blas.ldflags correctly (for example, for MKL this might be
-lmkl -lguide -lpthread or -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core
-lguide -liomp5 -lmkl_mc -lpthread).
Note: Make sure your BLAS libraries are available as dynamically-loadable libraries. ATLAS is often
installed only as a static library. Theano is not able to use this static library. Your ATLAS installation might
need to be modified to provide dynamically loadable libraries. (On Linux this typically means a library
whose name ends with .so. On Windows this will be a .dll, and on OS-X it might be either a .dylib or a .so.)
This might be just a problem with the way Theano passes compilation arguments to g++, but the problem is
not fixed yet.
Note: If you have problems linking with MKL, Intel Line Advisor and the MKL User Guide can help you
find the correct flags to use.
Using the GPU
The first thing you’ll need for Theano to use your GPU is Nvidia’s GPU-programming toolchain. You
should install at least the CUDA driver and the CUDA Toolkit, as described here. The CUDA Toolkit
installs a folder on your computer with subfolders bin, lib, include, and some more too. (Sanity check: The
bin subfolder should contain an nvcc program which is the compiler for GPU code.) This folder is called
the cuda root directory. You must also add the ‘lib’ subdirectory (and/or ‘lib64’ subdirectory if you have a
64-bit Linux computer) to your $LD_LIBRARY_PATH environment variable.
You must then tell Theano where the CUDA root folder is, and there are three ways to do it. Any one of
them is enough.
• Define a $CUDA_ROOT environment variable to equal the cuda root directory, as in CUDA_ROOT=/
path/to/cuda/root, or
• add a cuda.root flag to THEANO_FLAGS, as in THEANO_FLAGS='cuda.root=/path/to/
cuda/root', or
• add a [cuda] section to your .theanorc file containing the option root = /path/to/cuda/root.
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Note: On Debian, you can ask the software package manager to install it for you. We have a user report that
this works for Debian Wheezy (7.0). When you install it this way, you won’t always have the latest version,
but we were told that it gets updated regularly. One big advantage is that it will be updated automatically.
You can try the sudo apt-get install nvidia-cuda-toolkit command to install it.
Ubuntu instructions.
Once that is done, the only thing left is to change the device option to name the GPU device in your computer, and set the default floating point computations to float32. For example: THEANO_FLAGS='cuda.
root=/path/to/cuda/root,device=gpu,floatX=float32'. You can also set these options
in the .theanorc file’s [global] section:
[global]
device = gpu
floatX = float32
Note that:
• If your computer has multiple GPUs and you use ‘device=gpu’, the driver selects the one to use
(usually gpu0).
• You can use the program nvida-smi to change this policy.
• You can choose one specific GPU by specifying ‘device=gpuX’, with X the the corresponding GPU
index (0, 1, 2, ...)
• By default, when device indicates preference for GPU computations, Theano will fall back to the
CPU if there is a problem with the GPU. You can use the flag ‘force_device=True’ to instead raise an
error when Theano cannot use the GPU.
Once your setup is complete, head to Using the GPU to find how to verify everything is working properly.
Mac OS
There are various ways to install Theano dependencies on a Mac. Here we describe the process in detail
with Canopy, Anaconda, Homebrew or MacPorts but if you did it differently and it worked, please let us
know the details on the theano-users mailing-list, so that we can add alternate instructions here.
In academia: Enthought Canopy
If you are working in academia, the easiest way to install most of the dependencies is to install Canopy. If
you are affiliated with a university (as student or employee), you can download the installer for free.
The Canopy installation includes in particular Python (and the development headers), NumPy, SciPy, nose,
sphinx, pip, pydot (but not Graphviz, which is necessary for it to work) and the MKL implementation of
blas.
To install the latest Theano release execute this in a terminal:
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$ pip install Theano
If you want the bleeding edge version execute this command instead:
$ pip install --upgrade --no-deps git+git://github.com/Theano/Theano.git
See the section install_bleeding_edge for more information on the bleeding edge version.
Then you must install the compiler. See Installing the compiler below.
Note: If you use version 0.6 or later of Theano, we try to automatically link with the Canopy blas version.
Due to Mac OS peculiarities, this requires user intervention. We detect if the manipulation was done or not
and give an error message explaining what to do in case it hasn’t been done.
Anaconda
An easy way to install most of the dependencies is to install Anaconda. There is a free version available
to everybody. If you install their MKL Optimizations product (free for academic, ~30$ otherwise)
Theano will also be optimized as we will reuse the faster BLAS version automatically.
The Anaconda installation includes in particular Python (and the development headers), NumPy, SciPy,
nose, sphinx, pip, and a acceptable BLAS version.
After installing Anaconda, in a terminal execute this command to install the latest Theano release:
$ pip install Theano
To install the missing Theano optional dependency (pydot):
$ conda install pydot-ng
If you want the bleeding edge version instead execute this command:
$ pip install --upgrade --no-deps git+git://github.com/Theano/Theano.git
See the section install_bleeding_edge for more information on the bleeding edge version.
Then you must install the compiler. See Installing the compiler below.
Note: If you use version 0.6 or later of Theano, we try to automatically link with the python library. Due to
Mac OS peculiarities, this requires user intervention. We detect if the user did the modification and if not,
we tell him how to do it.
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Installing the compiler
Theano officially supports only clang on OS X. This can be installed by getting XCode from the App Store
and running it once to install the command-line tools.
If you still want to use g++ you can do so by setting its full path in the theano config flag gxx. Note that any
bug reports on Mac using g++ will be ignored unless it can be reproduced with clang.
Homebrew
Install python with homebrew:
$ brew install python # or python3 if you prefer
This will install pip. Then use pip to install numpy, scipy:
$ pip install numpy scipy
If you want to use openblas instead of Accelerate, you have to install numpy and scipy with hombrew:
$ brew tap homebrew/python
$ brew install numpy --with-openblas
$ brew install scipy --with-openblas
Then install theano as usual:
$ pip install Theano --user
Or for the bleeding-edge version:
$ pip install --upgrade --no-deps git+git://github.com/Theano/Theano.git
MacPorts
Using MacPorts to install all required Theano dependencies is easy, but be aware that it will take a long time
(a few hours) to build and install everything.
• MacPorts requires installing XCode first (which can be found in the Mac App Store), if you do not
have it already. If you can’t install it from the App Store, look in your MacOS X installation DVD for
an old version. Then update your Mac to update XCode.
• Download and install MacPorts, then ensure its package list is up-to-date with sudo port
selfupdate.
• Then, in order to install one or more of the required libraries, use port install, e.g. as follows:
$ sudo port install py27-numpy +atlas py27-scipy +atlas py27-pip
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This will install all the required Theano dependencies. gcc will be automatically installed (since it is
a SciPy dependency), but be aware that it takes a long time to compile (hours)! Having NumPy and
SciPy linked with ATLAS (an optimized BLAS implementation) is not mandatory, but recommended
if you care about performance.
• You might have some different versions of gcc, SciPy, NumPy, Python installed on your system,
perhaps via Xcode. It is a good idea to use either the MacPorts version of everything or some other
set of compatible versions (e.g. provided by Xcode or Fink). The advantages of MacPorts are the
transparency with which everything can be installed and the fact that packages are updated quite
frequently. The following steps describe how to make sure you are using the MacPorts version of
these packages.
• In order to use the MacPorts version of Python, you will probably need to explicitly select it with
sudo port select python python27. The reason this is necessary is because you may
have an Apple-provided Python (via, for example, an Xcode installation). After performing this
step, you should check that the symbolic link provided by which python points to the MacPorts
python. For instance, on MacOS X Lion with MacPorts 2.0.3, the output of which python is
/opt/local/bin/python and this symbolic link points to /opt/local/bin/python2.7.
When executing sudo port select python python27-apple (which you should not do),
the link points to /usr/bin/python2.7.
• Similarly, make sure that you are using the MacPorts-provided gcc: use sudo port select gcc
to see which gcc installs you have on the system. Then execute for instance sudo port select
gcc mp-gcc44 to create a symlink that points to the correct (MacPorts) gcc (version 4.4 in this
case).
• At this point, if you have not done so already, it may be a good idea to close and restart your terminal,
to make sure all configuration changes are properly taken into account.
• Afterwards, please check that the scipy module that is imported in Python is the right one (and is
a recent one). For instance, import scipy followed by print(scipy.__version__) and
print(scipy.__path__) should result in a version number of at least 0.7.0 and a path that starts
with /opt/local (the path where MacPorts installs its packages). If this is not the case, then you
might have some old installation of scipy in your PYTHONPATH so you should edit PYTHONPATH
accordingly.
• Please follow the same procedure with numpy.
• This is covered in the MacPorts installation process, but make sure that your PATH environment
variable contains /opt/local/bin and /opt/local/sbin before any other paths (to ensure
that the Python and gcc binaries that you installed with MacPorts are visible first).
• MacPorts does not create automatically nosetests and pip symlinks pointing to the MacPorts
version, so you can add them yourself with
$ sudo ln -s /opt/local/bin/nosetests-2.7 /opt/local/bin/
˓→nosetests
$ sudo ln -s /opt/local/bin/pip-2.7 /opt/local/bin/pip
• At this point you are ready to install Theano with
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$ sudo pip install Theano
And if you are in no hurry, you can run its test-suite with
$ python -c "import theano; theano.test()"
Using the GPU
You should be able to follow the Linux instructions to setup CUDA, but be aware of the following caveats:
• If you want to compile the CUDA SDK code, you may need to temporarily revert back to Apple’s gcc
(sudo port select gcc) as their Makefiles are not compatible with MacPort’s gcc.
• If CUDA seems unable to find a CUDA-capable GPU, you may need to manually toggle your GPU
on, which can be done with gfxCardStatus.
Once your setup is complete, head to Using the GPU to find how to verify everything is working properly.
Troubleshooting MacOS issues
Although the above steps should be enough, running Theano on a Mac may sometimes cause unexpected
crashes, typically due to multiple versions of Python or other system libraries. If you encounter such problems, you may try the following.
• You can ensure MacPorts shared libraries are given priority at run-time with export
LD_LIBRARY_PATH=/opt/local/lib:$LD_LIBRARY_PATH. In order to do the same at
compile time, you can add to your ~/.theanorc:
[gcc]
cxxflags = -L/opt/local/lib
• An obscure Bus error can sometimes be caused when linking Theano-generated object files
against the framework library in Leopard. For this reason, we have disabled linking with
-framework Python, since on most configurations this solves the Bus error problem. If this
default configuration causes problems with your Python/Theano installation and you think that linking
with -framework Python might help, then either set the THEANO_FLAGS environment variable
with THEANO_FLAGS=cmodule.mac_framework_link or edit your ~/.theanorc to contain
[cmodule]
mac_framework_link=True
• More generally, to investigate libraries issues, you can use the otool -L command on .so files
found under your ~/.theano directory. This will list shared libraries dependencies, and may help
identify incompatibilities.
Please inform us if you have trouble installing and running Theano on your Mac. We would be especially
interested in dependencies that we missed listing, alternate installation steps, GPU instructions, as well as
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tests that fail on your platform (use the [email protected] mailing list, but note
that you must first register to it, by going to theano-users).
Windows
install_windows provides step-by-step instructions on how to install Theano on 32- or 64-bit Windows
systems, using freely available tools and compilers.
Editing code in Visual Studio
You will find a Visual Studio solution file (Theano.sln) in the root of the Theano repository. Note that
this project file may not be kept up-to-date and is not officially supported by the core Theano developers: it
is provided for convenience only. Also, be aware that it will not make Theano use Visual Studio to compile
C files: it is only meant to provide an easy way to edit Theano code within the Visual Studio editor.
Windows Installation References
1. http://stackoverflow.com/questions/9047072/windows-python-version-and-vc-redistributable-version
2. http://stackoverflow.com/questions/1865069/how-to-compile-a-64-bit-application-using-visual-c-2010-express
3. http://blog.victorjabur.com/2011/06/05/compiling-python-2-7-modules-on-windows-32-and-64-using-msvc-2008-ex
4. http://stackoverflow.com/questions/126279/c99-stdint-h-header-and-ms-visual-studio
5. http://stackoverflow.com/questions/11182765/how-can-i-build-my-c-extensions-with-mingw-w64-in-python
6. https://mail.python.org/pipermail/python-announce-list/2014-September/010457.html
Generating the documentation
You can read the latest HTML documentation here. You can download the latest PDF documentation here.
We recommend you look at the documentation on the website, since it will be more current than the documentation included with the package.
If you really wish to build the documentation yourself, you will need sphinx, as described above. Issue the
following command:
python ./doc/scripts/docgen.py
Documentation is built into html/. The PDF of the documentation is html/theano.pdf.
6.2.4 Tutorial
Let us start an interactive session (e.g. with python or ipython) and import Theano.
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>>> from theano import *
Several of the symbols you will need to use are in the tensor subpackage of Theano. Let us import that
subpackage under a handy name like T (the tutorials will frequently use this convention).
>>> import theano.tensor as T
If that succeeded you are ready for the tutorial, otherwise check your installation (see Installing Theano).
Throughout the tutorial, bear in mind that there is a Glossary as well as index and modules links in the
upper-right corner of each page to help you out.
Prerequisites
Python tutorial
In this documentation, we suppose that the reader knows Python. Here is a small list of Python tutorials/exercises if you need to learn it or only need a refresher:
• Python Challenge
• Dive into Python
• Google Python Class
• Enthought Python course (free for academics)
We have a tutorial on how Python manages its memory.
NumPy refresher
Here are some quick guides to NumPy:
• Numpy quick guide for Matlab users
• Numpy User Guide
• More detailed Numpy tutorial
• 100 NumPy exercises
• Numpy tutorial
Matrix conventions for machine learning
Rows are horizontal and columns are vertical. Every row is an example. Therefore, inputs[10,5] is a matrix
of 10 examples where each example has dimension 5. If this would be the input of a neural network then
the weights from the input to the first hidden layer would represent a matrix of size (5, #hid).
Consider this array:
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>>> numpy.asarray([[1., 2], [3, 4], [5, 6]])
array([[ 1., 2.],
[ 3., 4.],
[ 5., 6.]])
>>> numpy.asarray([[1., 2], [3, 4], [5, 6]]).shape
(3, 2)
This is a 3x2 matrix, i.e. there are 3 rows and 2 columns.
To access the entry in the 3rd row (row #2) and the 1st column (column #0):
>>> numpy.asarray([[1., 2], [3, 4], [5, 6]])[2, 0]
5.0
To remember this, keep in mind that we read left-to-right, top-to-bottom, so each thing that is contiguous is
a row. That is, there are 3 rows and 2 columns.
Broadcasting
Numpy does broadcasting of arrays of different shapes during arithmetic operations. What this means in
general is that the smaller array (or scalar) is broadcasted across the larger array so that they have compatible
shapes. The example below shows an instance of broadcastaing:
>>> a =
>>> b =
>>> a *
array([
numpy.asarray([1.0, 2.0, 3.0])
2.0
b
2., 4., 6.])
The smaller array b (actually a scalar here, which works like a 0-d array) in this case is broadcasted to the
same size as a during the multiplication. This trick is often useful in simplifying how expression are written.
More detail about broadcasting can be found in the numpy user guide.
Basics
Baby Steps - Algebra
Adding two Scalars
To get us started with Theano and get a feel of what we’re working with, let’s make a simple function: add
two numbers together. Here is how you do it:
>>>
>>>
>>>
>>>
>>>
>>>
>>>
40
import numpy
import theano.tensor as T
from theano import function
x = T.dscalar('x')
y = T.dscalar('y')
z = x + y
f = function([x, y], z)
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And now that we’ve created our function we can use it:
>>> f(2, 3)
array(5.0)
>>> numpy.allclose(f(16.3, 12.1), 28.4)
True
Let’s break this down into several steps. The first step is to define two symbols (Variables) representing the
quantities that you want to add. Note that from now on, we will use the term Variable to mean “symbol” (in
other words, x, y, z are all Variable objects). The output of the function f is a numpy.ndarray with zero
dimensions.
If you are following along and typing into an interpreter, you may have noticed that there was a slight delay
in executing the function instruction. Behind the scene, f was being compiled into C code.
Step 1
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
In Theano, all symbols must be typed. In particular, T.dscalar is the type we assign to “0-dimensional
arrays (scalar) of doubles (d)”. It is a Theano Type.
dscalar is not a class. Therefore, neither x nor y are actually instances of dscalar. They are instances
of TensorVariable. x and y are, however, assigned the theano Type dscalar in their type field, as
you can see here:
>>> type(x)
<class 'theano.tensor.var.TensorVariable'>
>>> x.type
TensorType(float64, scalar)
>>> T.dscalar
TensorType(float64, scalar)
>>> x.type is T.dscalar
True
By calling T.dscalar with a string argument, you create a Variable representing a floating-point scalar
quantity with the given name. If you provide no argument, the symbol will be unnamed. Names are not
required, but they can help debugging.
More will be said in a moment regarding Theano’s inner structure. You could also learn more by looking
into Graph Structures.
Step 2
The second step is to combine x and y into their sum z:
>>> z = x + y
z is yet another Variable which represents the addition of x and y. You can use the pp function to pretty-print
out the computation associated to z.
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>>> from theano import pp
>>> print(pp(z))
(x + y)
Step 3
The last step is to create a function taking x and y as inputs and giving z as output:
>>> f = function([x, y], z)
The first argument to function is a list of Variables that will be provided as inputs to the function. The
second argument is a single Variable or a list of Variables. For either case, the second argument is what we
want to see as output when we apply the function. f may then be used like a normal Python function.
Note: As a shortcut, you can skip step 3, and just use a variable’s eval method. The eval() method
is not as flexible as function() but it can do everything we’ve covered in the tutorial so far. It has the
added benefit of not requiring you to import function() . Here is how eval() works:
>>> import numpy
>>> import theano.tensor as T
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
>>> z = x + y
>>> numpy.allclose(z.eval({x : 16.3, y : 12.1}), 28.4)
True
We passed eval() a dictionary mapping symbolic theano variables to the values to substitute for them,
and it returned the numerical value of the expression.
eval() will be slow the first time you call it on a variable – it needs to call function() to compile the
expression behind the scenes. Subsequent calls to eval() on that same variable will be fast, because the
variable caches the compiled function.
Adding two Matrices
You might already have guessed how to do this. Indeed, the only change from the previous example is that
you need to instantiate x and y using the matrix Types:
>>>
>>>
>>>
>>>
x
y
z
f
=
=
=
=
T.dmatrix('x')
T.dmatrix('y')
x + y
function([x, y], z)
dmatrix is the Type for matrices of doubles. Then we can use our new function on 2D arrays:
>>> f([[1, 2], [3, 4]], [[10, 20], [30, 40]])
array([[ 11., 22.],
[ 33., 44.]])
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The variable is a NumPy array. We can also use NumPy arrays directly as inputs:
>>> import numpy
>>> f(numpy.array([[1, 2], [3, 4]]), numpy.array([[10, 20], [30, 40]]))
array([[ 11., 22.],
[ 33., 44.]])
It is possible to add scalars to matrices, vectors to matrices, scalars to vectors, etc. The behavior of these
operations is defined by broadcasting.
The following types are available:
• byte: bscalar, bvector, bmatrix, brow, bcol, btensor3, btensor4
• 16-bit
integers:
wtensor4
wscalar, wvector, wmatrix, wrow, wcol, wtensor3,
• 32-bit
integers:
itensor4
iscalar, ivector, imatrix, irow, icol, itensor3,
• 64-bit
integers:
ltensor4
lscalar, lvector, lmatrix, lrow, lcol, ltensor3,
• float: fscalar, fvector, fmatrix, frow, fcol, ftensor3, ftensor4
• double: dscalar, dvector, dmatrix, drow, dcol, dtensor3, dtensor4
• complex: cscalar, cvector, cmatrix, crow, ccol, ctensor3, ctensor4
The previous list is not exhaustive and a guide to all types compatible with NumPy arrays may be found
here: tensor creation.
Note: You, the user—not the system architecture—have to choose whether your program will use 32- or
64-bit integers (i prefix vs. the l prefix) and floats (f prefix vs. the d prefix).
Exercise
import theano
a = theano.tensor.vector() # declare variable
out = a + a ** 10
# build symbolic expression
f = theano.function([a], out)
# compile function
print(f([0, 1, 2]))
[
0.
2.
1026.]
Modify and execute this code to compute this expression: a ** 2 + b ** 2 + 2 * a * b.
Solution
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More Examples
At this point it would be wise to begin familiarizing yourself more systematically with Theano’s fundamental
objects and operations by browsing this section of the library: Basic Tensor Functionality.
As the tutorial unfolds, you should also gradually acquaint yourself with the other relevant areas of the
library and with the relevant subjects of the documentation entrance page.
Logistic Function
Here’s another straightforward example, though a bit more elaborate than adding two numbers together.
Let’s say that you want to compute the logistic curve, which is given by:
𝑠(𝑥) =
1
1 + 𝑒−𝑥
Fig. 6.1: A plot of the logistic function, with x on the x-axis and s(x) on the y-axis.
You want to compute the function elementwise on matrices of doubles, which means that you want to apply
this function to each individual element of the matrix.
Well, what you do is this:
>>> import theano
>>> import theano.tensor as T
>>> x = T.dmatrix('x')
>>> s = 1 / (1 + T.exp(-x))
>>> logistic = theano.function([x], s)
>>> logistic([[0, 1], [-1, -2]])
array([[ 0.5
, 0.73105858],
[ 0.26894142, 0.11920292]])
The reason logistic is performed elementwise is because all of its operations—division, addition, exponentiation, and division—are themselves elementwise operations.
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It is also the case that:
𝑠(𝑥) =
1 + tanh(𝑥/2)
1
=
1 + 𝑒−𝑥
2
We can verify that this alternate form produces the same values:
>>> s2 = (1 + T.tanh(x / 2)) / 2
>>> logistic2 = theano.function([x], s2)
>>> logistic2([[0, 1], [-1, -2]])
array([[ 0.5
, 0.73105858],
[ 0.26894142, 0.11920292]])
Computing More than one Thing at the Same Time
Theano supports functions with multiple outputs. For example, we can compute the elementwise difference,
absolute difference, and squared difference between two matrices a and b at the same time:
>>>
>>>
>>>
>>>
>>>
a, b = T.dmatrices('a', 'b')
diff = a - b
abs_diff = abs(diff)
diff_squared = diff**2
f = theano.function([a, b], [diff, abs_diff, diff_squared])
Note: dmatrices produces as many outputs as names that you provide. It is a shortcut for allocating
symbolic variables that we will often use in the tutorials.
When we use the function f, it returns the three variables (the printing was reformatted for readability):
>>> f([[1, 1], [1, 1]], [[0, 1], [2, 3]])
[array([[ 1., 0.],
[-1., -2.]]), array([[ 1., 0.],
[ 1., 2.]]), array([[ 1., 0.],
[ 1., 4.]])]
Setting a Default Value for an Argument
Let’s say you want to define a function that adds two numbers, except that if you only provide one number,
the other input is assumed to be one. You can do it like this:
>>> from theano import In
>>> from theano import function
>>> x, y = T.dscalars('x', 'y')
>>> z = x + y
>>> f = function([x, In(y, value=1)], z)
>>> f(33)
array(34.0)
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>>> f(33, 2)
array(35.0)
This makes use of the In class which allows you to specify properties of your function’s parameters with
greater detail. Here we give a default value of 1 for y by creating a In instance with its value field set to
1.
Inputs with default values must follow inputs without default values (like Python’s functions). There can
be multiple inputs with default values. These parameters can be set positionally or by name, as in standard
Python:
>>> x, y, w = T.dscalars('x', 'y', 'w')
>>> z = (x + y) * w
>>> f = function([x, In(y, value=1), In(w, value=2, name='w_by_name')], z)
>>> f(33)
array(68.0)
>>> f(33, 2)
array(70.0)
>>> f(33, 0, 1)
array(33.0)
>>> f(33, w_by_name=1)
array(34.0)
>>> f(33, w_by_name=1, y=0)
array(33.0)
Note: In does not know the name of the local variables y and w that are passed as arguments. The
symbolic variable objects have name attributes (set by dscalars in the example above) and these are the
names of the keyword parameters in the functions that we build. This is the mechanism at work in In(y,
value=1). In the case of In(w, value=2, name='w_by_name'). We override the symbolic
variable’s name attribute with a name to be used for this function.
You may like to see Function in the library for more detail.
Using Shared Variables
It is also possible to make a function with an internal state. For example, let’s say we want to make an
accumulator: at the beginning, the state is initialized to zero. Then, on each function call, the state is
incremented by the function’s argument.
First let’s define the accumulator function. It adds its argument to the internal state, and returns the old state
value.
>>>
>>>
>>>
>>>
from theano import shared
state = shared(0)
inc = T.iscalar('inc')
accumulator = function([inc], state, updates=[(state, state+inc)])
This code introduces a few new concepts. The shared function constructs so-called shared variables.
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These are hybrid symbolic and non-symbolic variables whose value may be shared between multiple functions. Shared variables can be used in symbolic expressions just like the objects returned by dmatrices(.
..) but they also have an internal value that defines the value taken by this symbolic variable in all the
functions that use it. It is called a shared variable because its value is shared between many functions. The
value can be accessed and modified by the .get_value() and .set_value() methods. We will come
back to this soon.
The other new thing in this code is the updates parameter of function. updates must be supplied
with a list of pairs of the form (shared-variable, new expression). It can also be a dictionary whose keys are
shared-variables and values are the new expressions. Either way, it means “whenever this function runs, it
will replace the .value of each shared variable with the result of the corresponding expression”. Above,
our accumulator replaces the state‘s value with the sum of the state and the increment amount.
Let’s try it out!
>>> print(state.get_value())
0
>>> accumulator(1)
array(0)
>>> print(state.get_value())
1
>>> accumulator(300)
array(1)
>>> print(state.get_value())
301
It is possible to reset the state. Just use the .set_value() method:
>>> state.set_value(-1)
>>> accumulator(3)
array(-1)
>>> print(state.get_value())
2
As we mentioned above, you can define more than one function to use the same shared variable. These
functions can all update the value.
>>> decrementor = function([inc], state, updates=[(state, state-inc)])
>>> decrementor(2)
array(2)
>>> print(state.get_value())
0
You might be wondering why the updates mechanism exists. You can always achieve a similar result by
returning the new expressions, and working with them in NumPy as usual. The updates mechanism can be
a syntactic convenience, but it is mainly there for efficiency. Updates to shared variables can sometimes be
done more quickly using in-place algorithms (e.g. low-rank matrix updates). Also, Theano has more control
over where and how shared variables are allocated, which is one of the important elements of getting good
performance on the GPU.
It may happen that you expressed some formula using a shared variable, but you do not want to use its value.
In this case, you can use the givens parameter of function which replaces a particular node in a graph
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for the purpose of one particular function.
>>> fn_of_state = state * 2 + inc
>>> # The type of foo must match the shared variable we are replacing
>>> # with the ``givens``
>>> foo = T.scalar(dtype=state.dtype)
>>> skip_shared = function([inc, foo], fn_of_state, givens=[(state, foo)])
>>> skip_shared(1, 3) # we're using 3 for the state, not state.value
array(7)
>>> print(state.get_value()) # old state still there, but we didn't use it
0
The givens parameter can be used to replace any symbolic variable, not just a shared variable. You can
replace constants, and expressions, in general. Be careful though, not to allow the expressions introduced
by a givens substitution to be co-dependent, the order of substitution is not defined, so the substitutions
have to work in any order.
In practice, a good way of thinking about the givens is as a mechanism that allows you to replace any part
of your formula with a different expression that evaluates to a tensor of same shape and dtype.
Note: Theano shared variable broadcast pattern default to False for each dimensions. Shared variable size
can change over time, so we can’t use the shape to find the broadcastable pattern. If you want a different
pattern, just pass it as a parameter theano.shared(..., broadcastable=(True, False))
Copying functions
Theano functions can be copied, which can be useful for creating similar functions but with different shared
variables or updates. This is done using the copy() method of function objects. The optimized graph
of the original function is copied, so compilation only needs to be performed once.
Let’s start from the accumulator defined above. Let’s add the on_unused_input='ignore' parameter
in case we don’t want to use both of our current arguments in a future copy of the function (this isn’t
necessary on versions > 0.8.2):
>>> import theano
>>> import theano.tensor as T
>>> state = theano.shared(0)
>>> inc = T.iscalar('inc')
>>> accumulator = theano.function([inc], state, updates=[(state, state+inc)],
˓→on_unused_input='ignore')
We can use it to increment the state as usual:
>>> accumulator(10)
array(0)
>>> print(state.get_value())
10
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We can use copy() to create a similar accumulator but with its own internal state using the swap parameter, which is a dictionary of shared variables to exchange:
>>> new_state = theano.shared(0)
>>> new_accumulator = accumulator.copy(swap={state:new_state})
>>> new_accumulator(100)
[array(0)]
>>> print(new_state.get_value())
100
The state of the first function is left untouched:
>>> print(state.get_value())
10
We now create a copy with updates removed using the delete_updates parameter, which is set to
False by default. Notice our new copy doesn’t actually use the inc argument after removing the
updates parameter:
>>> null_accumulator = accumulator.copy(delete_updates=True)
As expected, the shared state is no longer updated:
>>> null_accumulator(9000)
[array(10)]
>>> print(state.get_value())
10
Using Random Numbers
Because in Theano you first express everything symbolically and afterwards compile this expression to get
functions, using pseudo-random numbers is not as straightforward as it is in NumPy, though also not too
complicated.
The way to think about putting randomness into Theano’s computations is to put random variables in your
graph. Theano will allocate a NumPy RandomStream object (a random number generator) for each such
variable, and draw from it as necessary. We will call this sort of sequence of random numbers a random
stream. Random streams are at their core shared variables, so the observations on shared variables hold here
as well. Theanos’s random objects are defined and implemented in RandomStreams and, at a lower level, in
RandomStreamsBase.
Brief Example
Here’s a brief example. The setup code is:
from
from
srng
rv_u
theano.tensor.shared_randomstreams import RandomStreams
theano import function
= RandomStreams(seed=234)
= srng.uniform((2,2))
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rv_n = srng.normal((2,2))
f = function([], rv_u)
g = function([], rv_n, no_default_updates=True)
#Not updating rv_n.rng
nearly_zeros = function([], rv_u + rv_u - 2 * rv_u)
Here, ‘rv_u’ represents a random stream of 2x2 matrices of draws from a uniform distribution. Likewise,
‘rv_n’ represents a random stream of 2x2 matrices of draws from a normal distribution. The distributions
that are implemented are defined in RandomStreams and, at a lower level, in raw_random. They only
work on CPU. See Other Implementations for GPU version.
Now let’s use these objects. If we call f(), we get random uniform numbers. The internal state of the random
number generator is automatically updated, so we get different random numbers every time.
>>> f_val0 = f()
>>> f_val1 = f()
#different numbers from f_val0
When we add the extra argument no_default_updates=True to function (as in g), then the random number generator state is not affected by calling the returned function. So, for example, calling g
multiple times will return the same numbers.
>>> g_val0 = g()
>>> g_val1 = g()
# different numbers from f_val0 and f_val1
# same numbers as g_val0!
An important remark is that a random variable is drawn at most once during any single function execution.
So the nearly_zeros function is guaranteed to return approximately 0 (except for rounding error) even though
the rv_u random variable appears three times in the output expression.
>>> nearly_zeros = function([], rv_u + rv_u - 2 * rv_u)
Seeding Streams
Random variables can be seeded individually or collectively.
You can seed just one random variable by seeding or assigning to the .rng attribute, using .rng.
set_value().
>>> rng_val = rv_u.rng.get_value(borrow=True)
>>> rng_val.seed(89234)
>>> rv_u.rng.set_value(rng_val, borrow=True)
# Get the rng for rv_u
# seeds the generator
# Assign back seeded rng
You can also seed all of the random variables allocated by a RandomStreams object by that object’s seed
method. This seed will be used to seed a temporary random number generator, that will in turn generate
seeds for each of the random variables.
>>> srng.seed(902340)
50
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Sharing Streams Between Functions
As usual for shared variables, the random number generators used for random variables are common between
functions. So our nearly_zeros function will update the state of the generators used in function f above.
For example:
>>> state_after_v0 = rv_u.rng.get_value().get_state()
>>> nearly_zeros()
# this affects rv_u's generator
array([[ 0., 0.],
[ 0., 0.]])
>>> v1 = f()
>>> rng = rv_u.rng.get_value(borrow=True)
>>> rng.set_state(state_after_v0)
>>> rv_u.rng.set_value(rng, borrow=True)
>>> v2 = f()
# v2 != v1
>>> v3 = f()
# v3 == v1
Copying Random State Between Theano Graphs
In some use cases, a user might want to transfer the “state” of all random number generators associated
with a given theano graph (e.g. g1, with compiled function f1 below) to a second graph (e.g. g2, with
function f2). This might arise for example if you are trying to initialize the state of a model, from the parameters of a pickled version of a previous model. For theano.tensor.shared_randomstreams.
RandomStreams and theano.sandbox.rng_mrg.MRG_RandomStreams this can be achieved by
copying elements of the state_updates parameter.
Each time a random variable is drawn from a RandomStreams object, a tuple is added to the state_updates
list. The first element is a shared variable, which represents the state of the random number generator
associated with this particular variable, while the second represents the theano graph corresponding to the
random number generation process (i.e. RandomFunction{uniform}.0).
An example of how “random states” can be transferred from one theano function to another is shown below.
>>>
>>>
>>>
>>>
>>>
>>>
from __future__ import print_function
import theano
import numpy
import theano.tensor as T
from theano.sandbox.rng_mrg import MRG_RandomStreams
from theano.tensor.shared_randomstreams import RandomStreams
>>> class Graph():
...
def __init__(self, seed=123):
...
self.rng = RandomStreams(seed)
...
self.y = self.rng.uniform(size=(1,))
>>> g1 = Graph(seed=123)
>>> f1 = theano.function([], g1.y)
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>>> g2 = Graph(seed=987)
>>> f2 = theano.function([], g2.y)
>>> # By default, the two functions are out of sync.
>>> f1()
array([ 0.72803009])
>>> f2()
array([ 0.55056769])
>>> def copy_random_state(g1, g2):
...
if isinstance(g1.rng, MRG_RandomStreams):
...
g2.rng.rstate = g1.rng.rstate
...
for (su1, su2) in zip(g1.rng.state_updates, g2.rng.state_updates):
...
su2[0].set_value(su1[0].get_value())
>>> # We now copy the state of the theano random number generators.
>>> copy_random_state(g1, g2)
>>> f1()
array([ 0.59044123])
>>> f2()
array([ 0.59044123])
Other Random Distributions
There are other distributions implemented.
Other Implementations
There are 2 other implementations based on MRG31k3p and CURAND. The RandomStream only work on
the CPU, MRG31k3p work on the CPU and GPU. CURAND only work on the GPU.
Note: To use you the MRG version easily, you can just change the import to:
from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams
A Real Example: Logistic Regression
The preceding elements are featured in this more realistic example. It will be used repeatedly.
import numpy
import theano
import theano.tensor as T
rng = numpy.random
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N = 400
feats = 784
# training sample size
# number of input variables
# generate a dataset: D = (input_values, target_class)
D = (rng.randn(N, feats), rng.randint(size=N, low=0, high=2))
training_steps = 10000
# Declare Theano symbolic variables
x = T.dmatrix("x")
y = T.dvector("y")
#
#
#
#
#
w
initialize the weight vector w randomly
this and the following bias variable b
are shared so they keep their values
between training iterations (updates)
= theano.shared(rng.randn(feats), name="w")
# initialize the bias term
b = theano.shared(0., name="b")
print("Initial model:")
print(w.get_value())
print(b.get_value())
# Construct Theano expression graph
p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b))
# Probability that target = 1
prediction = p_1 > 0.5
# The prediction thresholded
xent = -y * T.log(p_1) - (1-y) * T.log(1-p_1) # Cross-entropy loss function
cost = xent.mean() + 0.01 * (w ** 2).sum()# The cost to minimize
gw, gb = T.grad(cost, [w, b])
# Compute the gradient of the cost
# w.r.t weight vector w and
# bias term b
# (we shall return to this in a
# following section of this
˓→tutorial)
# Compile
train = theano.function(
inputs=[x,y],
outputs=[prediction, xent],
updates=((w, w - 0.1 * gw), (b, b - 0.1 * gb)))
predict = theano.function(inputs=[x], outputs=prediction)
# Train
for i in range(training_steps):
pred, err = train(D[0], D[1])
print("Final model:")
print(w.get_value())
print(b.get_value())
print("target values for D:")
print(D[1])
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print("prediction on D:")
print(predict(D[0]))
Derivatives in Theano
Computing Gradients
Now let’s use Theano for a slightly more sophisticated task: create a function which computes the derivative
of some expression y with respect to its parameter x. To do this we will use the macro T.grad. For instance,
we can compute the gradient of 𝑥2 with respect to 𝑥. Note that: 𝑑(𝑥2 )/𝑑𝑥 = 2 · 𝑥.
Here is the code to compute this gradient:
>>> import numpy
>>> import theano
>>> import theano.tensor as T
>>> from theano import pp
>>> x = T.dscalar('x')
>>> y = x ** 2
>>> gy = T.grad(y, x)
>>> pp(gy) # print out the gradient prior to optimization
'((fill((x ** TensorConstant{2}), TensorConstant{1.0}) * TensorConstant{2}) *
˓→(x ** (TensorConstant{2} - TensorConstant{1})))'
>>> f = theano.function([x], gy)
>>> f(4)
array(8.0)
>>> numpy.allclose(f(94.2), 188.4)
True
In this example, we can see from pp(gy) that we are computing the correct symbolic gradient. fill((x
** 2), 1.0) means to make a matrix of the same shape as x ** 2 and fill it with 1.0.
Note: The optimizer simplifies the symbolic gradient expression. You can see this by digging inside the
internal properties of the compiled function.
pp(f.maker.fgraph.outputs[0])
'(2.0 * x)'
After optimization there is only one Apply node left in the graph, which doubles the input.
We can also compute the gradient of complex expressions such as the logistic function defined above. It
turns out that the derivative of the logistic is: 𝑑𝑠(𝑥)/𝑑𝑥 = 𝑠(𝑥) · (1 − 𝑠(𝑥)).
>>>
>>>
>>>
>>>
>>>
54
x = T.dmatrix('x')
s = T.sum(1 / (1 + T.exp(-x)))
gs = T.grad(s, x)
dlogistic = theano.function([x], gs)
dlogistic([[0, 1], [-1, -2]])
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Fig. 6.2: A plot of the gradient of the logistic function, with x on the x-axis and 𝑑𝑠(𝑥)/𝑑𝑥 on the y-axis.
array([[ 0.25
,
[ 0.19661193,
0.19661193],
0.10499359]])
In general, for any scalar expression s, T.grad(s, w) provides the Theano expression for computing
𝜕𝑠
𝜕𝑤 . In this way Theano can be used for doing efficient symbolic differentiation (as the expression returned
by T.grad will be optimized during compilation), even for function with many inputs. (see automatic
differentiation for a description of symbolic differentiation).
Note: The second argument of T.grad can be a list, in which case the output is also a list. The order
in both lists is important: element i of the output list is the gradient of the first argument of T.grad with
respect to the i-th element of the list given as second argument. The first argument of T.grad has to be a
scalar (a tensor of size 1). For more information on the semantics of the arguments of T.grad and details
about the implementation, see this section of the library.
Additional information on the inner workings of differentiation may also be found in the more advanced
tutorial Extending Theano.
Computing the Jacobian
In Theano’s parlance, the term Jacobian designates the tensor comprising the first partial derivatives of the
output of a function with respect to its inputs. (This is a generalization of to the so-called Jacobian matrix
in Mathematics.) Theano implements the theano.gradient.jacobian() macro that does all that is
needed to compute the Jacobian. The following text explains how to do it manually.
In order to manually compute the Jacobian of some function y with respect to some parameter x we need to
use scan. What we do is to loop over the entries in y and compute the gradient of y[i] with respect to x.
Note: scan is a generic op in Theano that allows writing in a symbolic manner all kinds of recurrent
equations. While creating symbolic loops (and optimizing them for performance) is a hard task, effort is
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being done for improving the performance of scan. We shall return to scan later in this tutorial.
>>> import theano
>>> import theano.tensor as T
>>> x = T.dvector('x')
>>> y = x ** 2
>>> J, updates = theano.scan(lambda i, y,x : T.grad(y[i], x), sequences=T.
˓→arange(y.shape[0]), non_sequences=[y,x])
>>> f = theano.function([x], J, updates=updates)
>>> f([4, 4])
array([[ 8., 0.],
[ 0., 8.]])
What we do in this code is to generate a sequence of ints from 0 to y.shape[0] using T.arange. Then
we loop through this sequence, and at each step, we compute the gradient of element y[i] with respect to x.
scan automatically concatenates all these rows, generating a matrix which corresponds to the Jacobian.
Note: There are some pitfalls to be aware of regarding T.grad. One of them is that you cannot rewrite the above expression of the Jacobian as theano.scan(lambda y_i,x: T.grad(y_i,x),
sequences=y, non_sequences=x), even though from the documentation of scan this seems possible. The reason is that y_i will not be a function of x anymore, while y[i] still is.
Computing the Hessian
In Theano, the term Hessian has the usual mathematical acception: It is the matrix comprising the second
order partial derivative of a function with scalar output and vector input. Theano implements theano.
gradient.hessian() macro that does all that is needed to compute the Hessian. The following text
explains how to do it manually.
You can compute the Hessian manually similarly to the Jacobian. The only difference is that now, instead
of computing the Jacobian of some expression y, we compute the Jacobian of T.grad(cost,x), where
cost is some scalar.
>>> x = T.dvector('x')
>>> y = x ** 2
>>> cost = y.sum()
>>> gy = T.grad(cost, x)
>>> H, updates = theano.scan(lambda i, gy,x : T.grad(gy[i], x), sequences=T.
˓→arange(gy.shape[0]), non_sequences=[gy, x])
>>> f = theano.function([x], H, updates=updates)
>>> f([4, 4])
array([[ 2., 0.],
[ 0., 2.]])
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Jacobian times a Vector
Sometimes we can express the algorithm in terms of Jacobians times vectors, or vectors times Jacobians.
Compared to evaluating the Jacobian and then doing the product, there are methods that compute the desired
results while avoiding actual evaluation of the Jacobian. This can bring about significant performance gains.
A description of one such algorithm can be found here:
• Barak A. Pearlmutter, “Fast Exact Multiplication by the Hessian”, Neural Computation, 1994
While in principle we would want Theano to identify these patterns automatically for us, in practice, implementing such optimizations in a generic manner is extremely difficult. Therefore, we provide special
functions dedicated to these tasks.
R-operator
(𝑥)
The R operator is built to evaluate the product between a Jacobian and a vector, namely 𝜕𝑓𝜕𝑥
𝑣. The
formulation can be extended even for x being a matrix, or a tensor in general, case in which also the Jacobian
becomes a tensor and the product becomes some kind of tensor product. Because in practice we end up
needing to compute such expressions in terms of weight matrices, Theano supports this more generic form
of the operation. In order to evaluate the R-operation of expression y, with respect to x, multiplying the
Jacobian with v you need to do something similar to this:
>>> W = T.dmatrix('W')
>>> V = T.dmatrix('V')
>>> x = T.dvector('x')
>>> y = T.dot(x, W)
>>> JV = T.Rop(y, W, V)
>>> f = theano.function([W, V, x], JV)
>>> f([[1, 1], [1, 1]], [[2, 2], [2, 2]], [0,1])
array([ 2., 2.])
List of Op that implement Rop.
L-operator
In similitude to the R-operator, the L-operator would compute a row vector times the Jacobian. The mathe(𝑥)
matical formula would be 𝑣 𝜕𝑓𝜕𝑥
. The L-operator is also supported for generic tensors (not only for vectors).
Similarly, it can be implemented as follows:
>>> W = T.dmatrix('W')
>>> v = T.dvector('v')
>>> x = T.dvector('x')
>>> y = T.dot(x, W)
>>> VJ = T.Lop(y, W, v)
>>> f = theano.function([v,x], VJ)
>>> f([2, 2], [0, 1])
array([[ 0., 0.],
[ 2., 2.]])
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Note:
v, the point of evaluation, differs between the L-operator and the R-operator. For the Loperator, the point of evaluation needs to have the same shape as the output, whereas for the
R-operator this point should have the same shape as the input parameter. Furthermore, the results of these two operations differ. The result of the L-operator is of the same shape as the
input parameter, while the result of the R-operator has a shape similar to that of the output.
List of op with r op support.
Hessian times a Vector
If you need to compute the Hessian times a vector, you can make use of the above-defined operators to
do it more efficiently than actually computing the exact Hessian and then performing the product. Due to
the symmetry of the Hessian matrix, you have two options that will give you the same result, though these
options might exhibit differing performances. Hence, we suggest profiling the methods before using either
one of the two:
>>> x = T.dvector('x')
>>> v = T.dvector('v')
>>> y = T.sum(x ** 2)
>>> gy = T.grad(y, x)
>>> vH = T.grad(T.sum(gy * v), x)
>>> f = theano.function([x, v], vH)
>>> f([4, 4], [2, 2])
array([ 4., 4.])
or, making use of the R-operator:
>>> x = T.dvector('x')
>>> v = T.dvector('v')
>>> y = T.sum(x ** 2)
>>> gy = T.grad(y, x)
>>> Hv = T.Rop(gy, x, v)
>>> f = theano.function([x, v], Hv)
>>> f([4, 4], [2, 2])
array([ 4., 4.])
Final Pointers
• The grad function works symbolically: it receives and returns Theano variables.
• grad can be compared to a macro since it can be applied repeatedly.
• Scalar costs only can be directly handled by grad. Arrays are handled through repeated applications.
• Built-in functions allow to compute efficiently vector times Jacobian and vector times Hessian.
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• Work is in progress on the optimizations required to compute efficiently the full Jacobian and the
Hessian matrix as well as the Jacobian times vector.
Conditions
IfElse vs Switch
• Both ops build a condition over symbolic variables.
• IfElse takes a boolean condition and two variables as inputs.
• Switch takes a tensor as condition and two variables as inputs. switch is an elementwise operation
and is thus more general than ifelse.
• Whereas switch evaluates both output variables, ifelse is lazy and only evaluates one variable
with respect to the condition.
Example
from theano import tensor as T
from theano.ifelse import ifelse
import theano, time, numpy
a,b = T.scalars('a', 'b')
x,y = T.matrices('x', 'y')
z_switch = T.switch(T.lt(a, b), T.mean(x), T.mean(y))
z_lazy = ifelse(T.lt(a, b), T.mean(x), T.mean(y))
f_switch = theano.function([a, b, x, y], z_switch,
mode=theano.Mode(linker='vm'))
f_lazyifelse = theano.function([a, b, x, y], z_lazy,
mode=theano.Mode(linker='vm'))
val1 = 0.
val2 = 1.
big_mat1 = numpy.ones((10000, 1000))
big_mat2 = numpy.ones((10000, 1000))
n_times = 10
tic = time.clock()
for i in range(n_times):
f_switch(val1, val2, big_mat1, big_mat2)
print('time spent evaluating both values %f sec' % (time.clock() - tic))
tic = time.clock()
for i in range(n_times):
f_lazyifelse(val1, val2, big_mat1, big_mat2)
print('time spent evaluating one value %f sec' % (time.clock() - tic))
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In this example, the IfElse op spends less time (about half as much) than Switch since it computes only
one variable out of the two.
$ python ifelse_switch.py
time spent evaluating both values 0.6700 sec
time spent evaluating one value 0.3500 sec
Unless linker='vm' or linker='cvm' are used, ifelse will compute both variables and take the
same computation time as switch. Although the linker is not currently set by default to cvm, it will be in
the near future.
There is no automatic optimization replacing a switch with a broadcasted scalar to an ifelse, as this is
not always faster. See this ticket.
Note: If you use test values, then all branches of the IfElse will be computed. This is normal, as using
test_value means everything will be computed when we build it, due to Python’s greedy evaluation and the
semantic of test value. As we build both branches, they will be executed for test values. This doesn’t cause
any changes during the execution of the compiled Theano function.
Loop
Scan
• A general form of recurrence, which can be used for looping.
• Reduction and map (loop over the leading dimensions) are special cases of scan.
• You scan a function along some input sequence, producing an output at each time-step.
• The function can see the previous K time-steps of your function.
• sum() could be computed by scanning the z + x(i) function over a list, given an initial state of z=0.
• Often a for loop can be expressed as a scan() operation, and scan is the closest that Theano comes
to looping.
• Advantages of using scan over for loops:
– Number of iterations to be part of the symbolic graph.
– Minimizes GPU transfers (if GPU is involved).
– Computes gradients through sequential steps.
– Slightly faster than using a for loop in Python with a compiled Theano function.
– Can lower the overall memory usage by detecting the actual amount of memory needed.
The full documentation can be found in the library: Scan.
Scan Example: Computing tanh(x(t).dot(W) + b) elementwise
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import theano
import theano.tensor as T
import numpy as np
# defining the tensor variables
X = T.matrix("X")
W = T.matrix("W")
b_sym = T.vector("b_sym")
results, updates = theano.scan(lambda v: T.tanh(T.dot(v, W) + b_sym),
˓→sequences=X)
compute_elementwise = theano.function(inputs=[X, W, b_sym], outputs=results)
# test values
x = np.eye(2, dtype=theano.config.floatX)
w = np.ones((2, 2), dtype=theano.config.floatX)
b = np.ones((2), dtype=theano.config.floatX)
b[1] = 2
print(compute_elementwise(x, w, b))
# comparison with numpy
print(np.tanh(x.dot(w) + b))
[[
[
[[
[
0.96402758
0.96402758
0.96402758
0.96402758
0.99505475]
0.99505475]]
0.99505475]
0.99505475]]
Scan Example: Computing the sequence x(t) = tanh(x(t - 1).dot(W) + y(t).dot(U) + p(T - t).dot(V))
import theano
import theano.tensor as T
import numpy as np
# define tensor variables
X = T.vector("X")
W = T.matrix("W")
b_sym = T.vector("b_sym")
U = T.matrix("U")
Y = T.matrix("Y")
V = T.matrix("V")
P = T.matrix("P")
results, updates = theano.scan(lambda y, p, x_tm1: T.tanh(T.dot(x_tm1, W) + T.
˓→dot(y, U) + T.dot(p, V)),
sequences=[Y, P[::-1]], outputs_info=[X])
compute_seq = theano.function(inputs=[X, W, Y, U, P, V], outputs=results)
# test values
x = np.zeros((2), dtype=theano.config.floatX)
x[1] = 1
w = np.ones((2, 2), dtype=theano.config.floatX)
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y = np.ones((5,
y[0, :] = -3
u = np.ones((2,
p = np.ones((5,
p[0, :] = 3
v = np.ones((2,
2), dtype=theano.config.floatX)
2), dtype=theano.config.floatX)
2), dtype=theano.config.floatX)
2), dtype=theano.config.floatX)
print(compute_seq(x, w, y, u, p, v))
# comparison with numpy
x_res = np.zeros((5, 2), dtype=theano.config.floatX)
x_res[0] = np.tanh(x.dot(w) + y[0].dot(u) + p[4].dot(v))
for i in range(1, 5):
x_res[i] = np.tanh(x_res[i - 1].dot(w) + y[i].dot(u) + p[4-i].dot(v))
print(x_res)
[[-0.99505475 -0.99505475]
[ 0.96471973 0.96471973]
[ 0.99998585 0.99998585]
[ 0.99998771 0.99998771]
[ 1.
1.
]]
[[-0.99505475 -0.99505475]
[ 0.96471973 0.96471973]
[ 0.99998585 0.99998585]
[ 0.99998771 0.99998771]
[ 1.
1.
]]
Scan Example: Computing norms of lines of X
import theano
import theano.tensor as T
import numpy as np
# define tensor variable
X = T.matrix("X")
results, updates = theano.scan(lambda x_i: T.sqrt((x_i ** 2).sum()),
˓→sequences=[X])
compute_norm_lines = theano.function(inputs=[X], outputs=results)
# test value
x = np.diag(np.arange(1, 6, dtype=theano.config.floatX), 1)
print(compute_norm_lines(x))
# comparison with numpy
print(np.sqrt((x ** 2).sum(1)))
[ 1.
[ 1.
2.
2.
3.
3.
4.
4.
5.
5.
0.]
0.]
Scan Example: Computing norms of columns of X
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import theano
import theano.tensor as T
import numpy as np
# define tensor variable
X = T.matrix("X")
results, updates = theano.scan(lambda x_i: T.sqrt((x_i ** 2).sum()),
˓→sequences=[X.T])
compute_norm_cols = theano.function(inputs=[X], outputs=results)
# test value
x = np.diag(np.arange(1, 6, dtype=theano.config.floatX), 1)
print(compute_norm_cols(x))
# comparison with numpy
print(np.sqrt((x ** 2).sum(0)))
[ 0.
[ 0.
1.
1.
2.
2.
3.
3.
4.
4.
5.]
5.]
Scan Example: Computing trace of X
import
import
import
floatX
theano
theano.tensor as T
numpy as np
= "float32"
# define tensor variable
X = T.matrix("X")
results, updates = theano.scan(lambda i, j, t_f: T.cast(X[i, j] + t_f,
˓→floatX),
sequences=[T.arange(X.shape[0]), T.arange(X.shape[1])],
outputs_info=np.asarray(0., dtype=floatX))
result = results[-1]
compute_trace = theano.function(inputs=[X], outputs=result)
# test value
x = np.eye(5, dtype=theano.config.floatX)
x[0] = np.arange(5, dtype=theano.config.floatX)
print(compute_trace(x))
# comparison with numpy
print(np.diagonal(x).sum())
4.0
4.0
Scan Example: Computing the sequence x(t) = x(t - 2).dot(U) + x(t - 1).dot(V) + tanh(x(t - 1).dot(W) +
b)
import theano
import theano.tensor as T
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import numpy as np
# define tensor variables
X = T.matrix("X")
W = T.matrix("W")
b_sym = T.vector("b_sym")
U = T.matrix("U")
V = T.matrix("V")
n_sym = T.iscalar("n_sym")
results, updates = theano.scan(lambda x_tm2, x_tm1: T.dot(x_tm2, U) + T.dot(x_
˓→tm1, V) + T.tanh(T.dot(x_tm1, W) + b_sym),
n_steps=n_sym, outputs_info=[dict(initial=X, taps=[-2, ˓→1])])
compute_seq2 = theano.function(inputs=[X, U, V, W, b_sym, n_sym],
˓→outputs=results)
# test values
x = np.zeros((2, 2), dtype=theano.config.floatX) # the initial value must be
˓→able to return x[-2]
x[1, 1] = 1
w = 0.5 * np.ones((2, 2), dtype=theano.config.floatX)
u = 0.5 * (np.ones((2, 2), dtype=theano.config.floatX) - np.eye(2,
˓→dtype=theano.config.floatX))
v = 0.5 * np.ones((2, 2), dtype=theano.config.floatX)
n = 10
b = np.ones((2), dtype=theano.config.floatX)
print(compute_seq2(x, u, v, w, b, n))
# comparison with numpy
x_res = np.zeros((10, 2))
x_res[0] = x[0].dot(u) + x[1].dot(v) + np.tanh(x[1].dot(w) + b)
x_res[1] = x[1].dot(u) + x_res[0].dot(v) + np.tanh(x_res[0].dot(w) + b)
x_res[2] = x_res[0].dot(u) + x_res[1].dot(v) + np.tanh(x_res[1].dot(w) + b)
for i in range(2, 10):
x_res[i] = (x_res[i - 2].dot(u) + x_res[i - 1].dot(v) +
np.tanh(x_res[i - 1].dot(w) + b))
print(x_res)
[[
[
[
[
[
[
[
[
[
[
[[
[
[
64
1.40514825
2.88898899
4.34018291
6.53463142
9.82972243
14.22203814
20.07439936
28.12291843
39.1913681
54.28407732
1.40514825
2.88898899
4.34018291
1.40514825]
2.38898899]
4.34018291]
6.78463142]
9.82972243]
14.09703814]
20.07439936]
28.18541843]
39.1913681 ]
54.25282732]]
1.40514825]
2.38898899]
4.34018291]
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[
[
[
[
[
[
[
6.53463142
9.82972243
14.22203814
20.07439936
28.12291843
39.1913681
54.28407732
6.78463142]
9.82972243]
14.09703814]
20.07439936]
28.18541843]
39.1913681 ]
54.25282732]]
Scan Example: Computing the Jacobian of y = tanh(v.dot(A)) wrt x
import theano
import theano.tensor as T
import numpy as np
# define tensor variables
v = T.vector()
A = T.matrix()
y = T.tanh(T.dot(v, A))
results, updates = theano.scan(lambda i: T.grad(y[i], v), sequences=[T.
˓→arange(y.shape[0])])
compute_jac_t = theano.function([A, v], results, allow_input_downcast=True) #
˓→shape (d_out, d_in)
# test values
x = np.eye(5, dtype=theano.config.floatX)[0]
w = np.eye(5, 3, dtype=theano.config.floatX)
w[2] = np.ones((3), dtype=theano.config.floatX)
print(compute_jac_t(w, x))
# compare with numpy
print(((1 - np.tanh(x.dot(w)) ** 2) * w).T)
[[
[
[
[[
[
[
0.41997434
0.
0.
0.41997434
0.
0.
0.
1.
0.
0.
1.
0.
0.41997434
1.
1.
0.41997434
1.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
]
]
]]
]
]
]]
Note that we need to iterate over the indices of y and not over the elements of y. The reason is that scan
create a placeholder variable for its internal function and this placeholder variable does not have the same
dependencies than the variables that will replace it.
Scan Example: Accumulate number of loop during a scan
import theano
import theano.tensor as T
import numpy as np
# define shared variables
k = theano.shared(0)
n_sym = T.iscalar("n_sym")
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results, updates = theano.scan(lambda:{k:(k + 1)}, n_steps=n_sym)
accumulator = theano.function([n_sym], [], updates=updates, allow_input_
˓→downcast=True)
k.get_value()
accumulator(5)
k.get_value()
Scan Example: Computing tanh(v.dot(W) + b) * d where d is binomial
import theano
import theano.tensor as T
import numpy as np
# define tensor variables
X = T.matrix("X")
W = T.matrix("W")
b_sym = T.vector("b_sym")
# define shared random stream
trng = T.shared_randomstreams.RandomStreams(1234)
d=trng.binomial(size=W[1].shape)
results, updates = theano.scan(lambda v: T.tanh(T.dot(v, W) + b_sym) * d,
˓→sequences=X)
compute_with_bnoise = theano.function(inputs=[X, W, b_sym], outputs=results,
updates=updates, allow_input_downcast=True)
x = np.eye(10, 2, dtype=theano.config.floatX)
w = np.ones((2, 2), dtype=theano.config.floatX)
b = np.ones((2), dtype=theano.config.floatX)
print(compute_with_bnoise(x, w, b))
[[
[
[
[
[
[
[
[
[
[
0.96402758
0.
0.
0.76159416
0.76159416
0.
0.
0.
0.
0.76159416
0.
]
0.96402758]
0.
]
0.76159416]
0.
]
0.76159416]
0.76159416]
0.76159416]
0.
]
0.76159416]]
Note that if you want to use a random variable d that will not be updated through scan loops, you should
pass this variable as a non_sequences arguments.
Scan Example: Computing pow(A, k)
import theano
import theano.tensor as T
theano.config.warn.subtensor_merge_bug = False
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k = T.iscalar("k")
A = T.vector("A")
def inner_fct(prior_result, B):
return prior_result * B
# Symbolic description of the result
result, updates = theano.scan(fn=inner_fct,
outputs_info=T.ones_like(A),
non_sequences=A, n_steps=k)
# Scan has provided us with A ** 1 through A ** k. Keep only the last
# value. Scan notices this and does not waste memory saving them.
final_result = result[-1]
power = theano.function(inputs=[A, k], outputs=final_result,
updates=updates)
print(power(range(10), 2))
[
0.
1.
4.
9.
16.
25.
36.
49.
64.
81.]
Scan Example: Calculating a Polynomial
import numpy
import theano
import theano.tensor as T
theano.config.warn.subtensor_merge_bug = False
coefficients = theano.tensor.vector("coefficients")
x = T.scalar("x")
max_coefficients_supported = 10000
# Generate the components of the polynomial
full_range=theano.tensor.arange(max_coefficients_supported)
components, updates = theano.scan(fn=lambda coeff, power, free_var:
coeff * (free_var ** power),
outputs_info=None,
sequences=[coefficients, full_range],
non_sequences=x)
polynomial = components.sum()
calculate_polynomial = theano.function(inputs=[coefficients, x],
outputs=polynomial)
test_coeff = numpy.asarray([1, 0, 2], dtype=numpy.float32)
print(calculate_polynomial(test_coeff, 3))
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Exercise
Run both examples.
Modify and execute the polynomial example to have the reduction done by scan.
Solution
How Shape Information is Handled by Theano
It is not possible to strictly enforce the shape of a Theano variable when building a graph since the particular
value provided at run-time for a parameter of a Theano function may condition the shape of the Theano
variables in its graph.
Currently, information regarding shape is used in two ways in Theano:
• To generate faster C code for the 2d convolution on the CPU and the GPU, when the exact output
shape is known in advance.
• To remove computations in the graph when we only want to know the shape, but not the actual value
of a variable. This is done with the Op.infer_shape method.
Example:
>>> import theano
>>> x = theano.tensor.matrix('x')
>>> f = theano.function([x], (x ** 2).shape)
>>> theano.printing.debugprint(f)
MakeVector{dtype='int64'} [id A] ''
2
|Shape_i{0} [id B] ''
1
| |x [id C]
|Shape_i{1} [id D] ''
0
|x [id C]
The output of this compiled function does not contain any multiplication or power. Theano has removed
them to compute directly the shape of the output.
Shape Inference Problem
Theano propagates information about shape in the graph. Sometimes this can lead to errors. Consider this
example:
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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import numpy
import theano
x = theano.tensor.matrix('x')
y = theano.tensor.matrix('y')
z = theano.tensor.join(0, x, y)
xv = numpy.random.rand(5, 4)
yv = numpy.random.rand(3, 3)
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>>> f = theano.function([x, y], z.shape)
>>> theano.printing.debugprint(f)
MakeVector{dtype='int64'} [id A] ''
4
|Elemwise{Add}[(0, 0)] [id B] ''
3
| |Shape_i{0} [id C] ''
1
| | |x [id D]
| |Shape_i{0} [id E] ''
2
|
|y [id F]
|Shape_i{1} [id G] ''
0
|x [id D]
>>> f(xv, yv) # DOES NOT RAISE AN ERROR AS SHOULD BE.
array([8, 4])
>>> f = theano.function([x,y], z)# Do not take the shape.
>>> theano.printing.debugprint(f)
Join [id A] ''
0
|TensorConstant{0} [id B]
|x [id C]
|y [id D]
>>> f(xv, yv)
Traceback (most recent call last):
...
ValueError: ...
As you can see, when asking only for the shape of some computation (join in the example), an inferred
shape is computed directly, without executing the computation itself (there is no join in the first output or
debugprint).
This makes the computation of the shape faster, but it can also hide errors. In this example, the computation
of the shape of the output of join is done only based on the first input Theano variable, which leads to an
error.
This might happen with other ops such as elemwise and dot, for example. Indeed, to perform some
optimizations (for speed or stability, for instance), Theano assumes that the computation is correct and
consistent in the first place, as it does here.
You can detect those problems by running the code without this optimization, using the Theano flag
optimizer_excluding=local_shape_to_shape_i. You can also obtain the same effect by running in the modes FAST_COMPILE (it will not apply this optimization, nor most other optimizations) or
DebugMode (it will test before and after all optimizations (much slower)).
Specifing Exact Shape
Currently, specifying a shape is not as easy and flexible as we wish and we plan some upgrade. Here is the
current state of what can be done:
• You can pass the shape info directly to the ConvOp created when calling conv2d. You simply set the
parameters image_shape and filter_shape inside the call. They must be tuples of 4 elements.
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For example:
theano.tensor.nnet.conv2d(..., image_shape=(7, 3, 5, 5), filter_shape=(2, 3,
˓→4, 4))
• You can use the SpecifyShape op to add shape information anywhere in the graph. This allows
to perform some optimizations. In the following example, this makes it possible to precompute the
Theano function to a constant.
>>> import theano
>>> x = theano.tensor.matrix()
>>> x_specify_shape = theano.tensor.specify_shape(x, (2, 2))
>>> f = theano.function([x], (x_specify_shape ** 2).shape)
>>> theano.printing.debugprint(f)
DeepCopyOp [id A] ''
0
|TensorConstant{(2,) of 2} [id B]
Future Plans
The parameter “constant shape” will be added to theano.shared(). This is probably the
most frequent occurrence with shared variables. It will make the code simpler and will make
it possible to check that the shape does not change when updating the shared variable.
Advanced
Sparse
In general, sparse matrices provide the same functionality as regular matrices. The difference lies in the
way the elements of sparse matrices are represented and stored in memory. Only the non-zero elements of
the latter are stored. This has some potential advantages: first, this may obviously lead to reduced memory
usage and, second, clever storage methods may lead to reduced computation time through the use of sparse
specific algorithms. We usually refer to the generically stored matrices as dense matrices.
Theano’s sparse package provides efficient algorithms, but its use is not recommended in all cases or for
all matrices. As an obvious example, consider the case where the sparsity proportion is very low. The
sparsity proportion refers to the ratio of the number of zero elements to the number of all elements in a
matrix. A low sparsity proportion may result in the use of more space in memory since not only the actual
data is stored, but also the position of nearly every element of the matrix. This would also require more
computation time whereas a dense matrix representation along with regular optimized algorithms might do
a better job. Other examples may be found at the nexus of the specific purpose and structure of the matrices.
More documentation may be found in the SciPy Sparse Reference.
Since sparse matrices are not stored in contiguous arrays, there are several ways to represent them in memory. This is usually designated by the so-called format of the matrix. Since Theano’s sparse matrix
package is based on the SciPy sparse package, complete information about sparse matrices can be found in
the SciPy documentation. Like SciPy, Theano does not implement sparse formats for arrays with a number
of dimensions different from two.
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So far, Theano implements two formats of sparse matrix: csc and csr. Those are almost identical
except that csc is based on the columns of the matrix and csr is based on its rows. They both have
the same purpose: to provide for the use of efficient algorithms performing linear algebra operations. A
disadvantage is that they fail to give an efficient way to modify the sparsity structure of the underlying
matrix, i.e. adding new elements. This means that if you are planning to add new elements in a sparse
matrix very often in your computational graph, perhaps a tensor variable could be a better choice.
More documentation may be found in the Sparse Library Reference.
Before going further, here are the import statements that are assumed for the rest of the tutorial:
>>>
>>>
>>>
>>>
import theano
import numpy as np
import scipy.sparse as sp
from theano import sparse
Compressed Sparse Format
Theano supports two compressed sparse formats: csc and csr, respectively based on columns and rows.
They have both the same attributes: data, indices, indptr and shape.
• The data attribute is a one-dimensional ndarray which contains all the non-zero elements of the
sparse matrix.
• The indices and indptr attributes are used to store the position of the data in the sparse matrix.
• The shape attribute is exactly the same as the shape attribute of a dense (i.e. generic) matrix. It
can be explicitly specified at the creation of a sparse matrix if it cannot be infered from the first three
attributes.
Which format should I use?
At the end, the format does not affect the length of the data and indices attributes. They are both
completly fixed by the number of elements you want to store. The only thing that changes with the format is
indptr. In csc format, the matrix is compressed along columns so a lower number of columns will result
in less memory use. On the other hand, with the csr format, the matrix is compressed along the rows and
with a matrix that have a lower number of rows, csr format is a better choice. So here is the rule:
Note: If shape[0] > shape[1], use csc format. Otherwise, use csr.
Sometimes, since the sparse module is young, ops does not exist for both format. So here is what may be
the most relevent rule:
Note: Use the format compatible with the ops in your computation graph.
The documentation about the ops and their supported format may be found in the Sparse Library Reference.
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Handling Sparse in Theano
Most of the ops in Theano depend on the format of the sparse matrix. That is why there are two kinds
of constructors of sparse variables: csc_matrix and csr_matrix. These can be called with the usual
name and dtype parameters, but no broadcastable flags are allowed. This is forbidden since the
sparse package, as the SciPy sparse module, does not provide any way to handle a number of dimensions
different from two. The set of all accepted dtype for the sparse matrices can be found in sparse.
all_dtypes.
>>> sparse.all_dtypes
set(['int8', 'int16', 'int32', 'int64', 'uint8', 'uint16', 'uint32', 'uint64',
'float32', 'float64', 'complex64', 'complex128'])
To and Fro
To move back and forth from a dense matrix to a sparse matrix representation, Theano provides the
dense_from_sparse, csr_from_dense and csc_from_dense functions. No additional detail
must be provided. Here is an example that performs a full cycle from sparse to sparse:
>>> x = sparse.csc_matrix(name='x', dtype='float32')
>>> y = sparse.dense_from_sparse(x)
>>> z = sparse.csc_from_dense(y)
Properties and Construction
Although sparse variables do not allow direct access to their properties, this can be accomplished using the
csm_properties function. This will return a tuple of one-dimensional tensor variables that represents
the internal characteristics of the sparse matrix.
In order to reconstruct a sparse matrix from some properties, the functions CSC and CSR can be used. This
will create the sparse matrix in the desired format. As an example, the following code reconstructs a csc
matrix into a csr one.
>>>
>>>
>>>
>>>
>>>
>>>
[[0
[0
[1
>>>
[[0
[1
[1
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x = sparse.csc_matrix(name='x', dtype='int64')
data, indices, indptr, shape = sparse.csm_properties(x)
y = sparse.CSR(data, indices, indptr, shape)
f = theano.function([x], y)
a = sp.csc_matrix(np.asarray([[0, 1, 1], [0, 0, 0], [1, 0, 0]]))
print(a.toarray())
1 1]
0 0]
0 0]]
print(f(a).toarray())
0 1]
0 0]
0 0]]
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The last example shows that one format can be obtained from transposition of the other. Indeed, when
calling the transpose function, the sparse characteristics of the resulting matrix cannot be the same as
the one provided as input.
Structured Operation
Several ops are set to make use of the very peculiar structure of the sparse matrices. These ops are said to
be structured and simply do not perform any computations on the zero elements of the sparse matrix. They
can be thought as being applied only to the data attribute of the latter. Note that these structured ops provide
a structured gradient. More explication below.
>>> x = sparse.csc_matrix(name='x', dtype='float32')
>>> y = sparse.structured_add(x, 2)
>>> f = theano.function([x], y)
>>> a = sp.csc_matrix(np.asarray([[0, 0, -1], [0, -2, 1], [3, 0, 0]], dtype=
˓→'float32'))
>>> print(a.toarray())
[[ 0. 0. -1.]
[ 0. -2. 1.]
[ 3. 0. 0.]]
>>> print(f(a).toarray())
[[ 0. 0. 1.]
[ 0. 0. 3.]
[ 5. 0. 0.]]
Gradient
The gradients of the ops in the sparse module can also be structured. Some ops provide a flag to indicate if
the gradient is to be structured or not. The documentation can be used to determine if the gradient of an op is
regular or structured or if its implementation can be modified. Similarly to structured ops, when a structured
gradient is calculated, the computation is done only for the non-zero elements of the sparse matrix.
More documentation regarding the gradients of specific ops can be found in the Sparse Library Reference.
Using the GPU
For an introductory discussion of Graphical Processing Units (GPU) and their use for intensive parallel
computation purposes, see GPGPU.
One of Theano’s design goals is to specify computations at an abstract level, so that the internal function
compiler has a lot of flexibility about how to carry out those computations. One of the ways we take
advantage of this flexibility is in carrying out calculations on a graphics card.
There are two ways currently to use a gpu, one of which only supports NVIDIA cards (CUDA backend)
and the other, in development, that should support any OpenCL device as well as NVIDIA cards (GpuArray
Backend).
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CUDA backend
If you have not done so already, you will need to install Nvidia’s GPU-programming toolchain (CUDA) and
configure Theano to use it. We provide installation instructions for Linux, MacOS and Windows.
Testing Theano with GPU
To see if your GPU is being used, cut and paste the following program into a file and run it.
from theano import function, config, shared, sandbox
import theano.tensor as T
import numpy
import time
vlen = 10 * 30 * 768
iters = 1000
# 10 x #cores x # threads per core
rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), config.floatX))
f = function([], T.exp(x))
print(f.maker.fgraph.toposort())
t0 = time.time()
for i in range(iters):
r = f()
t1 = time.time()
print("Looping %d times took %f seconds" % (iters, t1 - t0))
print("Result is %s" % (r,))
if numpy.any([isinstance(x.op, T.Elemwise) for x in f.maker.fgraph.
˓→toposort()]):
print('Used the cpu')
else:
print('Used the gpu')
The program just computes the exp() of a bunch of random numbers. Note that we use the shared
function to make sure that the input x is stored on the graphics device.
If I run this program (in check1.py) with device=cpu, my computer takes a little over 3 seconds, whereas
on the GPU it takes just over 0.64 seconds. The GPU will not always produce the exact same floating-point
numbers as the CPU. As a benchmark, a loop that calls numpy.exp(x.get_value()) takes about 46
seconds.
$ THEANO_FLAGS=mode=FAST_RUN,device=cpu,floatX=float32 python check1.py
[Elemwise{exp,no_inplace}(<TensorType(float32, vector)>)]
Looping 1000 times took 3.06635117531 seconds
Result is [ 1.23178029 1.61879337 1.52278066 ..., 2.20771813 2.29967761
1.62323284]
Used the cpu
$ THEANO_FLAGS=mode=FAST_RUN,device=gpu,floatX=float32 python check1.py
Using gpu device 0: GeForce GTX 580
[GpuElemwise{exp,no_inplace}(<CudaNdarrayType(float32, vector)>),
˓→HostFromGpu(GpuElemwise{exp,no_inplace}.0)]
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Looping 1000 times took 0.638810873032 seconds
Result is [ 1.23178029 1.61879349 1.52278066 ...,
1.62323296]
Used the gpu
2.20771813
2.29967761
Note that GPU operations in Theano require for now floatX to be float32 (see also below).
Returning a Handle to Device-Allocated Data
The speedup is not greater in the preceding example because the function is returning its result as a NumPy
ndarray which has already been copied from the device to the host for your convenience. This is what makes
it so easy to swap in device=gpu, but if you don’t mind less portability, you might gain a bigger speedup
by changing the graph to express a computation with a GPU-stored result. The gpu_from_host op means
“copy the input from the host to the GPU” and it is optimized away after the T.exp(x) is replaced by a
GPU version of exp().
from theano import function, config, shared, sandbox
import theano.sandbox.cuda.basic_ops
import theano.tensor as T
import numpy
import time
vlen = 10 * 30 * 768
iters = 1000
# 10 x #cores x # threads per core
rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), 'float32'))
f = function([], sandbox.cuda.basic_ops.gpu_from_host(T.exp(x)))
print(f.maker.fgraph.toposort())
t0 = time.time()
for i in range(iters):
r = f()
t1 = time.time()
print("Looping %d times took %f seconds" % (iters, t1 - t0))
print("Result is %s" % (r,))
print("Numpy result is %s" % (numpy.asarray(r),))
if numpy.any([isinstance(x.op, T.Elemwise) for x in f.maker.fgraph.
˓→toposort()]):
print('Used the cpu')
else:
print('Used the gpu')
The output from this program is
$ THEANO_FLAGS=mode=FAST_RUN,device=gpu,floatX=float32 python check2.py
Using gpu device 0: GeForce GTX 580
[GpuElemwise{exp,no_inplace}(<CudaNdarrayType(float32, vector)>)]
Looping 1000 times took 0.34898686409 seconds
Result is <CudaNdarray object at 0x6a7a5f0>
Numpy result is [ 1.23178029 1.61879349 1.52278066 ..., 2.20771813 2.
˓→29967761
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1.62323296]
Used the gpu
Here we’ve shaved off about 50% of the run-time by simply not copying the resulting array back to the
host. The object returned by each function call is now not a NumPy array but a “CudaNdarray” which can
be converted to a NumPy ndarray by the normal NumPy casting mechanism using something like numpy.
asarray().
For even more speed you can play with the borrow flag. See Borrowing when Constructing Function
Objects.
What Can Be Accelerated on the GPU
The performance characteristics will change as we continue to optimize our implementations, and vary from
device to device, but to give a rough idea of what to expect right now:
• Only computations with float32 data-type can be accelerated. Better support for float64 is expected in
upcoming hardware but float64 computations are still relatively slow (Jan 2010).
• Matrix multiplication, convolution, and large element-wise operations can be accelerated a lot (5-50x)
when arguments are large enough to keep 30 processors busy.
• Indexing, dimension-shuffling and constant-time reshaping will be equally fast on GPU as on CPU.
• Summation over rows/columns of tensors can be a little slower on the GPU than on the CPU.
• Copying of large quantities of data to and from a device is relatively slow, and often cancels most
of the advantage of one or two accelerated functions on that data. Getting GPU performance largely
hinges on making data transfer to the device pay off.
Tips for Improving Performance on GPU
• Consider adding floatX=float32 to your .theanorc file if you plan to do a lot of GPU work.
• Use the Theano flag allow_gc=False. See GPU Async capabilities
• Prefer constructors like matrix, vector and scalar to dmatrix, dvector and dscalar
because the former will give you float32 variables when floatX=float32.
• Ensure that your output variables have a float32 dtype and not float64. The more float32 variables are
in your graph, the more work the GPU can do for you.
• Minimize tranfers to the GPU device by using shared float32 variables to store frequently-accessed
data (see shared()). When using the GPU, float32 tensor shared variables are stored on the GPU
by default to eliminate transfer time for GPU ops using those variables.
• If you aren’t happy with the performance you see, try running your script with profile=True flag.
This should print some timing information at program termination. Is time being used sensibly? If an
op or Apply is taking more time than its share, then if you know something about GPU programming,
have a look at how it’s implemented in theano.sandbox.cuda. Check the line similar to Spent Xs(X%)
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in cpu op, Xs(X%) in gpu op and Xs(X%) in transfer op. This can tell you if not enough of your graph
is on the GPU or if there is too much memory transfer.
• Use nvcc options. nvcc supports those options to speed up some computations: -ftz=true to flush denormals values to zeros., –prec-div=false and –prec-sqrt=false options to speed up division and square
root operation by being less precise. You can enable all of them with the nvcc.flags=–use_fast_math
Theano flag or you can enable them individually as in this example: nvcc.flags=-ftz=true –precdiv=false.
• To investigate whether if all the Ops in the computational graph are running on GPU. It is possible to
debug or check your code by providing a value to assert_no_cpu_op flag, i.e. warn, for warning raise
for raising an error or pdb for putting a breakpoint in the computational graph if there is a CPU Op.
GPU Async capabilities
Ever since Theano 0.6 we started to use the asynchronous capability of GPUs. This allows us to be faster
but with the possibility that some errors may be raised later than when they should occur. This can cause
difficulties when profiling Theano apply nodes. There is a NVIDIA driver feature to help with these issues.
If you set the environment variable CUDA_LAUNCH_BLOCKING=1 then all kernel calls will be automatically synchronized. This reduces performance but provides good profiling and appropriately placed error
messages.
This feature interacts with Theano garbage collection of intermediate results. To get the most of this feature, you need to disable the gc as it inserts synchronization points in the graph. Set the Theano flag
allow_gc=False to get even faster speed! This will raise the memory usage.
Changing the Value of Shared Variables
To change the value of a shared variable, e.g.
to provide new data to processes, use
shared_variable.set_value(new_value). For a lot more detail about this, see Understanding
Memory Aliasing for Speed and Correctness.
Exercise
Consider again the logistic regression:
import numpy
import theano
import theano.tensor as T
rng = numpy.random
N = 400
feats = 784
D = (rng.randn(N, feats).astype(theano.config.floatX),
rng.randint(size=N,low=0, high=2).astype(theano.config.floatX))
training_steps = 10000
# Declare Theano symbolic variables
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x = T.matrix("x")
y = T.vector("y")
w = theano.shared(rng.randn(feats).astype(theano.config.floatX), name="w")
b = theano.shared(numpy.asarray(0., dtype=theano.config.floatX), name="b")
x.tag.test_value = D[0]
y.tag.test_value = D[1]
# Construct Theano expression graph
p_1 = 1 / (1 + T.exp(-T.dot(x, w)-b)) # Probability of having a one
prediction = p_1 > 0.5 # The prediction that is done: 0 or 1
xent = -y*T.log(p_1) - (1-y)*T.log(1-p_1) # Cross-entropy
cost = xent.mean() + 0.01*(w**2).sum() # The cost to optimize
gw,gb = T.grad(cost, [w,b])
# Compile expressions to functions
train = theano.function(
inputs=[x,y],
outputs=[prediction, xent],
updates=[(w, w-0.01*gw), (b, b-0.01*gb)],
name = "train")
predict = theano.function(inputs=[x], outputs=prediction,
name = "predict")
if any([x.op.__class__.__name__ in ['Gemv', 'CGemv', 'Gemm', 'CGemm'] for x in
train.maker.fgraph.toposort()]):
print('Used the cpu')
elif any([x.op.__class__.__name__ in ['GpuGemm', 'GpuGemv'] for x in
train.maker.fgraph.toposort()]):
print('Used the gpu')
else:
print('ERROR, not able to tell if theano used the cpu or the gpu')
print(train.maker.fgraph.toposort())
for i in range(training_steps):
pred, err = train(D[0], D[1])
print("target values for D")
print(D[1])
print("prediction on D")
print(predict(D[0]))
Modify and execute this example to run on GPU with floatX=float32 and time it using the command
line time python file.py. (Of course, you may use some of your answer to the exercise in section
Configuration Settings and Compiling Mode.)
Is there an increase in speed from CPU to GPU?
Where does it come from? (Use profile=True flag.)
What can be done to further increase the speed of the GPU version? Put your ideas to test.
Note:
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• Only 32 bit floats are currently supported (development is in progress).
• Shared variables with float32 dtype are by default moved to the GPU memory space.
• There is a limit of one GPU per process.
• Use the Theano flag device=gpu to require use of the GPU device.
• Use device=gpu{0, 1, ...} to specify which GPU if you have more than one.
• Apply the Theano flag floatX=float32 (through theano.config.floatX) in your code.
• Cast inputs before storing them into a shared variable.
• Circumvent the automatic cast of int32 with float32 to float64:
– Insert manual cast in your code or use [u]int{8,16}.
– Insert manual cast around the mean operator (this involves division by length, which is an int64).
– Notice that a new casting mechanism is being developed.
Solution
GpuArray Backend
If you have not done so already, you will need to install libgpuarray as well as at least one computing toolkit.
Instructions for doing so are provided at libgpuarray.
While all types of devices are supported if using OpenCL, for the remainder of this section, whatever compute device you are using will be referred to as GPU.
Warning: While it is fully our intention to support OpenCL, as of May 2014 this support is still in its
infancy. A lot of very useful ops still do not support it because they were ported from the old backend
with minimal change.
Testing Theano with GPU
To see if your GPU is being used, cut and paste the following program into a file and run it.
from theano import function, config, shared, tensor, sandbox
import numpy
import time
vlen = 10 * 30 * 768
iters = 1000
# 10 x #cores x # threads per core
rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), config.floatX))
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f = function([], tensor.exp(x))
print(f.maker.fgraph.toposort())
t0 = time.time()
for i in range(iters):
r = f()
t1 = time.time()
print("Looping %d times took %f seconds" % (iters, t1 - t0))
print("Result is %s" % (r,))
if numpy.any([isinstance(x.op, tensor.Elemwise) and
('Gpu' not in type(x.op).__name__)
for x in f.maker.fgraph.toposort()]):
print('Used the cpu')
else:
print('Used the gpu')
The program just compute exp() of a bunch of random numbers. Note that we use the theano.
shared() function to make sure that the input x is stored on the GPU.
$ THEANO_FLAGS=device=cpu python check1.py
[Elemwise{exp,no_inplace}(<TensorType(float64, vector)>)]
Looping 1000 times took 2.6071999073 seconds
Result is [ 1.23178032 1.61879341 1.52278065 ..., 2.20771815
1.62323285]
Used the cpu
$ THEANO_FLAGS=device=cuda0 python check1.py
Using device cuda0: GeForce GTX 275
[GpuElemwise{exp,no_inplace}(<GpuArray<float64>>),
˓→HostFromGpu(gpuarray)(GpuElemwise{exp,no_inplace}.0)]
Looping 1000 times took 2.28562092781 seconds
Result is [ 1.23178032 1.61879341 1.52278065 ..., 2.20771815
1.62323285]
Used the gpu
2.29967753
2.29967753
Returning a Handle to Device-Allocated Data
By default functions that execute on the GPU still return a standard numpy ndarray. A transfer operation
is inserted just before the results are returned to ensure a consistent interface with CPU code. This allows
changing the deivce some code runs on by only replacing the value of the device flag without touching
the code.
If you don’t mind a loss of flexibility, you can ask theano to return the GPU object directly. The following
code is modifed to do just that.
from theano import function, config, shared, tensor, sandbox
import numpy
import time
vlen = 10 * 30 * 768
iters = 1000
80
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rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), config.floatX))
f = function([], sandbox.gpuarray.basic_ops.gpu_from_host(tensor.exp(x)))
print(f.maker.fgraph.toposort())
t0 = time.time()
for i in range(iters):
r = f()
t1 = time.time()
print("Looping %d times took %f seconds" % (iters, t1 - t0))
print("Result is %s" % (numpy.asarray(r),))
if numpy.any([isinstance(x.op, tensor.Elemwise) and
('Gpu' not in type(x.op).__name__)
for x in f.maker.fgraph.toposort()]):
print('Used the cpu')
else:
print('Used the gpu')
Here the theano.sandbox.gpuarray.basic.gpu_from_host() call means “copy input to the
GPU”. However during the optimization phase, since the result will already be on th gpu, it will be removed.
It is used here to tell theano that we want the result on the GPU.
The output is
$ THEANO_FLAGS=device=cuda0 python check2.py
Using device cuda0: GeForce GTX 275
[GpuElemwise{exp,no_inplace}(<GpuArray<float64>>)]
Looping 1000 times took 0.455810785294 seconds
Result is [ 1.23178032 1.61879341 1.52278065 ...,
1.62323285]
Used the gpu
2.20771815
2.29967753
While the time per call appears to be much lower than the two previous invocations (and should indeed be
lower, since we avoid a transfer) the massive speedup we obtained is in part due to asynchronous nature of
execution on GPUs, meaning that the work isn’t completed yet, just ‘launched’. We’ll talk about that later.
The object returned is a GpuArray from pygpu. It mostly acts as a numpy ndarray with some exceptions due
to its data being on the GPU. You can copy it to the host and convert it to a regular ndarray by using usual
numpy casting such as numpy.asarray().
For even more speed, you can play with the borrow flag. See Borrowing when Constructing Function
Objects.
What Can be Accelerated on the GPU
The performance characteristics will of course vary from device to device, and also as we refine our implementation.
This backend supports all regular theano data types (float32, float64, int, ...) however GPU support varies
and some units can’t deal with double (float64) or small (less than 32 bits like int16) data types. You will
get an error at compile time or runtime if this is the case.
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By default all inputs will get transferred to GPU. You can prevent an input from getting transferred by setting
its tag.target attribute to ‘cpu’.
Complex support is untested and most likely completely broken.
In general, large operations like matrix multiplication, or element-wise operations with large inputs, will be
significatly faster.
GPU Async Capabilities
By default, all operations on the GPU are run asynchronously. This means that they are only scheduled to
run and the function returns. This is made somewhat transparently by the underlying libgpuarray.
A forced synchronization point is introduced when doing memory transfers between device and host.
It is possible to force synchronization for a particular GpuArray by calling its sync() method. This is
useful to get accurate timings when doing benchmarks.
Software for Directly Programming a GPU
Leaving aside Theano which is a meta-programmer, there are:
• CUDA: GPU programming API by NVIDIA based on extension to C (CUDA C)
– Vendor-specific
– Numeric libraries (BLAS, RNG, FFT) are maturing.
• OpenCL: multi-vendor version of CUDA
– More general, standardized.
– Fewer libraries, lesser spread.
• PyCUDA: Python bindings to CUDA driver interface allow to access Nvidia’s CUDA parallel computation API from Python
– Convenience:
Makes it easy to do GPU meta-programming from within Python.
Abstractions to compile low-level CUDA code from Python (pycuda.driver.
SourceModule).
GPU memory buffer (pycuda.gpuarray.GPUArray).
Helpful documentation.
– Completeness: Binding to all of CUDA’s driver API.
– Automatic error checking: All CUDA errors are automatically translated into Python exceptions.
– Speed: PyCUDA’s base layer is written in C++.
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– Good memory management of GPU objects:
Object cleanup tied to lifetime of objects (RAII, ‘Resource Acquisition Is Initialization’).
Makes it much easier to write correct, leak- and crash-free code.
PyCUDA knows about dependencies (e.g. it won’t detach from a context before all memory
allocated in it is also freed).
(This is adapted from PyCUDA’s documentation and Andreas Kloeckner’s website on PyCUDA.)
• PyOpenCL: PyCUDA for OpenCL
Learning to Program with PyCUDA
If you already enjoy a good proficiency with the C programming language, you may easily leverage your
knowledge by learning, first, to program a GPU with the CUDA extension to C (CUDA C) and, second, to
use PyCUDA to access the CUDA API with a Python wrapper.
The following resources will assist you in this learning process:
• CUDA API and CUDA C: Introductory
– NVIDIA’s slides
– Stein’s (NYU) slides
• CUDA API and CUDA C: Advanced
– MIT IAP2009 CUDA (full coverage: lectures, leading Kirk-Hwu textbook, examples, additional
resources)
– Course U. of Illinois (full lectures, Kirk-Hwu textbook)
– NVIDIA’s knowledge base (extensive coverage, levels from introductory to advanced)
– practical issues (on the relationship between grids, blocks and threads; see also linked and related
issues on same page)
– CUDA optimisation
• PyCUDA: Introductory
– Kloeckner’s slides
– Kloeckner’ website
• PYCUDA: Advanced
– PyCUDA documentation website
The following examples give a foretaste of programming a GPU with PyCUDA. Once you feel competent
enough, you may try yourself on the corresponding exercises.
Example: PyCUDA
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# (from PyCUDA's documentation)
import pycuda.autoinit
import pycuda.driver as drv
import numpy
from pycuda.compiler import SourceModule
mod = SourceModule("""
__global__ void multiply_them(float *dest, float *a, float *b)
{
const int i = threadIdx.x;
dest[i] = a[i] * b[i];
}
""")
multiply_them = mod.get_function("multiply_them")
a = numpy.random.randn(400).astype(numpy.float32)
b = numpy.random.randn(400).astype(numpy.float32)
dest = numpy.zeros_like(a)
multiply_them(
drv.Out(dest), drv.In(a), drv.In(b),
block=(400,1,1), grid=(1,1))
assert numpy.allclose(dest, a*b)
print(dest)
Exercise
Run the preceding example.
Modify and execute to work for a matrix of shape (20, 10). Example: Theano + PyCUDA
import numpy, theano
import theano.misc.pycuda_init
from pycuda.compiler import SourceModule
import theano.sandbox.cuda as cuda
class PyCUDADoubleOp(theano.Op):
__props__ = ()
def make_node(self, inp):
inp = cuda.basic_ops.gpu_contiguous(
cuda.basic_ops.as_cuda_ndarray_variable(inp))
assert inp.dtype == "float32"
return theano.Apply(self, [inp], [inp.type()])
def make_thunk(self, node, storage_map, _, _2):
mod = SourceModule("""
__global__ void my_fct(float * i0, float * o0, int size) {
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int i = blockIdx.x*blockDim.x + threadIdx.x;
if(i<size){
o0[i] = i0[i]*2;
}
}""")
pycuda_fct = mod.get_function("my_fct")
inputs = [storage_map[v] for v in node.inputs]
outputs = [storage_map[v] for v in node.outputs]
def thunk():
z = outputs[0]
if z[0] is None or z[0].shape != inputs[0][0].shape:
z[0] = cuda.CudaNdarray.zeros(inputs[0][0].shape)
grid = (int(numpy.ceil(inputs[0][0].size / 512.)), 1)
pycuda_fct(inputs[0][0], z[0], numpy.intc(inputs[0][0].size),
block=(512, 1, 1), grid=grid)
return thunk
Use this code to test it:
>>>
>>>
>>>
>>>
>>>
x = theano.tensor.fmatrix()
f = theano.function([x], PyCUDADoubleOp()(x))
xv = numpy.ones((4, 5), dtype="float32")
assert numpy.allclose(f(xv), xv*2)
print(numpy.asarray(f(xv)))
Exercise
Run the preceding example.
Modify and execute to multiply two matrices: x * y.
Modify and execute to return two outputs: x + y and x - y.
(Notice that Theano’s current elemwise fusion optimization is only applicable to computations involving a
single output. Hence, to gain efficiency over the basic solution that is asked here, the two operations would
have to be jointly optimized explicitly in the code.)
Modify and execute to support stride (i.e. to avoid constraining the input to be C-contiguous).
Note
• See Other Implementations to know how to handle random numbers on the GPU.
• The mode FAST_COMPILE disables C code, so also disables the GPU. You can use the Theano flag
optimizer=’fast_compile’ to speed up compilation and keep the GPU.
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Using multiple GPUs
Theano has a feature to allow the use of multiple GPUs at the same time in one function. The multiple gpu
feature requires the use of the GpuArray Backend backend, so make sure that works correctly.
In order to keep a reasonably high level of abstraction you do not refer to device names directly for multiplegpu use. You instead refer to what we call context names. These are then mapped to a device using the theano
configuration. This allows portability of models between machines.
Warning: The code is rather new and is still considered experimental at this point. It has been tested
and seems to perform correctly in all cases observed, but make sure to double-check your results before
publishing a paper or anything of the sort.
Note: For data-parallelism, you probably are better using platoon.
Defining the context map
The mapping from context names to devices is done through the config.contexts option. The format
looks like this:
dev0->cuda0;dev1->cuda1
Let’s break it down. First there is a list of mappings. Each of these mappings is separeted by a semicolon ‘;’.
There can be any number of such mappings, but in the example above we have two of them: dev0->cuda0
and dev1->cuda1.
The mappings themselves are composed of a context name followed by the two characters ‘->’ and the
device name. The context name is a simple string which does not have any special meaning for Theano. For
parsing reasons, the context name cannot contain the sequence ‘->’ or ‘;’. To avoid confusion context names
that begin with ‘cuda’ or ‘opencl’ are disallowed. The device name is a device in the form that gpuarray
expects like ‘cuda0’ or ‘opencl0:0’.
Note: Since there are a bunch of shell special characters in the syntax, defining this on the command-line
will require proper quoting, like this:
$ THEANO_FLAGS="contexts=dev0->cuda0"
When you define a context map, if config.print_active_device is True (the default), Theano will
print the mappings as they are defined. This will look like this:
$ THEANO_FLAGS="contexts=dev0->cuda0;dev1->cuda1" python -c 'import theano'
Mapped name dev0 to device cuda0: GeForce GTX TITAN X
Mapped name dev1 to device cuda1: GeForce GTX TITAN X
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If you don’t have enough GPUs for a certain model, you can assign the same device to more than one name.
You can also assign extra names that a model doesn’t need to some other devices. However, a proliferation of
names is not always a good idea since theano often assumes that different context names will be on different
devices and will optimize accordingly. So you may get faster performance for a single name and a single
device.
Note: It is often the case that multi-gpu operation requires or assumes that all the GPUs involved are
equivalent. This is not the case for this implementation. Since the user has the task of distrubuting the jobs
across the different device a model can be built on the assumption that one of the GPU is slower or has
smaller memory.
A simple graph on two GPUs
The following simple program works on two GPUs. It builds a function which perform two dot products on
two different GPUs.
import numpy
import theano
v01 = theano.shared(numpy.random.random((1024,
target='dev0')
v02 = theano.shared(numpy.random.random((1024,
target='dev0')
v11 = theano.shared(numpy.random.random((1024,
target='dev1')
v12 = theano.shared(numpy.random.random((1024,
target='dev1')
1024)).astype('float32'),
1024)).astype('float32'),
1024)).astype('float32'),
1024)).astype('float32'),
f = theano.function([], [theano.tensor.dot(v01, v02),
theano.tensor.dot(v11, v12)])
f()
This model requires a context map with assignations for ‘dev0’ and ‘dev1’. It should run twice as fast when
the devices are different.
Explicit transfers of data
Since operations themselves cannot work on more than one device, they will pick a device to work on based
on their inputs and automatically insert transfers for any input which is not on the right device.
However you may want some explicit control over where and how these transfers are done at some points.
This is done by using the new transfer() method that is present on variables. It works for moving data
between GPUs and also between the host and the GPUs. Here is a example.
import theano
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v = theano.tensor.fmatrix()
# Move to the device associated with 'gpudev'
gv = v.transfer('gpudev')
# Move back to the cpu
cv = gv.transfer('cpu')
Of course you can mix transfers and operations in any order you choose. However you should try to minimize transfer operations because they will introduce overhead any may reduce performance.
Advanced configuration and debugging
Configuration Settings and Compiling Modes
Configuration
The config module contains several attributes that modify Theano’s behavior. Many of these attributes
are examined during the import of the theano module and several are assumed to be read-only.
As a rule, the attributes in the config module should not be modified inside the user code.
Theano’s code comes with default values for these attributes, but you can override them from your .
theanorc file, and override those values in turn by the THEANO_FLAGS environment variable.
The order of precedence is:
1. an assignment to theano.config.<property>
2. an assignment in THEANO_FLAGS
3. an assignment in the .theanorc file (or the file indicated in THEANORC)
You can display the current/effective configuration at any time by printing theano.config. For example, to
see a list of all active configuration variables, type this from the command-line:
python -c 'import theano; print(theano.config)' | less
For more detail, see Configuration in the library.
Exercise
Consider the logistic regression:
import numpy
import theano
import theano.tensor as T
rng = numpy.random
N = 400
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feats = 784
D = (rng.randn(N, feats).astype(theano.config.floatX),
rng.randint(size=N,low=0, high=2).astype(theano.config.floatX))
training_steps = 10000
# Declare Theano symbolic variables
x = T.matrix("x")
y = T.vector("y")
w = theano.shared(rng.randn(feats).astype(theano.config.floatX), name="w")
b = theano.shared(numpy.asarray(0., dtype=theano.config.floatX), name="b")
x.tag.test_value = D[0]
y.tag.test_value = D[1]
# Construct Theano expression graph
p_1 = 1 / (1 + T.exp(-T.dot(x, w)-b)) # Probability of having a one
prediction = p_1 > 0.5 # The prediction that is done: 0 or 1
xent = -y*T.log(p_1) - (1-y)*T.log(1-p_1) # Cross-entropy
cost = xent.mean() + 0.01*(w**2).sum() # The cost to optimize
gw,gb = T.grad(cost, [w,b])
# Compile expressions to functions
train = theano.function(
inputs=[x,y],
outputs=[prediction, xent],
updates=[(w, w-0.01*gw), (b, b-0.01*gb)],
name = "train")
predict = theano.function(inputs=[x], outputs=prediction,
name = "predict")
if any([x.op.__class__.__name__ in ['Gemv', 'CGemv', 'Gemm', 'CGemm'] for x in
train.maker.fgraph.toposort()]):
print('Used the cpu')
elif any([x.op.__class__.__name__ in ['GpuGemm', 'GpuGemv'] for x in
train.maker.fgraph.toposort()]):
print('Used the gpu')
else:
print('ERROR, not able to tell if theano used the cpu or the gpu')
print(train.maker.fgraph.toposort())
for i in range(training_steps):
pred, err = train(D[0], D[1])
print("target values for D")
print(D[1])
print("prediction on D")
print(predict(D[0]))
Modify and execute this example to run on CPU (the default) with floatX=float32 and time the execution
using the command line time python file.py. Save your code as it will be useful later on.
Note:
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• Apply the Theano flag floatX=float32 (through theano.config.floatX) in your code.
• Cast inputs before storing them into a shared variable.
• Circumvent the automatic cast of int32 with float32 to float64:
– Insert manual cast in your code or use [u]int{8,16}.
– Insert manual cast around the mean operator (this involves division by length, which is an int64).
– Note that a new casting mechanism is being developed.
Solution
Mode
Every time theano.function is called, the symbolic relationships between the input and output Theano
variables are optimized and compiled. The way this compilation occurs is controlled by the value of the
mode parameter.
Theano defines the following modes by name:
• 'FAST_COMPILE': Apply just a few graph optimizations and only use Python implementations. So
GPU is disabled.
• 'FAST_RUN': Apply all optimizations and use C implementations where possible.
• 'DebugMode': Verify the correctness of all optimizations, and compare C and Python
implementations. This mode can take much longer than the other modes, but can identify
several kinds of problems.
• 'NanGuardMode': Same optimization as FAST_RUN, but check if a node generate nans.
The default mode is typically FAST_RUN, but it can be controlled via the configuration variable config.
mode, which can be overridden by passing the keyword argument to theano.function.
short
Full constructor
name
FAST_COMPILE
compile.mode.Mode(linker='py',
optimizer='fast_compile')
FAST_RUN compile.mode.Mode(linker='cvm',
optimizer='fast_run')
DebugModecompile.debugmode.DebugMode()
What does it do?
Python implementations only, quick and
cheap graph transformations
C implementations where available, all
available graph transformations.
Both implementations where available,
all available graph transformations.
Note: For debugging purpose, there also exists a MonitorMode (which has no short name). It can be
used to step through the execution of a function: see the debugging FAQ for details.
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Linkers
A mode is composed of 2 things: an optimizer and a linker. Some modes, like NanGuardMode and
DebugMode, add logic around the optimizer and linker. NanGuardMode and DebugMode use their own
linker.
You can select which linker to use with the Theano flag config.linker. Here is a table to compare the
different linkers.
Overhead
Definition
cvm
gc1 Raise error by
op
yes yes
“++”
cvm_nogc
c|py2
c|py_nogc
c
no
yes
no
no
yes
yes
yes
yes
“+”
“+++”
“++”
“+”
py
NanGuardMode
DebugMode
yes
no
yes
no
“+++”
“++++”
As c|py, but the runtime algo to execute the code
is in c
As cvm, but without gc
Try C code. If none exists for an op, use Python
As c|py, but without gc
Use only C code (if none available for an op,
raise an error)
Use only Python code
Check if nodes generate NaN
no
yes
VERY
HIGH
linker
Make many checks on what Theano computes
For more detail, see Mode in the library.
Using DebugMode
While normally you should use the FAST_RUN or FAST_COMPILE mode, it is useful at first (especially
when you are defining new kinds of expressions or new optimizations) to run your code using the DebugMode (available via mode='DebugMode). The DebugMode is designed to run several self-checks
and assertions that can help diagnose possible programming errors leading to incorrect output. Note that
DebugMode is much slower than FAST_RUN or FAST_COMPILE so use it only during development (not
when you launch 1000 processes on a cluster!).
DebugMode is used as follows:
x = T.dvector('x')
f = theano.function([x], 10 * x, mode='DebugMode')
f([5])
f([0])
f([7])
1
Garbage collection of intermediate results during computation. Otherwise, their memory space used by the ops is kept between
Theano function calls, in order not to reallocate memory, and lower the overhead (make it faster...).
2
Default
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If any problem is detected, DebugMode will raise an exception according to what went wrong, either at
call time (f(5)) or compile time ( f = theano.function(x, 10 * x, mode='DebugMode')).
These exceptions should not be ignored; talk to your local Theano guru or email the users list if you cannot
make the exception go away.
Some kinds of errors can only be detected for certain input value combinations. In the example above, there
is no way to guarantee that a future call to, say f(-1), won’t cause a problem. DebugMode is not a silver
bullet.
If you instantiate DebugMode using the constructor (see DebugMode) rather than the keyword
DebugMode you can configure its behaviour via constructor arguments. The keyword version of DebugMode (which you get by using mode='DebugMode') is quite strict.
For more detail, see DebugMode in the library.
ProfileMode
Note: ProfileMode is deprecated. Use config.profile instead.
Printing/Drawing Theano graphs
Theano provides the functions theano.printing.pprint() and theano.printing.
debugprint() to print a graph to the terminal before or after compilation. pprint() is more
compact and math-like, debugprint() is more verbose. Theano also provides pydotprint() that
creates an image of the function. You can read about them in printing – Graph Printing and Symbolic Print
Statement.
Note:
When printing Theano functions, they can sometimes be hard to read.
To
help with this, you can disable some Theano optimizations by using the Theano flag:
optimizer_excluding=fusion:inplace. Do not use this during real job execution, as this
will make the graph slower and use more memory.
Consider again the logistic regression example:
>>> import numpy
>>> import theano
>>> import theano.tensor as T
>>> rng = numpy.random
>>> # Training data
>>> N = 400
>>> feats = 784
>>> D = (rng.randn(N, feats).astype(theano.config.floatX), rng.randint(size=N,
˓→low=0, high=2).astype(theano.config.floatX))
>>> training_steps = 10000
>>> # Declare Theano symbolic variables
>>> x = T.matrix("x")
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>>> y = T.vector("y")
>>> w = theano.shared(rng.randn(feats).astype(theano.config.floatX), name="w")
>>> b = theano.shared(numpy.asarray(0., dtype=theano.config.floatX), name="b")
>>> x.tag.test_value = D[0]
>>> y.tag.test_value = D[1]
>>> # Construct Theano expression graph
>>> p_1 = 1 / (1 + T.exp(-T.dot(x, w)-b)) # Probability of having a one
>>> prediction = p_1 > 0.5 # The prediction that is done: 0 or 1
>>> # Compute gradients
>>> xent = -y*T.log(p_1) - (1-y)*T.log(1-p_1) # Cross-entropy
>>> cost = xent.mean() + 0.01*(w**2).sum() # The cost to optimize
>>> gw,gb = T.grad(cost, [w,b])
>>> # Training and prediction function
>>> train = theano.function(inputs=[x,y], outputs=[prediction, xent],
˓→updates=[[w, w-0.01*gw], [b, b-0.01*gb]], name = "train")
>>> predict = theano.function(inputs=[x], outputs=prediction, name = "predict
˓→")
Pretty Printing
>>> theano.printing.pprint(prediction)
'gt((TensorConstant{1} / (TensorConstant{1} + exp(((-(x \\dot w)) - b)))),
TensorConstant{0.5})'
Debug Print
The pre-compilation graph:
>>> theano.printing.debugprint(prediction)
Elemwise{gt,no_inplace} [id A] ''
|Elemwise{true_div,no_inplace} [id B] ''
| |DimShuffle{x} [id C] ''
| | |TensorConstant{1} [id D]
| |Elemwise{add,no_inplace} [id E] ''
|
|DimShuffle{x} [id F] ''
|
| |TensorConstant{1} [id D]
|
|Elemwise{exp,no_inplace} [id G] ''
|
|Elemwise{sub,no_inplace} [id H] ''
|
|Elemwise{neg,no_inplace} [id I] ''
|
| |dot [id J] ''
|
|
|x [id K]
|
|
|w [id L]
|
|DimShuffle{x} [id M] ''
|
|b [id N]
|DimShuffle{x} [id O] ''
|TensorConstant{0.5} [id P]
The post-compilation graph:
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>>> theano.printing.debugprint(predict)
Elemwise{Composite{GT(scalar_sigmoid((-((-i0) - i1))), i2)}} [id A] ''
|...Gemv{inplace} [id B] ''
3
| |AllocEmpty{dtype='float64'} [id C] ''
2
| | |Shape_i{0} [id D] ''
1
| |
|x [id E]
| |TensorConstant{1.0} [id F]
| |x [id E]
| |w [id G]
| |TensorConstant{0.0} [id H]
|InplaceDimShuffle{x} [id I] ''
0
| |b [id J]
|TensorConstant{(1,) of 0.5} [id K]
4
Picture Printing of Graphs
The pre-compilation graph:
>>> theano.printing.pydotprint(prediction, outfile="pics/logreg_pydotprint_
˓→prediction.png", var_with_name_simple=True)
The output file is available at pics/logreg_pydotprint_prediction.png
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The post-compilation graph:
>>> theano.printing.pydotprint(predict, outfile="pics/logreg_pydotprint_
˓→predict.png", var_with_name_simple=True)
The output file is available at pics/logreg_pydotprint_predict.png
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The optimized training graph:
>>> theano.printing.pydotprint(train, outfile="pics/logreg_pydotprint_train.
˓→png", var_with_name_simple=True)
The output file is available at pics/logreg_pydotprint_train.png
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Interactive Graph Visualization
The new d3viz module complements theano.printing.pydotprint() to visualize complex
graph structures. Instead of creating a static image, it generates an HTML file, which allows to dynamically inspect graph structures in a web browser. Features include zooming, drag-and-drop, editing node
labels, or coloring nodes by their compute time.
=> d3viz <=
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Debugging Theano: FAQ and Troubleshooting
There are many kinds of bugs that might come up in a computer program. This page is structured as a
FAQ. It provides recipes to tackle common problems, and introduces some of the tools that we use to find
problems in our own Theano code, and even (it happens) in Theano’s internals, in Using DebugMode.
Isolating the Problem/Testing Theano Compiler
You can run your Theano function in a DebugMode. This tests the Theano optimizations and helps to find
where NaN, inf and other problems come from.
Interpreting Error Messages
Even in its default configuration, Theano tries to display useful error messages. Consider the following
faulty code.
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import numpy as np
import theano
import theano.tensor as T
x = T.vector()
y = T.vector()
z = x + x
z = z + y
f = theano.function([x, y], z)
f(np.ones((2,)), np.ones((3,)))
Running the code above we see:
Traceback (most recent call last):
...
ValueError: Input dimension mis-match. (input[0].shape[0] = 3, input[1].
˓→shape[0] = 2)
Apply node that caused the error: Elemwise{add,no_inplace}(
˓→<TensorType(float64, vector)>, <TensorType(float64, vector)>,
˓→<TensorType(float64, vector)>)
Inputs types: [TensorType(float64, vector), TensorType(float64, vector),
˓→TensorType(float64, vector)]
Inputs shapes: [(3,), (2,), (2,)]
Inputs strides: [(8,), (8,), (8,)]
Inputs scalar values: ['not scalar', 'not scalar', 'not scalar']
HINT: Re-running with most Theano optimization disabled could give you a back˓→traces when this node was created. This can be done with by setting the
˓→Theano flags 'optimizer=fast_compile'. If that does not work, Theano
˓→optimization can be disabled with 'optimizer=None'.
HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint of this
˓→apply node.
Arguably the most useful information is approximately half-way through the error message, where the kind
of error is displayed along with its cause (ValueError: Input dimension mis-match. (input[0].shape[0] = 3,
input[1].shape[0] = 2). Below it, some other information is given, such as the apply node that caused the
error, as well as the input types, shapes, strides and scalar values.
The two hints can also be helpful when debugging. Using the theano flag optimizer=fast_compile
or optimizer=None can often tell you the faulty line, while exception_verbosity=high will
display a debugprint of the apply node. Using these hints, the end of the error message becomes :
Backtrace when the node is created:
File "test0.py", line 8, in <module>
z = z + y
Debugprint of the apply node:
Elemwise{add,no_inplace} [id A] <TensorType(float64, vector)> ''
|Elemwise{add,no_inplace} [id B] <TensorType(float64, vector)> ''
| |<TensorType(float64, vector)> [id C] <TensorType(float64, vector)>
| |<TensorType(float64, vector)> [id C] <TensorType(float64, vector)>
|<TensorType(float64, vector)> [id D] <TensorType(float64, vector)>
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We can here see that the error can be traced back to the line z = z + y. For this example, using
optimizer=fast_compile worked. If it did not, you could set optimizer=None or use test values.
Using Test Values
As of v.0.4.0, Theano has a new mechanism by which graphs are executed on-the-fly, before a theano.
function is ever compiled. Since optimizations haven’t been applied at this stage, it is easier for the
user to locate the source of some bug. This functionality is enabled through the config flag theano.
config.compute_test_value. Its use is best shown through the following example. Here, we use
exception_verbosity=high and optimizer=fast_compile, which would not tell you the line
at fault. optimizer=None would and it could therefore be used instead of test values.
import numpy
import theano
import theano.tensor as T
# compute_test_value is 'off' by default, meaning this feature is inactive
theano.config.compute_test_value = 'off' # Use 'warn' to activate this feature
# configure shared variables
W1val = numpy.random.rand(2, 10, 10).astype(theano.config.floatX)
W1 = theano.shared(W1val, 'W1')
W2val = numpy.random.rand(15, 20).astype(theano.config.floatX)
W2 = theano.shared(W2val, 'W2')
# input which will be of shape (5,10)
x = T.matrix('x')
# provide Theano with a default test-value
#x.tag.test_value = numpy.random.rand(5, 10)
# transform the shared variable in some way. Theano does not
# know off hand that the matrix func_of_W1 has shape (20, 10)
func_of_W1 = W1.dimshuffle(2, 0, 1).flatten(2).T
# source of error: dot product of 5x10 with 20x10
h1 = T.dot(x, func_of_W1)
# do more stuff
h2 = T.dot(h1, W2.T)
# compile and call the actual function
f = theano.function([x], h2)
f(numpy.random.rand(5, 10))
Running the above code generates the following error message:
Traceback (most recent call last):
File "test1.py", line 31, in <module>
f(numpy.random.rand(5, 10))
File "PATH_TO_THEANO/theano/compile/function_module.py", line 605, in __
˓→call__
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self.fn.thunks[self.fn.position_of_error])
File "PATH_TO_THEANO/theano/compile/function_module.py", line 595, in __
˓→call__
outputs = self.fn()
ValueError: Shape mismatch: x has 10 cols (and 5 rows) but y has 20 rows (and
˓→10 cols)
Apply node that caused the error: Dot22(x, DimShuffle{1,0}.0)
Inputs types: [TensorType(float64, matrix), TensorType(float64, matrix)]
Inputs shapes: [(5, 10), (20, 10)]
Inputs strides: [(80, 8), (8, 160)]
Inputs scalar values: ['not scalar', 'not scalar']
Debugprint of the apply node:
Dot22 [id A] <TensorType(float64, matrix)> ''
|x [id B] <TensorType(float64, matrix)>
|DimShuffle{1,0} [id C] <TensorType(float64, matrix)> ''
|Flatten{2} [id D] <TensorType(float64, matrix)> ''
|DimShuffle{2,0,1} [id E] <TensorType(float64, 3D)> ''
|W1 [id F] <TensorType(float64, 3D)>
HINT: Re-running with most Theano optimization disabled could give you a back˓→traces when this node was created. This can be done with by setting the
˓→Theano flags 'optimizer=fast_compile'. If that does not work, Theano
˓→optimization can be disabled with 'optimizer=None'.
If the above is not informative enough, by instrumenting the code ever so slightly, we can get Theano to
reveal the exact source of the error.
# enable on-the-fly graph computations
theano.config.compute_test_value = 'warn'
...
# input which will be of shape (5, 10)
x = T.matrix('x')
# provide Theano with a default test-value
x.tag.test_value = numpy.random.rand(5, 10)
In the above, we are tagging the symbolic matrix x with a special test value. This allows Theano to evaluate symbolic expressions on-the-fly (by calling the perform method of each op), as they are being defined. Sources of error can thus be identified with much more precision and much earlier in the compilation
pipeline. For example, running the above code yields the following error message, which properly identifies
line 24 as the culprit.
Traceback (most recent call last):
File "test2.py", line 24, in <module>
h1 = T.dot(x, func_of_W1)
File "PATH_TO_THEANO/theano/tensor/basic.py", line 4734, in dot
return _dot(a, b)
File "PATH_TO_THEANO/theano/gof/op.py", line 545, in __call__
required = thunk()
File "PATH_TO_THEANO/theano/gof/op.py", line 752, in rval
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r = p(n, [x[0] for x in i], o)
File "PATH_TO_THEANO/theano/tensor/basic.py", line 4554, in perform
z[0] = numpy.asarray(numpy.dot(x, y))
ValueError: matrices are not aligned
The compute_test_value mechanism works as follows:
• Theano constants and shared variables are used as is. No need to instrument them.
• A Theano variable (i.e. dmatrix, vector, etc.) should be given a special test value through the
attribute tag.test_value.
• Theano automatically instruments intermediate results. As such, any quantity derived from x will be
given a tag.test_value automatically.
compute_test_value can take the following values:
• off: Default behavior. This debugging mechanism is inactive.
• raise: Compute test values on the fly. Any variable for which a test value is required, but not
provided by the user, is treated as an error. An exception is raised accordingly.
• warn: Idem, but a warning is issued instead of an Exception.
• ignore: Silently ignore the computation of intermediate test values, if a variable is missing a test
value.
Note: This feature is currently incompatible with Scan and also with ops which do not implement a
perform method.
“How do I Print an Intermediate Value in a Function?”
Theano provides a ‘Print’ op to do this.
import numpy
import theano
x = theano.tensor.dvector('x')
x_printed = theano.printing.Print('this is a very important value')(x)
f = theano.function([x], x * 5)
f_with_print = theano.function([x], x_printed * 5)
#this runs the graph without any printing
assert numpy.all( f([1, 2, 3]) == [5, 10, 15])
#this runs the graph with the message, and value printed
assert numpy.all( f_with_print([1, 2, 3]) == [5, 10, 15])
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this is a very important value __str__ = [ 1.
2.
3.]
Since Theano runs your program in a topological order, you won’t have precise control over the order in
which multiple Print() ops are evaluted. For a more precise inspection of what’s being computed where,
when, and how, see the discussion “How do I Step through a Compiled Function?”.
Warning: Using this Print Theano Op can prevent some Theano optimization from being applied.
This can also happen with stability optimization. So if you use this Print and have nan, try to remove
them to know if this is the cause or not.
“How do I Print a Graph?” (before or after compilation)
Theano provides two functions (theano.pp() and theano.printing.debugprint()) to print a
graph to the terminal before or after compilation. These two functions print expression graphs in different
ways: pp() is more compact and math-like, debugprint() is more verbose. Theano also provides
theano.printing.pydotprint() that creates a png image of the function.
You can read about them in printing – Graph Printing and Symbolic Print Statement.
“The Function I Compiled is Too Slow, what’s up?”
First, make sure you’re running in FAST_RUN mode. Even though FAST_RUN is the default mode, insist by
passing mode='FAST_RUN' to theano.function (or theano.make) or by setting config.mode
to FAST_RUN.
Second, try the Theano ProfileMode. This will tell you which Apply nodes, and which ops are eating up
your CPU cycles.
Tips:
• Use the flags floatX=float32 to require type float32 instead of float64; Use the Theano constructors matrix(),vector(),... instead of dmatrix(), dvector(),... since they respectively involve the default
types float32 and float64.
• Check in the profile mode that there is no Dot op in the post-compilation graph while you are
multiplying two matrices of the same type. Dot should be optimized to dot22 when the inputs are
matrices and of the same type. This can still happen when using floatX=float32 when one of
the inputs of the graph is of type float64.
“Why does my GPU function seem to be slow?”
When you compile a theano function, if you do not get the speedup that you expect over the CPU performance of the same code. It is oftentimes due to the fact that some Ops might be running on CPU instead
GPU. If that is the case, you can use assert_no_cpu_op to check if there is a CPU Op on your computational
graph. assert_no_cpu_op can take the following one of the three options:
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• warn: Raise a warning
• pdb: Stop with a pdb in the computational graph during the compilation
• raise: Raise an error, if there is a CPU Op in the computational graph.
It is possible to use this mode by providing the flag in THEANO_FLAGS, such as:
THEANO_FLAGS="float32,device=gpu,assert_no_cpu_op='raise'" python test.
py
But note that this optimization will not catch all the CPU Ops, it might miss some Ops.
“How do I Step through a Compiled Function?”
You can use MonitorMode to inspect the inputs and outputs of each node being executed when the function is called. The code snipped below shows how to print all inputs and outputs:
from __future__ import print_function
import theano
def inspect_inputs(i, node, fn):
print(i, node, "input(s) value(s):", [input[0] for input in fn.inputs],
end='')
def inspect_outputs(i, node, fn):
print(" output(s) value(s):", [output[0] for output in fn.outputs])
x = theano.tensor.dscalar('x')
f = theano.function([x], [5 * x],
mode=theano.compile.MonitorMode(
pre_func=inspect_inputs,
post_func=inspect_outputs))
f(3)
0 Elemwise{mul,no_inplace}(TensorConstant{5.0}, x) input(s) value(s):
˓→[array(5.0), array(3.0)] output(s) value(s): [array(15.0)]
When using these inspect_inputs and inspect_outputs functions with MonitorMode, you
should see [potentially a lot of] printed output. Every Apply node will be printed out, along with its
position in the graph, the arguments to the functions perform or c_code and the output it computed.
Admittedly, this may be a huge amount of output to read through if you are using big tensors... but you can
choose to add logic that would, for instance, print something out only if a certain kind of op were used, at a
certain program position, or only if a particular value showed up in one of the inputs or outputs. A typical
example is to detect when NaN values are added into computations, which can be achieved as follows:
import numpy
import theano
# This is the current suggested detect_nan implementation to
# show you how it work. That way, you can modify it for your
# need. If you want exactly this method, you can use
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# ``theano.compile.monitormode.detect_nan`` that will always
# contain the current suggested version.
def detect_nan(i, node, fn):
for output in fn.outputs:
if (not isinstance(output[0], numpy.random.RandomState) and
numpy.isnan(output[0]).any()):
print('*** NaN detected ***')
theano.printing.debugprint(node)
print('Inputs : %s' % [input[0] for input in fn.inputs])
print('Outputs: %s' % [output[0] for output in fn.outputs])
break
x = theano.tensor.dscalar('x')
f = theano.function([x], [theano.tensor.log(x) * x],
mode=theano.compile.MonitorMode(
post_func=detect_nan))
f(0) # log(0) * 0 = -inf * 0 = NaN
*** NaN detected ***
Elemwise{Composite{(log(i0) * i0)}} [id A] ''
|x [id B]
Inputs : [array(0.0)]
Outputs: [array(nan)]
To help understand what is happening in your graph, you can disable the local_elemwise_fusion
and all inplace optimizations. The first is a speed optimization that merges elemwise operations together.
This makes it harder to know which particular elemwise causes the problem. The second optimization
makes some ops’ outputs overwrite their inputs. So, if an op creates a bad output, you will not be able to see
the input that was overwriten in the post_func function. To disable those optimizations (with a Theano
version after 0.6rc3), define the MonitorMode like this:
mode = theano.compile.MonitorMode(post_func=detect_nan).excluding(
'local_elemwise_fusion', 'inplace')
f = theano.function([x], [theano.tensor.log(x) * x],
mode=mode)
Note:
The Theano flags optimizer_including, optimizer_excluding and
optimizer_requiring aren’t used by the MonitorMode, they are used only by the default
mode. You can’t use the default mode with MonitorMode, as you need to define what you monitor.
To be sure all inputs of the node are available during the call to post_func, you must also disable the
garbage collector. Otherwise, the execution of the node can garbage collect its inputs that aren’t needed
anymore by the Theano function. This can be done with the Theano flag:
allow_gc=False
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How to Use pdb
In the majority of cases, you won’t be executing from the interactive shell but from a set of Python scripts.
In such cases, the use of the Python debugger can come in handy, especially as your models become more
complex. Intermediate results don’t necessarily have a clear name and you can get exceptions which are
hard to decipher, due to the “compiled” nature of the functions.
Consider this example script (“ex.py”):
import theano
import numpy
import theano.tensor as T
a = T.dmatrix('a')
b = T.dmatrix('b')
f = theano.function([a, b], [a * b])
# matrices chosen so dimensions are unsuitable for multiplication
mat1 = numpy.arange(12).reshape((3, 4))
mat2 = numpy.arange(25).reshape((5, 5))
f(mat1, mat2)
This is actually so simple the debugging could be done easily, but it’s for illustrative purposes. As the
matrices can’t be multiplied element-wise (unsuitable shapes), we get the following exception:
File "ex.py", line 14, in <module>
f(mat1, mat2)
File "/u/username/Theano/theano/compile/function_module.py", line 451, in __
˓→call__
File "/u/username/Theano/theano/gof/link.py", line 271, in streamline_default_
˓→f
File "/u/username/Theano/theano/gof/link.py", line 267, in streamline_default_
˓→f
File "/u/username/Theano/theano/gof/cc.py", line 1049, in execute ValueError:
˓→('Input dimension mis-match. (input[0].shape[0] = 3, input[1].shape[0] = 5)
˓→', Elemwise{mul,no_inplace}(a, b), Elemwise{mul,no_inplace}(a, b))
The call stack contains some useful information to trace back the source of the error. There’s the script
where the compiled function was called – but if you’re using (improperly parameterized) prebuilt modules,
the error might originate from ops in these modules, not this script. The last line tells us about the op that
caused the exception. In this case it’s a “mul” involving variables with names “a” and “b”. But suppose we
instead had an intermediate result to which we hadn’t given a name.
After learning a few things about the graph structure in Theano, we can use the Python debugger to explore
the graph, and then we can get runtime information about the error. Matrix dimensions, especially, are
useful to pinpoint the source of the error. In the printout, there are also 2 of the 4 dimensions of the matrices
involved, but for the sake of example say we’d need the other dimensions to pinpoint the error. First, we
re-launch with the debugger module and run the program with “c”:
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python -m pdb ex.py
> /u/username/experiments/doctmp1/ex.py(1)<module>()
-> import theano
(Pdb) c
Then we get back the above error printout, but the interpreter breaks in that state. Useful commands here
are
• “up” and “down” (to move up and down the call stack),
• “l” (to print code around the line in the current stack position),
• “p variable_name” (to print the string representation of ‘variable_name’),
• “p dir(object_name)”, using the Python dir() function to print the list of an object’s members
Here, for example, I do “up”, and a simple “l” shows me there’s a local variable “node”. This is the “node”
from the computation graph, so by following the “node.inputs”, “node.owner” and “node.outputs” links I
can explore around the graph.
That graph is purely symbolic (no data, just symbols to manipulate it abstractly). To get information about
the actual parameters, you explore the “thunk” objects, which bind the storage for the inputs (and outputs)
with the function itself (a “thunk” is a concept related to closures). Here, to get the current node’s first
input’s shape, you’d therefore do “p thunk.inputs[0][0].shape”, which prints out “(3, 4)”.
Dumping a Function to help debug
If you are reading this, there is high chance that you emailed our mailing list and we asked you to read this
section. This section explain how to dump all the parameter passed to theano.function(). This is
useful to help us reproduce a problem during compilation and it doesn’t request you to make a self contained
example.
For this to work, we need to be able to import the code for all Op in the graph. So if you create your own
Op, we will need this code. Otherwise, we won’t be able to unpickle it. We already have all the Ops from
Theano and Pylearn2.
# Replace this line:
theano.function(...)
# with
theano.function_dump(filename, ...)
# Where filename is a string to a file that we will write to.
Then send us filename.
class theano.tests.breakpoint.PdbBreakpoint(name)
This is an identity-like op with the side effect of enforcing a conditional breakpoint, inside a theano
function, based on a symbolic scalar condition.
Parameters name (String) – name of the conditional breakpoint. To be printed when
the breakpoint is activated.
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Note WARNING. At least one of the outputs of the op must be used otherwise the op will
be removed from the Theano graph due to its outputs being unused
Note
WARNING. Employing the function inside a theano graph can prevent Theano
from applying certain optimizations to improve performance, reduce memory
consumption and/or reduce numerical instability.
Detailed explanation: As of 2014-12-01 the PdbBreakpoint op is not known by any
optimization. Setting a PdbBreakpoint op in the middle of a pattern that is usually
optimized out will block the optimization.
Example:
import theano
import theano.tensor as T
from theano.tests.breakpoint import PdbBreakpoint
input = T.fvector()
target = T.fvector()
# Mean squared error between input and target
mse = (input - target) ** 2
# Conditional breakpoint to be activated if the total MSE is higher
# than 100. The breakpoint will monitor the inputs, targets as well
# as the individual error values
breakpointOp = PdbBreakpoint("MSE too high")
condition = T.gt(mse.sum(), 100)
mse, monitored_input, monitored_target = breakpointOp(condition, mse,
input, target)
# Compile the theano function
fct = theano.function([input, target], mse)
# Use the function
print fct([10, 0], [10, 5]) # Will NOT activate the breakpoint
print fct([0, 0], [10, 5]) # Will activate the breakpoint
Dealing with NaNs
Having a model yielding NaNs or Infs is quite common if some of the tiny components in your model are
not set properly. NaNs are hard to deal with because sometimes it is caused by a bug or error in the code,
sometimes it’s because of the numerical stability of your computational environment (library versions, etc.),
and even, sometimes it relates to your algorithm. Here we try to outline common issues which cause the
model to yield NaNs, as well as provide nails and hammers to diagnose it.
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Check Superparameters and Weight Initialization
Most frequently, the cause would be that some of the hyperparameters, especially learning rates, are set
incorrectly. A high learning rate can blow up your whole model into NaN outputs even within one epoch of
training. So the first and easiest solution is try to lower it. Keep halving your learning rate until you start to
get resonable output values.
Other hyperparameters may also play a role. For example, are your training algorithms involve regularization terms? If so, are their corresponding penalties set reasonably? Search a wider hyperparameter space
with a few (one or two) training epochs each to see if the NaNs could disappear.
Some models can be very sensitive to the initialization of weight vectors. If those weights are not initialized
in a proper range, then it is not surprising that the model ends up with yielding NaNs.
Run in NanGuardMode, DebugMode, or MonitorMode
If adjusting hyperparameters doesn’t work for you, you can still get help from Theano’s NanGuardMode.
Change the mode of your theano function to NanGuardMode and run them again. The NanGuardMode will
monitor all input/output variables in each node, and raises an error if NaNs are detected. For how to use the
NanGuardMode, please refer to nanguardmode.
DebugMode can also help. Run your code in DebugMode with flag mode=DebugMode,DebugMode.
check_py=False. This will give you clue about which op is causing this problem, and then you can
inspect that op in more detail. For details of using DebugMode, please refer to debugmode.
Theano’s MonitorMode provides another helping hand. It can be used to step through the execution of a
function. You can inspect the inputs and outputs of each node being executed when the function is called.
For how to use that, please check “How do I Step through a Compiled Function?”.
Numerical Stability
After you have located the op which causes the problem, it may turn out that the NaNs yielded by that op
are related to numerical issues. For example, 1/𝑙𝑜𝑔(𝑝(𝑥) + 1) may result in NaNs for those nodes who have
learned to yield a low probability p(x) for some input x.
Algorithm Related
In the most difficult situations, you may go through the above steps and find nothing wrong. If the above
methods fail to uncover the cause, there is a good chance that something is wrong with your algorithm. Go
back to the mathematics and find out if everything is derived correctly.
Cuda Specific Option
The Theano flag nvcc.fastmath=True can genarate NaN. Don’t set this flag while debugging NaN.
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Profiling Theano function
Note: This method replace the old ProfileMode. Do not use ProfileMode anymore.
Besides checking for errors, another important task is to profile your code in terms of speed and/or memory
usage.
You can profile your functions using either of the following two options:
1. Use Theano flag config.profile to enable profiling.
• To enable the memory profiler use the Theano flag: config.profile_memory in addition to config.profile.
• Moreover, to enable the profiling of Theano optimization phase, use the Theano flag:
config.profile_optimizer in addition to config.profile.
• You can also use the Theano flags profiling.n_apply, profiling.n_ops and
profiling.min_memory_size to modify the quantity of information printed.
2. Pass the argument profile=True to the function theano.function. And then call f.profile.print_
• Use this option when you want to profile not all the functions but one or more specific
function(s).
• You can also combine the profile of many functions:
The profiler will output one profile per Theano function and profile that is the sum of the printed profiles.
Each profile contains 4 sections: global info, class info, Ops info and Apply node info.
In the global section, the “Message” is the name of the Theano function. theano.function() has an optional
parameter name that defaults to None. Change it to something else to help you profile many Theano
functions. In that section, we also see the number of times the function was called (1) and the total time
spent in all those calls. The time spent in Function.fn.__call__ and in thunks is useful to understand Theano
overhead.
Also, we see the time spent in the two parts of the compilation process: optimization (modify the graph
to make it more stable/faster) and the linking (compile c code and make the Python callable returned by
function).
The class, Ops and Apply nodes sections are the same information: information about the Apply node that
ran. The Ops section takes the information from the Apply section and merge the Apply nodes that have
exactly the same op. If two Apply nodes in the graph have two Ops that compare equal, they will be merged.
Some Ops like Elemwise, will not compare equal, if their parameters differ (the scalar being executed). So
the class section will merge more Apply nodes then the Ops section.
Note that the profile also shows which Ops were running a c implementation.
Developers wishing to optimize the performance of their graph should focus on the worst offending Ops and
Apply nodes – either by optimizing an implementation, providing a missing C implementation, or by writing
a graph optimization that eliminates the offending Op altogether. You should strongly consider emailing one
of our lists about your issue before spending too much time on this.
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Here is an example output when we disable some Theano optimizations to give you a better idea of the
difference between sections. With all optimizations enabled, there would be only one op left in the graph.
Note: To profile the peak memory usage on the GPU you need to do:
* In the file theano/sandbox/cuda/cuda_ndarray.cu, set the macro
COMPUTE_GPU_MEM_USED to 1.
* Then call theano.sandbox.cuda.theano_allocated()
It return a tuple with two ints. The first is the current GPU
memory allocated by Theano. The second is the peak GPU memory
that was allocated by Theano.
Do not always enable this, as this slows down memory allocation and free. As this slows down the computation, this will affect speed profiling. So don’t use both at the same time.
to run the example:
THEANO_FLAGS=optimizer_excluding=fusion:inplace,profile=True
doc/tutorial/profiling_example.py
python
The output:
Function profiling
==================
Message: None
Time in 1 calls to Function.__call__: 5.698204e-05s
Time in Function.fn.__call__: 1.192093e-05s (20.921%)
Time in thunks: 6.198883e-06s (10.879%)
Total compile time: 3.642474e+00s
Theano Optimizer time: 7.326508e-02s
Theano validate time: 3.712177e-04s
Theano Linker time (includes C, CUDA code generation/compiling): 9.
˓→584920e-01s
Class
--<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Class
˓→name>
100.0%
100.0%
0.000s
2.07e-06s
C
3
3
˓→<class 'theano.tensor.elemwise.Elemwise'>
... (remaining 0 Classes account for
0.00%(0.00s) of the runtime)
Ops
--<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Op
˓→name>
65.4%
65.4%
0.000s
2.03e-06s
C
2
2
˓→Elemwise{add,no_inplace}
34.6%
100.0%
0.000s
2.15e-06s
C
1
1
˓→Elemwise{mul,no_inplace}
... (remaining 0 Ops account for
0.00%(0.00s) of the runtime)
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Apply
-----<% time> <sum %> <apply time> <time per call> <#call> <id> <Apply name>
50.0%
50.0%
0.000s
3.10e-06s
1
0
Elemwise{add,no_
˓→inplace}(x, y)
34.6%
84.6%
0.000s
2.15e-06s
1
2
Elemwise{mul,no_
˓→inplace}(TensorConstant{(1,) of 2.0}, Elemwise{add,no_inplace}.0)
15.4%
100.0%
0.000s
9.54e-07s
1
1
Elemwise{add,no_
˓→inplace}(Elemwise{add,no_inplace}.0, z)
... (remaining 0 Apply instances account for 0.00%(0.00s) of the runtime)
Further readings
Graph Structures
Debugging or profiling code written in Theano is not that simple if you do not know what goes on under the
hood. This chapter is meant to introduce you to a required minimum of the inner workings of Theano.
The first step in writing Theano code is to write down all mathematical relations using symbolic placeholders
(variables). When writing down these expressions you use operations like +, -, **, sum(), tanh(). All
these are represented internally as ops. An op represents a certain computation on some type of inputs
producing some type of output. You can see it as a function definition in most programming languages.
Theano represents symbolic mathematical computations as graphs. These graphs are composed of interconnected Apply, Variable and Op nodes. Apply node represents the application of an op to some variables. It is
important to draw the difference between the definition of a computation represented by an op and its application to some actual data which is represented by the apply node. Furthermore, data types are represented
by Type instances. Here is a piece of code and a diagram showing the structure built by that piece of code.
This should help you understand how these pieces fit together:
Code
import theano.tensor as T
x = T.dmatrix('x')
y = T.dmatrix('y')
z = x + y
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Diagram
Arrows represent references to the Python objects pointed at. The blue box is an Apply node. Red boxes are
Variable nodes. Green circles are Ops. Purple boxes are Types.
When we create Variables and then Apply Ops to them to make more Variables, we build a bi-partite,
directed, acyclic graph. Variables point to the Apply nodes representing the function application producing
them via their owner field. These Apply nodes point in turn to their input and output Variables via their
inputs and outputs fields. (Apply instances also contain a list of references to their outputs, but
those pointers don’t count in this graph.)
The owner field of both x and y point to None because they are not the result of another computation. If
one of them was the result of another computation, it’s owner field would point to another blue box like z
does, and so on.
Note that the Apply instance’s outputs points to z, and z.owner points back to the Apply instance.
Traversing the graph
The graph can be traversed starting from outputs (the result of some computation) down to its inputs using
the owner field. Take for example the following code:
>>> import theano
>>> x = theano.tensor.dmatrix('x')
>>> y = x * 2.
If you enter type(y.owner) you get <class 'theano.gof.graph.Apply'>, which is the apply
node that connects the op and the inputs to get this output. You can now print the name of the op that is
applied to get y:
>>> y.owner.op.name
'Elemwise{mul,no_inplace}'
Hence, an elementwise multiplication is used to compute y. This multiplication is done between the inputs:
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>>> len(y.owner.inputs)
2
>>> y.owner.inputs[0]
x
>>> y.owner.inputs[1]
DimShuffle{x,x}.0
Note that the second input is not 2 as we would have expected. This is because 2 was first broadcasted to a
matrix of same shape as x. This is done by using the op DimShuffle :
>>> type(y.owner.inputs[1])
<class 'theano.tensor.var.TensorVariable'>
>>> type(y.owner.inputs[1].owner)
<class 'theano.gof.graph.Apply'>
>>> y.owner.inputs[1].owner.op
<theano.tensor.elemwise.DimShuffle object at 0x106fcaf10>
>>> y.owner.inputs[1].owner.inputs
[TensorConstant{2.0}]
Starting from this graph structure it is easier to understand how automatic differentiation proceeds and how
the symbolic relations can be optimized for performance or stability.
Graph Structures
The following section outlines each type of structure that may be used in a Theano-built computation graph.
The following structures are explained: Apply, Constant, Op, Variable and Type.
Apply
An Apply node is a type of internal node used to represent a computation graph in Theano. Unlike Variable
nodes, Apply nodes are usually not manipulated directly by the end user. They may be accessed via a
Variable’s owner field.
An Apply node is typically an instance of the Apply class. It represents the application of an Op on one
or more inputs, where each input is a Variable. By convention, each Op is responsible for knowing how to
build an Apply node from a list of inputs. Therefore, an Apply node may be obtained from an Op and a list
of inputs by calling Op.make_node(*inputs).
Comparing with the Python language, an Apply node is Theano’s version of a function call whereas an Op
is Theano’s version of a function definition.
An Apply instance has three important fields:
op An Op that determines the function/transformation being applied here.
inputs A list of Variables that represent the arguments of the function.
outputs A list of Variables that represent the return values of the function.
An Apply instance can be created by calling gof.Apply(op, inputs, outputs).
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Op
An Op in Theano defines a certain computation on some types of inputs, producing some types of outputs.
It is equivalent to a function definition in most programming languages. From a list of input Variables and
an Op, you can build an Apply node representing the application of the Op to the inputs.
It is important to understand the distinction between an Op (the definition of a function) and an Apply node
(the application of a function). If you were to interpret the Python language using Theano’s structures, code
going like def f(x): ... would produce an Op for f whereas code like a = f(x) or g(f(4),
5) would produce an Apply node involving the f Op.
Type
A Type in Theano represents a set of constraints on potential data objects. These constraints allow Theano
to tailor C code to handle them and to statically optimize the computation graph. For instance, the irow type
in the theano.tensor package gives the following constraints on the data the Variables of type irow
may contain:
1. Must be an instance of numpy.ndarray: isinstance(x, numpy.ndarray)
2. Must be an array of 32-bit integers: str(x.dtype) == 'int32'
3. Must have a shape of 1xN: len(x.shape) == 2 and x.shape[0] == 1
Knowing these restrictions, Theano may generate C code for addition, etc. that declares the right data types
and that contains the right number of loops over the dimensions.
Note that a Theano Type is not equivalent to a Python type or class. Indeed, in Theano, irow and dmatrix
both use numpy.ndarray as the underlying type for doing computations and storing data, yet they are
different Theano Types. Indeed, the constraints set by dmatrix are:
1. Must be an instance of numpy.ndarray: isinstance(x, numpy.ndarray)
2. Must be an array of 64-bit floating point numbers: str(x.dtype) == 'float64'
3. Must have a shape of MxN, no restriction on M or N: len(x.shape) == 2
These restrictions are different from those of irow which are listed above.
There are cases in which a Type can fully correspond to a Python type, such as the double Type we will
define here, which corresponds to Python’s float. But, it’s good to know that this is not necessarily the
case. Unless specified otherwise, when we say “Type” we mean a Theano Type.
Variable
A Variable is the main data structure you work with when using Theano. The symbolic inputs that you
operate on are Variables and what you get from applying various Ops to these inputs are also Variables. For
example, when I type
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>>> import theano
>>> x = theano.tensor.ivector()
>>> y = -x
x and y are both Variables, i.e. instances of the Variable class. The Type of both x and y is theano.
tensor.ivector.
Unlike x, y is a Variable produced by a computation (in this case, it is the negation of x). y is the Variable
corresponding to the output of the computation, while x is the Variable corresponding to its input. The
computation itself is represented by another type of node, an Apply node, and may be accessed through
y.owner.
More specifically, a Variable is a basic structure in Theano that represents a datum at a certain point in
computation. It is typically an instance of the class Variable or one of its subclasses.
A Variable r contains four important fields:
type a Type defining the kind of value this Variable can hold in computation.
owner this is either None or an Apply node of which the Variable is an output.
index the integer such that owner.outputs[index] is r (ignored if owner is None)
name a string to use in pretty-printing and debugging.
Variable has one special subclass: Constant.
Constant
A Constant is a Variable with one extra field, data (only settable once). When used in a computation graph
as the input of an Op application, it is assumed that said input will always take the value contained in the
constant’s data field. Furthermore, it is assumed that the Op will not under any circumstances modify the
input. This means that a constant is eligible to participate in numerous optimizations: constant inlining in C
code, constant folding, etc.
A constant does not need to be specified in a function‘s list of inputs. In fact, doing so will raise an
exception.
Graph Structures Extension
When we start the compilation of a Theano function, we compute some extra information. This section
describes a portion of the information that is made available. Not everything is described, so email theanodev if you need something that is missing.
The graph gets cloned at the start of compilation, so modifications done during compilation won’t affect the
user graph.
Each variable receives a new field called clients. It is a list with references to every place in the graph
where this variable is used. If its length is 0, it means the variable isn’t used. Each place where it is used is
described by a tuple of 2 elements. There are two types of pairs:
• The first element is an Apply node.
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• The first element is the string “output”. It means the function outputs this variable.
In both types of pairs, the second element of the tuple is an index, such that: var.clients[*][0].
inputs[index] or fgraph.outputs[index] is that variable.
>>> import theano
>>> v = theano.tensor.vector()
>>> f = theano.function([v], (v+1).sum())
>>> theano.printing.debugprint(f)
Sum{acc_dtype=float64} [id A] ''
1
|Elemwise{add,no_inplace} [id B] ''
0
|TensorConstant{(1,) of 1.0} [id C]
|<TensorType(float64, vector)> [id D]
>>> # Sorted list of all nodes in the compiled graph.
>>> topo = f.maker.fgraph.toposort()
>>> topo[0].outputs[0].clients
[(Sum{acc_dtype=float64}(Elemwise{add,no_inplace}.0), 0)]
>>> topo[1].outputs[0].clients
[('output', 0)]
>>> # An internal variable
>>> var = topo[0].outputs[0]
>>> client = var.clients[0]
>>> client
(Sum{acc_dtype=float64}(Elemwise{add,no_inplace}.0), 0)
>>> type(client[0])
<class 'theano.gof.graph.Apply'>
>>> assert client[0].inputs[client[1]] is var
>>> # An output of the graph
>>> var = topo[1].outputs[0]
>>> client = var.clients[0]
>>> client
('output', 0)
>>> assert f.maker.fgraph.outputs[client[1]] is var
Automatic Differentiation
Having the graph structure, computing automatic differentiation is simple. The only thing tensor.
grad() has to do is to traverse the graph from the outputs back towards the inputs through all apply
nodes (apply nodes are those that define which computations the graph does). For each such apply node,
its op defines how to compute the gradient of the node’s outputs with respect to its inputs. Note that if an
op does not provide this information, it is assumed that the gradient is not defined. Using the chain rule
these gradients can be composed in order to obtain the expression of the gradient of the graph’s output with
respect to the graph’s inputs.
A following section of this tutorial will examine the topic of differentiation in greater detail.
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Optimizations
When compiling a Theano function, what you give to the theano.function is actually a graph (starting
from the output variables you can traverse the graph up to the input variables). While this graph structure
shows how to compute the output from the input, it also offers the possibility to improve the way this
computation is carried out. The way optimizations work in Theano is by identifying and replacing certain
patterns in the graph with other specialized patterns that produce the same results but are either faster or
more stable. Optimizations can also detect identical subgraphs and ensure that the same values are not
computed twice or reformulate parts of the graph to a GPU specific version.
For example, one (simple) optimization that Theano uses is to replace the pattern
𝑥𝑦
𝑦
by x.
Further information regarding the optimization process and the specific optimizations that are applicable is
respectively available in the library and on the entrance page of the documentation.
Example
Symbolic programming involves a change of paradigm: it will become clearer as we apply it. Consider the
following example of optimization:
>>> import theano
>>> a = theano.tensor.vector("a")
# declare symbolic variable
>>> b = a + a ** 10
# build symbolic expression
>>> f = theano.function([a], b)
# compile function
>>> print(f([0, 1, 2]))
# prints `array([0,2,1026])`
[
0.
2. 1026.]
>>> theano.printing.pydotprint(b, outfile="./pics/symbolic_graph_unopt.png",
˓→var_with_name_simple=True)
The output file is available at ./pics/symbolic_graph_unopt.png
>>> theano.printing.pydotprint(f, outfile="./pics/symbolic_graph_opt.png",
˓→var_with_name_simple=True)
The output file is available at ./pics/symbolic_graph_opt.png
We used theano.printing.pydotprint() to visualize the optimized graph (right), which is much
more compact than the unoptimized graph (left).
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Unoptimized graph
Optimized graph
Loading and Saving
Python’s standard way of saving class instances and reloading them is the pickle mechanism. Many Theano
objects can be serialized (and deserialized) by pickle, however, a limitation of pickle is that it does not
save the code or data of a class along with the instance of the class being serialized. As a result, reloading
objects created by a previous version of a class can be really problematic.
Thus, you will want to consider different mechanisms depending on the amount of time you anticipate
between saving and reloading. For short-term (such as temp files and network transfers), pickling of the
Theano objects or classes is possible. For longer-term (such as saving models from an experiment) you
should not rely on pickled Theano objects; we recommend loading and saving the underlying shared objects
as you would in the course of any other Python program.
The Basics of Pickling
The two modules pickle and cPickle have the same functionalities, but cPickle, coded in C, is much
faster.
>>> from six.moves import cPickle
You can serialize (or save, or pickle) objects to a file with cPickle.dump:
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>>> f = open('obj.save', 'wb')
>>> cPickle.dump(my_obj, f, protocol=cPickle.HIGHEST_PROTOCOL)
>>> f.close()
Note:
If you want your saved object to be stored efficiently, don’t forget to use cPickle.
HIGHEST_PROTOCOL. The resulting file can be dozens of times smaller than with the default protocol.
Note: Opening your file in binary mode ('b') is required for portability (especially between Unix and
Windows).
To de-serialize (or load, or unpickle) a pickled file, use cPickle.load:
>>> f = open('obj.save', 'rb')
>>> loaded_obj = cPickle.load(f)
>>> f.close()
You can pickle several objects into the same file, and load them all (in the same order):
>>> f = open('objects.save', 'wb')
>>> for obj in [obj1, obj2, obj3]:
...
cPickle.dump(obj, f, protocol=cPickle.HIGHEST_PROTOCOL)
>>> f.close()
Then:
>>>
>>>
>>>
...
>>>
f = open('objects.save', 'rb')
loaded_objects = []
for i in range(3):
loaded_objects.append(cPickle.load(f))
f.close()
For more details about pickle’s usage, see Python documentation.
Short-Term Serialization
If you are confident that the class instance you are serializing will be deserialized by a compatible version
of the code, pickling the whole model is an adequate solution. It would be the case, for instance, if you are
saving models and reloading them during the same execution of your program, or if the class you’re saving
has been really stable for a while.
You can control what pickle will save from your object, by defining a __getstate__ method, and similarly
__setstate__.
This will be especially useful if, for instance, your model class contains a link to the data set currently in
use, that you probably don’t want to pickle along every instance of your model.
For instance, you can define functions along the lines of:
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def __getstate__(self):
state = dict(self.__dict__)
del state['training_set']
return state
def __setstate__(self, d):
self.__dict__.update(d)
self.training_set = cPickle.load(open(self.training_set_file, 'rb'))
Robust Serialization
This type of serialization uses some helper functions particular to Theano. It serializes the object using
Python’s pickling protocol, but any ndarray or CudaNdarray objects contained within the object are
saved separately as NPY files. These NPY files and the Pickled file are all saved together in single ZIP-file.
The main advantage of this approach is that you don’t even need Theano installed in order to look at the
values of shared variables that you pickled. You can just load the parameters manually with numpy.
import numpy
numpy.load('model.zip')
This approach could be beneficial if you are sharing your model with people who might not have Theano
installed, who are using a different Python version, or if you are planning to save your model for a long time
(in which case version mismatches might make it difficult to unpickle objects).
See theano.misc.pkl_utils.dump() and theano.misc.pkl_utils.load().
Long-Term Serialization
If the implementation of the class you want to save is quite unstable, for instance if functions are created or
removed, class members are renamed, you should save and load only the immutable (and necessary) part of
your class.
You can do that by defining __getstate__ and __setstate__ functions as above, maybe defining the attributes
you want to save, rather than the ones you don’t.
For instance, if the only parameters you want to save are a weight matrix W and a bias b, you can define:
def __getstate__(self):
return (self.W, self.b)
def __setstate__(self, state):
W, b = state
self.W = W
self.b = b
If at some point in time W is renamed to weights and b to bias, the older pickled files will still be usable, if
you update these functions to reflect the change in name:
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def __getstate__(self):
return (self.weights, self.bias)
def __setstate__(self, state):
W, b = state
self.weights = W
self.bias = b
For more information on advanced use of pickle and its internals, see Python’s pickle documentation.
PyCUDA/CUDAMat/Gnumpy compatibility
PyCUDA
Currently, PyCUDA and Theano have different objects to store GPU data. The two implementations do not
support the same set of features. Theano’s implementation is called CudaNdarray and supports strides. It
also only supports the float32 dtype. PyCUDA’s implementation is called GPUArray and doesn’t support
strides. However, it can deal with all NumPy and CUDA dtypes.
We are currently working on having the same base object for both that will also mimic Numpy. Until this is
ready, here is some information on how to use both objects in the same script.
Transfer
You can use the theano.misc.pycuda_utils module to convert GPUArray to and from CudaNdarray. The functions to_cudandarray(x, copyif=False) and to_gpuarray(x) return a new object that occupies the same memory space as the original. Otherwise it raises a ValueError. Because GPUArrays don’t support strides, if the CudaNdarray is strided, we could copy it to have a non-strided copy. The
resulting GPUArray won’t share the same memory region. If you want this behavior, set copyif=True in
to_gpuarray.
Compiling with PyCUDA
You can use PyCUDA to compile CUDA functions that work directly on CudaNdarrays. Here is an example
from the file theano/misc/tests/test_pycuda_theano_simple.py:
import
import
import
import
import
import
import
import
sys
numpy
theano
theano.sandbox.cuda as cuda_ndarray
theano.misc.pycuda_init
pycuda
pycuda.driver as drv
pycuda.gpuarray
def test_pycuda_theano():
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"""Simple example with pycuda function and Theano CudaNdarray object."""
from pycuda.compiler import SourceModule
mod = SourceModule("""
__global__ void multiply_them(float *dest, float *a, float *b)
{
const int i = threadIdx.x;
dest[i] = a[i] * b[i];
}
""")
multiply_them = mod.get_function("multiply_them")
a = numpy.random.randn(100).astype(numpy.float32)
b = numpy.random.randn(100).astype(numpy.float32)
# Test with Theano object
ga = cuda_ndarray.CudaNdarray(a)
gb = cuda_ndarray.CudaNdarray(b)
dest = cuda_ndarray.CudaNdarray.zeros(a.shape)
multiply_them(dest, ga, gb,
block=(400, 1, 1), grid=(1, 1))
assert (numpy.asarray(dest) == a * b).all()
Theano Op using a PyCUDA function
You can use a GPU function compiled with PyCUDA in a Theano op:
import numpy, theano
import theano.misc.pycuda_init
from pycuda.compiler import SourceModule
import theano.sandbox.cuda as cuda
class PyCUDADoubleOp(theano.Op):
__props__ = ()
def make_node(self, inp):
inp = cuda.basic_ops.gpu_contiguous(
cuda.basic_ops.as_cuda_ndarray_variable(inp))
assert inp.dtype == "float32"
return theano.Apply(self, [inp], [inp.type()])
def make_thunk(self, node, storage_map, _, _2):
mod = SourceModule("""
__global__ void my_fct(float * i0, float * o0, int size) {
int i = blockIdx.x * blockDim.x + threadIdx.x;
if(i<size){
o0[i] = i0[i] * 2;
}
}""")
pycuda_fct = mod.get_function("my_fct")
inputs = [ storage_map[v] for v in node.inputs]
outputs = [ storage_map[v] for v in node.outputs]
def thunk():
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z = outputs[0]
if z[0] is None or z[0].shape!=inputs[0][0].shape:
z[0] = cuda.CudaNdarray.zeros(inputs[0][0].shape)
grid = (int(numpy.ceil(inputs[0][0].size / 512.)),1)
pycuda_fct(inputs[0][0], z[0], numpy.intc(inputs[0][0].size),
block=(512, 1, 1), grid=grid)
thunk.lazy = False
return thunk
CUDAMat
There are functions for conversion between CUDAMat objects and Theano’s CudaNdArray objects.
They obey the same principles as Theano’s PyCUDA functions and can be found in theano.misc.
cudamat_utils.py.
WARNING: There is a peculiar problem associated with stride/shape with those converters. In order to
work, the test needs a transpose and reshape...
Gnumpy
There are conversion functions between Gnumpy garray objects and Theano CudaNdArray objects. They
are also similar to Theano’s PyCUDA functions and can be found in theano.misc.gnumpy_utils.
py.
Understanding Memory Aliasing for Speed and Correctness
The aggressive reuse of memory is one of the ways through which Theano makes code fast, and it is important for the correctness and speed of your program that you understand how Theano might alias buffers.
This section describes the principles based on which Theano handles memory, and explains when you might
want to alter the default behaviour of some functions and methods for faster performance.
The Memory Model: Two Spaces
There are some simple principles that guide Theano’s handling of memory. The main idea is that there is a
pool of memory managed by Theano, and Theano tracks changes to values in that pool.
• Theano manages its own memory space, which typically does not overlap with the memory of normal
Python variables that non-Theano code creates.
• Theano functions only modify buffers that are in Theano’s memory space.
• Theano’s memory space includes the buffers allocated to store shared variables and the temporaries
used to evaluate functions.
• Physically, Theano’s memory space may be spread across the host, a GPU device(s), and in the future
may even include objects on a remote machine.
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• The memory allocated for a shared variable buffer is unique: it is never aliased to another shared
variable.
• Theano’s managed memory is constant while Theano functions are not running and Theano’s library
code is not running.
• The default behaviour of a function is to return user-space values for outputs, and to expect user-space
values for inputs.
The distinction between Theano-managed memory and user-managed memory can be broken down by
some Theano functions (e.g. shared, get_value and the constructors for In and Out) by using a
borrow=True flag. This can make those methods faster (by avoiding copy operations) at the expense of
risking subtle bugs in the overall program (by aliasing memory).
The rest of this section is aimed at helping you to understand when it is safe to use the borrow=True
argument and reap the benefits of faster code.
Borrowing when Creating Shared Variables
A borrow argument can be provided to the shared-variable constructor.
import numpy, theano
np_array = numpy.ones(2, dtype='float32')
s_default = theano.shared(np_array)
s_false
= theano.shared(np_array, borrow=False)
s_true
= theano.shared(np_array, borrow=True)
By default (s_default) and when explicitly setting borrow=False, the shared variable we construct gets
a [deep] copy of np_array. So changes we subsequently make to np_array have no effect on our shared
variable.
np_array += 1 # now it is an array of 2.0 s
print(s_default.get_value())
print(s_false.get_value())
print(s_true.get_value())
[ 1.
[ 1.
[ 2.
1.]
1.]
2.]
If we are running this with the CPU as the device, then changes we make to np_array right away will
show up in s_true.get_value() because NumPy arrays are mutable, and s_true is using the np_array
object as it’s internal buffer.
However, this aliasing of np_array and s_true is not guaranteed to occur, and may occur only temporarily
even if it occurs at all. It is not guaranteed to occur because if Theano is using a GPU device, then the
borrow flag has no effect. It may occur only temporarily because if we call a Theano function that updates
the value of s_true the aliasing relationship may or may not be broken (the function is allowed to update the
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shared variable by modifying its buffer, which will preserve the aliasing, or by changing which buffer the
variable points to, which will terminate the aliasing).
Take home message:
It is a safe practice (and a good idea) to use borrow=True in a shared variable constructor when the
shared variable stands for a large object (in terms of memory footprint) and you do not want to create
copies of it in memory.
It is not a reliable technique to use borrow=True to modify shared variables through side-effect, because with some devices (e.g. GPU devices) this technique will not work.
Borrowing when Accessing Value of Shared Variables
Retrieving
A borrow argument can also be used to control how a shared variable’s value is retrieved.
s = theano.shared(np_array)
v_false = s.get_value(borrow=False) # N.B. borrow default is False
v_true = s.get_value(borrow=True)
When borrow=False is passed to get_value, it means that the return value may not be aliased to any
part of Theano’s internal memory. When borrow=True is passed to get_value, it means that the return
value might be aliased to some of Theano’s internal memory. But both of these calls might create copies of
the internal memory.
The reason that borrow=True might still make a copy is that the internal representation of a shared
variable might not be what you expect. When you create a shared variable by passing a NumPy array
for example, then get_value() must return a NumPy array too. That’s how Theano can make the GPU
use transparent. But when you are using a GPU (or in the future perhaps a remote machine), then the
numpy.ndarray is not the internal representation of your data. If you really want Theano to return its internal
representation and never copy it then you should use the return_internal_type=True argument to
get_value. It will never cast the internal object (always return in constant time), but might return various
datatypes depending on contextual factors (e.g. the compute device, the dtype of the NumPy array).
v_internal = s.get_value(borrow=True, return_internal_type=True)
It is possible to use borrow=False in conjunction with return_internal_type=True, which will
return a deep copy of the internal object. This is primarily for internal debugging, not for typical use.
For the transparent use of different type of optimization Theano can make, there is the policy that
get_value() always return by default the same object type it received when the shared variable was
created. So if you created manually data on the gpu and create a shared variable on the gpu with this data,
get_value will always return gpu data even when return_internal_type=False.
Take home message:
It is safe (and sometimes much faster) to use get_value(borrow=True) when your code does not
modify the return value. Do not use this to modify a ‘‘shared‘‘ variable by side-effect because it will make
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your code device-dependent. Modification of GPU variables through this sort of side-effect is impossible.
Assigning
Shared variables also have a set_value method that can accept an optional borrow=True argument.
The semantics are similar to those of creating a new shared variable - borrow=False is the default and
borrow=True means that Theano may reuse the buffer you provide as the internal storage for the variable.
A standard pattern for manually updating the value of a shared variable is as follows:
s.set_value(
some_inplace_fn(s.get_value(borrow=True)),
borrow=True)
This pattern works regardless of the computing device, and when the latter makes it possible to expose
Theano’s internal variables without a copy, then it proceeds as fast as an in-place update.
When shared variables are allocated on the GPU, the transfers to and from the GPU device memory can
be costly. Here are a few tips to ensure fast and efficient use of GPU memory and bandwidth:
• Prior to Theano 0.3.1, set_value did not work in-place on the GPU. This meant that, sometimes,
GPU memory for the new value would be allocated before the old memory was released. If you’re
running near the limits of GPU memory, this could cause you to run out of GPU memory unnecessarily.
Solution: update to a newer version of Theano.
• If you are going to swap several chunks of data in and out of a shared variable repeatedly, you
will want to reuse the memory that you allocated the first time if possible - it is both faster and more
memory efficient.
Solution: upgrade to a recent version of Theano (>0.3.0) and consider padding your source data to
make sure that every chunk is the same size.
• It is also worth mentioning that, current GPU copying routines support only contiguous memory. So
Theano must make the value you provide C-contiguous prior to copying it. This can require an extra
copy of the data on the host.
Solution: make sure that the value you assign to a CudaNdarraySharedVariable is already Ccontiguous.
(Further information on the current implementation of the GPU version of set_value() can be found
here: sandbox.cuda.var – The Variables for Cuda-allocated arrays)
Borrowing when Constructing Function Objects
A borrow argument can also be provided to the In and Out objects that control how theano.
function handles its argument[s] and return value[s].
import theano, theano.tensor
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x = theano.tensor.matrix()
y = 2 * x
f = theano.function([theano.In(x, borrow=True)], theano.Out(y, borrow=True))
Borrowing an input means that Theano will treat the argument you provide as if it were part of Theano’s
pool of temporaries. Consequently, your input may be reused as a buffer (and overwritten!) during the
computation of other variables in the course of evaluating that function (e.g. f).
Borrowing an output means that Theano will not insist on allocating a fresh output buffer every time you
call the function. It will possibly reuse the same one as on a previous call, and overwrite the old content.
Consequently, it may overwrite old return values through side-effect. Those return values may also be
overwritten in the course of evaluating another compiled function (for example, the output may be aliased
to a shared variable). So be careful to use a borrowed return value right away before calling any more
Theano functions. The default is of course to not borrow internal results.
It is also possible to pass a return_internal_type=True flag to the Out variable which has the same
interpretation as the return_internal_type flag to the shared variable’s get_value function.
Unlike get_value(), the combination of return_internal_type=True and borrow=True arguments to Out() are not guaranteed to avoid copying an output value. They are just hints that give more
flexibility to the compilation and optimization of the graph.
For GPU graphs, this borrowing can have a major speed impact. See the following code:
from theano import function, config, shared, sandbox, tensor, Out
import numpy
import time
vlen = 10 * 30 * 768
iters = 1000
# 10 x # cores x # threads per core
rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), config.floatX))
f1 = function([], sandbox.cuda.basic_ops.gpu_from_host(tensor.exp(x)))
f2 = function([],
Out(sandbox.cuda.basic_ops.gpu_from_host(tensor.exp(x)),
borrow=True))
t0 = time.time()
for i in range(iters):
r = f1()
t1 = time.time()
no_borrow = t1 - t0
t0 = time.time()
for i in range(iters):
r = f2()
t1 = time.time()
print(
"Looping %s times took %s seconds without borrow "
"and %s seconds with borrow" % (iters, no_borrow, (t1 - t0))
)
if numpy.any([isinstance(x.op, tensor.Elemwise) and
('Gpu' not in type(x.op).__name__)
for x in f1.maker.fgraph.toposort()]):
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print('Used the cpu')
else:
print('Used the gpu')
Which produces this output:
$ THEANO_FLAGS=device=gpu0,floatX=float32 python test1.py
Using gpu device 0: GeForce GTX 275
Looping 1000 times took 0.368273973465 seconds without borrow and 0.
˓→0240728855133 seconds with borrow.
Used the gpu
Take home message:
When an input x to a function is not needed after the function returns and you would like to make it available
to Theano as additional workspace, then consider marking it with In(x, borrow=True). It may make
the function faster and reduce its memory requirement. When a return value y is large (in terms of memory
footprint), and you only need to read from it once, right away when it’s returned, then consider marking it
with an Out(y, borrow=True).
Python Memory Management
One of the major challenges in writing (somewhat) large-scale Python programs is to keep memory usage
at a minimum. However, managing memory in Python is easy—if you just don’t care. Python allocates
memory transparently, manages objects using a reference count system, and frees memory when an object’s
reference count falls to zero. In theory, it’s swell. In practice, you need to know a few things about Python
memory management to get a memory-efficient program running. One of the things you should know, or at
least get a good feel about, is the sizes of basic Python objects. Another thing is how Python manages its
memory internally.
So let us begin with the size of basic objects. In Python, there’s not a lot of primitive data types: there
are ints, longs (an unlimited precision version of ints), floats (which are doubles), tuples, strings, lists,
dictionaries, and classes.
Basic Objects
What is the size of int? A programmer with a C or C++ background will probably guess that the size of
a machine-specific int is something like 32 bits, maybe 64; and that therefore it occupies at most 8 bytes.
But is that so in Python?
Let us first write a function that shows the sizes of objects (recursively if necessary):
import sys
def show_sizeof(x, level=0):
print "\t" * level, x.__class__, sys.getsizeof(x), x
if hasattr(x, '__iter__'):
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if hasattr(x, 'items'):
for xx in x.items():
show_sizeof(xx, level + 1)
else:
for xx in x:
show_sizeof(xx, level + 1)
We can now use the function to inspect the sizes of the different basic data types:
show_sizeof(None)
show_sizeof(3)
show_sizeof(2**63)
show_sizeof(102947298469128649161972364837164)
show_
˓→sizeof(918659326943756134897561304875610348756384756193485761304875613948576297485698417)
If you have a 32-bit 2.7x Python, you’ll see:
8 None
12 3
22 9223372036854775808
28 102947298469128649161972364837164
48
˓→918659326943756134897561304875610348756384756193485761304875613948576297485698417
and if you have a 64-bit 2.7x Python, you’ll see:
16 None
24 3
36 9223372036854775808
40 102947298469128649161972364837164
60
˓→918659326943756134897561304875610348756384756193485761304875613948576297485698417
Let us focus on the 64-bit version (mainly because that’s what we need the most often in our case). None
takes 16 bytes. int takes 24 bytes, three times as much memory as a C int64_t, despite being some kind
of “machine-friendly” integer. Long integers (unbounded precision), used to represent integers larger than
263 -1, have a minimum size of 36 bytes. Then it grows linearly in the logarithm of the integer represented.
Python’s floats are implementation-specific but seem to be C doubles. However, they do not eat up only 8
bytes:
show_sizeof(3.14159265358979323846264338327950288)
Outputs
16 3.14159265359
on a 32-bit platform and
24 3.14159265359
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on a 64-bit platform. That’s again, three times the size a C programmer would expect. Now, what about
strings?
show_sizeof("")
show_sizeof("My hovercraft is full of eels")
outputs, on a 32 bit platform:
21
50 My hovercraft is full of eels
and
37
66 My hovercraft is full of eels
An empty string costs 37 bytes in a 64-bit environment! Memory used by string then linearly grows in the
length of the (useful) string.
***
Other structures commonly used, tuples, lists, and dictionaries are worthwhile to examine. Lists (which are
implemented as array lists, not as linked lists, with everything it entails) are arrays of references to Python
objects, allowing them to be heterogeneous. Let us look at our sizes:
show_sizeof([])
show_sizeof([4, "toaster", 230.1])
outputs
32 []
44 [4, 'toaster', 230.1]
on a 32-bit platform and
72 []
96 [4, 'toaster', 230.1]
on a 64-bit platform. An empty list eats up 72 bytes. The size of an empty, 64-bit C++ std::list() is
only 16 bytes, 4-5 times less. What about tuples? (and dictionaries?):
show_sizeof({})
show_sizeof({'a':213, 'b':2131})
outputs, on a 32-bit box
136 {}
136 {'a': 213, 'b': 2131}
32 ('a', 213)
22 a
12 213
32 ('b', 2131)
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22 b
12 2131
and
280 {}
280 {'a': 213, 'b': 2131}
72 ('a', 213)
38 a
24 213
72 ('b', 2131)
38 b
24 2131
for a 64-bit box.
This last example is particularly interesting because it “doesn’t add up.” If we look at individual key/value
pairs, they take 72 bytes (while their components take 38+24=62 bytes, leaving 10 bytes for the pair itself),
but the dictionary takes 280 bytes (rather than a strict minimum of 144=72×2 bytes). The dictionary is
supposed to be an efficient data structure for search and the two likely implementations will use more space
that strictly necessary. If it’s some kind of tree, then we should pay the cost of internal nodes that contain a
key and two pointers to children nodes; if it’s a hash table, then we must have some room with free entries
to ensure good performance.
The (somewhat) equivalent std::map C++ structure takes 48 bytes when created (that is, empty). An
empty C++ string takes 8 bytes (then allocated size grows linearly the size of the string). An integer takes 4
bytes (32 bits).
***
Why does all this matter? It seems that whether an empty string takes 8 bytes or 37 doesn’t change anything
much. That’s true. That’s true until you need to scale. Then, you need to be really careful about how many
objects you create to limit the quantity of memory your program uses. It is a problem in real-life applications.
However, to devise a really good strategy about memory management, we must not only consider the sizes
of objects, but how many and in which order they are created. It turns out to be very important for Python
programs. One key element to understand is how Python allocates its memory internally, which we will
discuss next.
Internal Memory Management
To speed-up memory allocation (and reuse) Python uses a number of lists for small objects. Each list will
contain objects of similar size: there will be a list for objects 1 to 8 bytes in size, one for 9 to 16, etc. When
a small object needs to be created, either we reuse a free block in the list, or we allocate a new one.
There are some internal details on how Python manages those lists into blocks, pools, and “arena”: a number
of block forms a pool, pools are gathered into arena, etc., but they’re not very relevant to the point we want to
make (if you really want to know, read Evan Jones’ ideas on how to improve Python’s memory allocation).
The important point is that those lists never shrink.
Indeed: if an item (of size x) is deallocated (freed by lack of reference) its location is not returned to Python’s
global memory pool (and even less to the system), but merely marked as free and added to the free list of
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items of size x. The dead object’s location will be reused if another object of compatible size is needed. If
there are no dead objects available, new ones are created.
If small objects memory is never freed, then the inescapable conclusion is that, like goldfishes, these small
object lists only keep growing, never shrinking, and that the memory footprint of your application is dominated by the largest number of small objects allocated at any given point.
***
Therefore, one should work hard to allocate only the number of small objects necessary for one task, favoring
(otherwise unpythonèsque) loops where only a small number of elements are created/processed rather than
(more pythonèsque) patterns where lists are created using list generation syntax then processed.
While the second pattern is more à la Python, it is rather the worst case: you end up creating lots of small
objects that will come populate the small object lists, and even once the list is dead, the dead objects (now
all in the free lists) will still occupy a lot of memory.
***
The fact that the free lists grow does not seem like much of a problem because the memory it contains
is still accessible to the Python program. But from the OS’s perspective, your program’s size is the total
(maximum) memory allocated to Python. Since Python returns memory to the OS on the heap (that allocates
other objects than small objects) only on Windows, if you run on Linux, you can only see the total memory
used by your program increase.
***
Let us prove my point using memory_profiler, a Python add-on module (which depends on the
python-psutil package) by Fabian Pedregosa (the module’s github page). This add-on provides the
decorator @profile that allows one to monitor one specific function memory usage. It is extremely simple to use. Let us consider the following program:
import copy
import memory_profiler
@profile
def function():
x = list(range(1000000))
y = copy.deepcopy(x)
del x
return y
# allocate a big list
if __name__ == "__main__":
function()
invoking
python -m memory_profiler memory-profile-me.py
prints, on a 64-bit computer
Filename: memory-profile-me.py
Line #
Mem usage
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Increment
Line Contents
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================================================
4
@profile
5
9.11 MB
0.00 MB
def function():
6
40.05 MB
30.94 MB
x = list(range(1000000)) # allocate a
˓→big list
7
89.73 MB
49.68 MB
y = copy.deepcopy(x)
8
82.10 MB
-7.63 MB
del x
9
82.10 MB
0.00 MB
return y
This program creates a list of n=1,000,000 ints (n x 24 bytes = ~23 MB) and an additional list of references
(n x 8 bytes = ~7.6 MB), which amounts to a total memory usage of ~31 MB. copy.deepcopy copies
both lists, which allocates again ~50 MB (I am not sure where the additional overhead of 50 MB - 31 MB =
19 MB comes from). The interesting part is del x: it deletes x, but the memory usage only decreases by
7.63 MB! This is because del only deletes the reference list, not the actual integer values, which remain on
the heap and cause a memory overhead of ~23 MB.
This example allocates in total ~73 MB, which is more than twice the amount of memory needed to store a
single list of ~31 MB. You can see that memory can increase surprisingly if you are not careful!
Note that you might get different results on a different platform or with a different python version.
Pickle
On a related note: is pickle wasteful?
Pickle is the standard way of (de)serializing Python objects to file. What is its memory footprint? Does it
create extra copies of the data or is it rather smart about it? Consider this short example:
import memory_profiler
import pickle
import random
def random_string():
return "".join([chr(64 + random.randint(0, 25)) for _ in xrange(20)])
@profile
def create_file():
x = [(random.random(),
random_string(),
random.randint(0, 2 ** 64))
for _ in xrange(1000000)]
pickle.dump(x, open('machin.pkl', 'w'))
@profile
def load_file():
y = pickle.load(open('machin.pkl', 'r'))
return y
if __name__=="__main__":
create_file()
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#load_file()
With one invocation to profile the creation of the pickled data, and one invocation to re-read it (you comment
out the function not to be called). Using memory_profiler, the creation uses a lot of memory:
Filename: test-pickle.py
Line #
Mem usage
Increment
Line Contents
================================================
8
@profile
9
9.18 MB
0.00 MB
def create_file():
10
9.33 MB
0.15 MB
x=[ (random.random(),
11
random_string(),
12
random.randint(0,2**64))
13
246.11 MB
236.77 MB
for _ in xrange(1000000) ]
14
15
481.64 MB
235.54 MB
pickle.dump(x,open('machin.pkl','w'))
and re-reading a bit less:
Filename: test-pickle.py
Line #
Mem usage
Increment
Line Contents
================================================
18
@profile
19
9.18 MB
0.00 MB
def load_file():
20
311.02 MB
301.83 MB
y=pickle.load(open('machin.pkl','r'))
21
311.02 MB
0.00 MB
return y
So somehow, pickling is very bad for memory consumption. The initial list takes up more or less 230MB,
but pickling it creates an extra 230-something MB worth of memory allocation.
Unpickling, on the other hand, seems fairly efficient. It does create more memory than the original list
(300MB instead of 230-something) but it does not double the quantity of allocated memory.
Overall, then, (un)pickling should be avoided for memory-sensitive applications. What are the alternatives?
Pickling preserves all the structure of a data structure, so you can recover it exactly from the pickled file at a
later time. However, that might not always be needed. If the file is to contain a list as in the example above,
then maybe a simple flat, text-based, file format is in order. Let us see what it gives.
A naïve implementation would give:
import memory_profiler
import random
import pickle
def random_string():
return "".join([chr(64 + random.randint(0, 25)) for _ in xrange(20)])
@profile
def create_file():
x = [(random.random(),
random_string(),
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random.randint(0, 2 ** 64))
for _ in xrange(1000000) ]
f = open('machin.flat', 'w')
for xx in x:
print >>f, xx
f.close()
@profile
def load_file():
y = []
f = open('machin.flat', 'r')
for line in f:
y.append(eval(line))
f.close()
return y
if __name__== "__main__":
create_file()
#load_file()
Creating the file:
Filename: test-flat.py
Line #
Mem usage
Increment
Line Contents
================================================
8
@profile
9
9.19 MB
0.00 MB
def create_file():
10
9.34 MB
0.15 MB
x=[ (random.random(),
11
random_string(),
12
random.randint(0, 2**64))
13
246.09 MB
236.75 MB
for _ in xrange(1000000) ]
14
15
246.09 MB
0.00 MB
f=open('machin.flat', 'w')
16
308.27 MB
62.18 MB
for xx in x:
17
print >>f, xx
and reading the file back:
Filename: test-flat.py
Line #
Mem usage
Increment
Line Contents
================================================
20
@profile
21
9.19 MB
0.00 MB
def load_file():
22
9.34 MB
0.15 MB
y=[]
23
9.34 MB
0.00 MB
f=open('machin.flat', 'r')
24
300.99 MB
291.66 MB
for line in f:
25
300.99 MB
0.00 MB
y.append(eval(line))
26
301.00 MB
0.00 MB
return y
Memory consumption on writing is now much better. It still creates a lot of temporary small objects (for
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60MB’s worth), but it’s not doubling memory usage. Reading is comparable (using only marginally less
memory).
This particular example is trivial but it generalizes to strategies where you don’t load the whole thing first
then process it but rather read a few items, process them, and reuse the allocated memory. Loading data to
a Numpy array, for example, one could first create the Numpy array, then read the file line by line to fill the
array: this allocates one copy of the whole data. Using pickle, you would allocate the whole data (at least)
twice: once by pickle, and once through Numpy.
Or even better yet: use Numpy (or PyTables) arrays. But that’s a different topic. In the mean time, you can
have a look at loading and saving another tutorial in the Theano/doc/tutorial directory.
***
Python design goals are radically different than, say, C design goals. While the latter is designed to give
you good control on what you’re doing at the expense of more complex and explicit programming, the
former is designed to let you code rapidly while hiding most (if not all) of the underlying implementation
details. While this sounds nice, in a production environment ignoring the implementation inefficiencies of
a language can bite you hard, and sometimes when it’s too late. I think that having a good feel of how
inefficient Python is with memory management (by design!) will play an important role in whether or not
your code meets production requirements, scales well, or, on the contrary, will be a burning hell of memory.
Multi cores support in Theano
BLAS operation
BLAS is an interface for some mathematic operations between two vectors, a vector and a matrix or two
matrices (e.g. the dot product between vector/matrix and matrix/matrix). Many different implementations
of that interface exist and some of them are parallelized.
Theano tries to use that interface as frequently as possible for performance reasons. So if Theano links to a
parallel implementation, those operations will run in parallel in Theano.
The most frequent way to control the number of threads used is via the OMP_NUM_THREADS environment
variable. Set it to the number of threads you want to use before starting the Python process. Some BLAS
implementations support other environment variables.
To test if you BLAS supports OpenMP/Multiple cores, you can use the theano/misc/check_blas.py script
from the command line like this:
OMP_NUM_THREADS=1 python theano/misc/check_blas.py -q
OMP_NUM_THREADS=2 python theano/misc/check_blas.py -q
Parallel element wise ops with OpenMP
Because element wise ops work on every tensor entry independently they can be easily parallelized using
OpenMP.
To use OpenMP you must set the openmp flag to True.
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You can use the flag openmp_elemwise_minsize to set the minimum tensor size for which the operation is parallelized because for short tensors using OpenMP can slow down the operation. The default value
is 200000.
For simple (fast) operations you can obtain a speed-up with very large tensors while for more complex
operations you can obtain a good speed-up also for smaller tensors.
There is a script elemwise_openmp_speedup.py in theano/misc/ which you can use to tune the
value of openmp_elemwise_minsize for your machine. The script runs two elemwise operations (a
fast one and a slow one) for a vector of size openmp_elemwise_minsize with and without OpenMP
and shows the time difference between the cases.
The only way to control the number of threads used is via the OMP_NUM_THREADS environment variable.
Set it to the number of threads you want to use before starting the Python process. You can test this with
this command:
OMP_NUM_THREADS=2 python theano/misc/elemwise_openmp_speedup.py
#The output
Fast op time without openmp 0.000533s with openmp 0.000474s speedup 1.12
Slow op time without openmp 0.002987s with openmp 0.001553s speedup 1.92
Frequently Asked Questions
How to update a subset of weights?
If you want to update only a subset of a weight matrix (such as some rows or some columns) that are used
in the forward propogation of each iteration, then the cost function should be defined in a way that it only
depends on the subset of weights that are used in that iteration.
For example if you want to learn a lookup table, e.g. used for word embeddings, where each row is a vector
of weights representing the embedding that the model has learned for a word, in each iteration, the only
rows that should get updated are those containing embeddings used during the forward propagation. Here is
how the theano function should be written:
Defining a shared variable for the lookup table
lookup_table = theano.shared(matrix_ndarray)
Getting a subset of the table (some rows or some columns) by passing an integer vector of indices corresponding to those rows or columns.
subset = lookup_table[vector_of_indices]
From now on, use only ‘subset’. Do not call lookup_table[vector_of_indices] again. This causes problems
with grad as this will create new variables.
Defining cost which depends only on subset and not the entire lookup_table
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cost = something that depends on subset
g = theano.grad(cost, subset)
There are two ways for updating the parameters: Either use inc_subtensor or set_subtensor. It is recommended to use inc_subtensor. Some theano optimizations do the conversion between the two functions, but
not in all cases.
updates = inc_subtensor(subset, g*lr)
OR
updates = set_subtensor(subset, subset + g*lr)
Currently we just cover the case here, not if you use inc_subtensor or set_subtensor with other types of
indexing.
Defining the theano function
f = theano.function(..., updates=[(lookup_table, updates)])
Note that you can compute the gradient of the cost function w.r.t. the entire lookup_table, and the gradient
will have nonzero rows only for the rows that were selected during forward propagation. If you use gradient
descent to update the parameters, there are no issues except for unnecessary computation, e.g. you will
update the lookup table parameters with many zero gradient rows. However, if you want to use a different
optimization method like rmsprop or Hessian-Free optimization, then there will be issues. In rmsprop, you
keep an exponentially decaying squared gradient by whose square root you divide the current gradient to
rescale the update step component-wise. If the gradient of the lookup table row which corresponds to a rare
word is very often zero, the squared gradient history will tend to zero for that row because the history of
that row decays towards zero. Using Hessian-Free, you will get many zero rows and columns. Even one of
them would make it non-invertible. In general, it would be better to compute the gradient only w.r.t. to those
lookup table rows or columns which are actually used during the forward propagation.
6.2.5 Extending Theano
This advanced tutorial is for users who want to extend Theano with new Types, new Operations (Ops), and
new graph optimizations. This first page of the tutorial mainly focuses on the Python implementation of an
Op and then proposes an overview of the most important methods that define an op. The second page of the
tutorial (Extending Theano with a C Op) provides then information on the C implementation of an Op. The
rest of the tutorial goes more in depth on advanced topics related to Ops, such as how to write efficient code
for an Op and how to write an optimization to speed up the execution of an Op.
Along the way, this tutorial also introduces many aspects of how Theano works, so it is also good for you if
you are interested in getting more under the hood with Theano itself.
Note: Before tackling this more advanced presentation, it is highly recommended to read the introductory
Tutorial, especially the sections that introduce the Theano Graphs, as providing a novel Theano op requires
a basic understanting of the Theano Graphs.
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See also the Developer Start Guide for information regarding the versioning framework, namely about git
and GitHub, regarding the development workflow and how to make a quality contribution.
Creating a new Op: Python implementation
So suppose you have looked through the library documentation and you don’t see a function that does what
you want.
If you can implement something in terms of existing Ops, you should do that. Odds are your function that
uses existing Theano expressions is short, has no bugs, and potentially profits from optimizations that have
already been implemented.
However, if you cannot implement an Op in terms of existing Ops, you have to write a new one. Don’t
worry, Theano was designed to make it easy to add new Ops, Types, and Optimizations.
As an illustration, this tutorial shows how to write a simple Python-based operations which performs operations on Type, double<Double>. .. It also shows how to implement tests that .. ensure the proper
working of an op.
Note: This is an introductury tutorial and as such it does not cover how to make an op that returns a
view or modifies the values in its inputs. Thus, all ops created with the instructions described here MUST
return newly allocated memory or reuse the memory provided in the parameter output_storage of the
perform() function. See Views and inplace operations for an explanation on how to do this.
If your op returns a view or changes the value of its inputs without doing as prescribed in that page, Theano
will run, but will return correct results for some graphs and wrong results for others.
It is recommended that you run your tests in DebugMode (Theano flag mode=DebugMode) since it verifies
if your op behaves correctly in this regard.
Theano Graphs refresher
Theano represents symbolic mathematical computations as graphs. Those graphs are bi-partite graphs
(graphs with 2 types of nodes), they are composed of interconnected Apply and Variable nodes. Variable nodes represent data in the graph, either inputs, outputs or intermediary values. As such, Inputs and
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Outputs of a graph are lists of Theano Variable nodes. Apply nodes perform computation on these variables
to produce new variables. Each Apply node has a link to an instance of Op which describes the computation
to perform. This tutorial details how to write such an Op instance. Please refers to Graph Structures for a
more detailed explanation about the graph structure.
Op’s basic methods
An op is any Python object which inherits from gof.Op. This section provides an overview of the basic
methods you typically have to implement to make a new op. It does not provide extensive coverage of all
the possibilities you may encounter or need. For that refer to Op’s contract.
import theano
class MyOp(theano.Op):
# Properties attribute
__props__ = ()
#itypes and otypes attributes are
#compulsory if make_node method is not defined.
#They're the type of input and output respectively
itypes = None
otypes = None
#Compulsory if itypes and otypes are not defined
def make_node(self, *inputs):
pass
# Python implementation:
def perform(self, node, inputs_storage, output_storage):
pass
# Other type of implementation
# C implementation: [see theano web site for other functions]
def c_code(self, node, inputs, outputs, sub):
pass
# Other implementations (pycuda, ...):
def make_thunk(self, node, storage_map, _, _2):
pass
# optional:
check_input = True
def __init__(self, *args):
pass
def grad(self, inputs, g):
pass
def R_op(self, inputs, eval_points):
pass
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def infer_shape(node, input_shapes):
pass
An op has to implement some methods defined in the the interface of gof.Op. More specifically, it is
mandatory for an op to define either the method make_node() or itypes, otypes and one of the implementation methods, either perform(), Op.c_code() or make_thunk(). method make_node()
and one of the implementation methods, either perform(), Op.c_code() or make_thunk().
make_node() method creates an Apply node representing the application of the op on the
inputs provided. This method is reponsible for three things:
• it first checks that the input Variables types are compatible with the current op. If the
op cannot be applied on the provided input types, it must raises an exception (such as
TypeError).
• it operates on the Variables found in *inputs in Theano’s symbolic language to infer the
type of the symbolic output Variables. It creates output Variables of a suitable symbolic
Type to serve as the outputs of this op’s application.
• it creates an Apply instance with the input and output Variable, and return the Apply
instance.
perform() method defines the Python implementation of an op. It takes several arguments:
• node is a reference to an Apply node which was previously obtained via the Op‘s
make_node() method. It is typically not used in simple ops, but it contains symbolic
information that could be required for complex ops.
• inputs is a list of references to data which can be operated on using non-symbolic
statements, (i.e., statements in Python, Numpy).
• output_storage is a list of storage cells where the output is to be stored. There is one
storage cell for each output of the op. The data put in output_storage must match the
type of the symbolic output. It is forbidden to change the length of the list(s) contained
in output_storage. A function Mode may allow output_storage elements to
persist between evaluations, or it may reset output_storage cells to hold a value
of None. It can also pre-allocate some memory for the op to use. This feature can allow
perform to reuse memory between calls, for example. If there is something preallocated
in the output_storage, it will be of the good dtype, but can have the wrong shape
and have any stride pattern.
perform() method must be determined by the inputs. That is to say, when applied to identical
inputs the method must return the same outputs.
gof.Op allows some other way to define the op implentation. For instance, it is possible to
define Op.c_code() to provide a C-implementation to the op. Please refers to tutorial Extending Theano with a C Op for a description of Op.c_code() and other related c_methods.
Note that an op can provide both Python and C implementation.
make_thunk() method is another alternative to perform(). It returns a thunk. A thunk is
defined as a zero-arguments function which encapsulates the computation to be performed by
an op on the arguments of its corresponding node. It takes several parameters:
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• node is the Apply instance for which a thunk is requested,
• storage_map is a dict of lists which maps variables to a one-element lists holding
the variable’s current value. The one-element list acts as pointer to the value and allows
sharing that “pointer” with other nodes and instances.
• compute_map is also a dict of lists. It maps variables to one-element lists holding
booleans. If the value is 0 then the variable has not been computed and the value should
not be considered valid. If the value is 1 the variable has been computed and the value is
valid. If the value is 2 the variable has been garbage-collected and is no longer valid, but
shouldn’t be required anymore for this call. The returned function must ensure that it sets
the computed variables as computed in the compute_map.
make_thunk() is useful if you want to generate code and compile it yourself. For example,
this allows you to use PyCUDA to compile GPU code.
If make_thunk() is defined by an op, it will be used by Theano to obtain the op’s implementation. perform() and Op.c_code() will be ignored.
If make_node() is not defined, the itypes and otypes are used by the Op’s
make_node() method to implement the functionality of make_node() method mentioned
above.
Op’s auxiliary methods
There are other methods that can be optionally defined by the op:
The __str__() method provides a meaningful string representation of your op.
__eq__() and __hash__() define respectivelly equality between two ops and the hash
of an op instance. They will be used by the optimization phase to merge nodes that are doing equivalent computations (same inputs, same operation). Two ops that are equal according
__eq__() should return the same output when they are applied on the same inputs.
The __props__ lists the properties that influence how the computation is performed (Ususally
these are those that you set in __init__()). It must be a tuple. If you don’t have any
properties, then you should set this attribute to the emtpy tuple ().
__props__ enables the automatic generation of appropriate __eq__() and __hash__().
Given the method __eq__(), automatically generated from __props__, two ops will be
equal if they have the same values for all the properties listed in __props__. Given to
the method __hash__() automatically generated from __props__, two ops will be have
the same hash if they have the same values for all the properties listed in __props__.
__props__ will also generate a suitable __str__() for your op. This requires development version after September 1st, 2014 or version 0.7.
The infer_shape() method allows to infer the shape of the op output variables, without
actually computing the outputs. It takes as input node, a reference to the op Apply node, and
a list of Theano symbolic Varables (i0_shape, i1_shape, ...) which are the shape of the
op input Variables. infer_shape() returns a list where each element is a tuple representing
the shape of one output. This could be helpful if one only needs the shape of the output instead
of the actual outputs, which can be useful, for instance, for optimization procedures.
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The grad() method is required if you want to differentiate some cost whose expression includes your op. The gradient may be specified symbolically in this method. It takes two arguments inputs and output_gradients which are both lists of symbolic Theano Variables
and those must be operated on using Theano’s symbolic language. The grad method must return a list containing one Variable for each input. Each returned Variable represents the gradient
with respect to that input computed based on the symbolic gradients with respect to each output.
If the output is not differentiable with respect to an input then this method should be defined
to return a variable of type NullType for that input. Likewise, if you have not implemented the
grad computation for some input, you may return a variable of type NullType for that input.
Please refer to grad() for a more detailed view.
The R_op() method is needed if you want theano.tensor.Rop to work with your op.
This function implements the application of the R-operator on the function represented by your
op. Let assume that function is 𝑓 , with input 𝑥, applying the R-operator means computing the
Jacobian of 𝑓 and right-multiplying it by 𝑣, the evaluation point, namely: 𝜕𝑓
𝜕𝑥 𝑣.
The optional boolean check_input attribute is used to specify if you want the types used in
your op to check their inputs in their c_code. It can be used to speed up compilation, reduce
overhead (particularly for scalars) and reduce the number of generated C files.
Example: Op definition
import theano
#Using make_node
class DoubleOp1(theano.Op):
__props__ = ()
def make_node(self, x):
x = theano.tensor.as_tensor_variable(x)
# Note: using x_.type() is dangerous, as it copies x's broadcasting
# behaviour
return theano.Apply(self, [x], [x.type()])
def perform(self, node, inputs, output_storage):
x = inputs[0]
z = output_storage[0]
z[0] = x * 2
def infer_shape(self, node, i0_shapes):
return i0_shapes
def grad(self, inputs, output_grads):
return [output_grads[0] * 2]
def R_op(self, inputs, eval_points):
# R_op can receive None as eval_points.
# That mean there is no diferientiable path through that input
# If this imply that you cannot compute some outputs,
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# return None for those.
if eval_points[0] is None:
return eval_points
return self.grad(inputs, eval_points)
doubleOp1 = DoubleOp1()
#Using itypes and otypes
class DoubleOp2(theano.Op):
__props__ = ()
itypes = [theano.tensor.dmatrix]
otypes = [theano.tensor.dmatrix]
def perform(self, node, inputs, output_storage):
x = inputs[0]
z = output_storage[0]
z[0] = x * 2
def infer_shape(self, node, i0_shapes):
return i0_shapes
def grad(self, inputs, output_grads):
return [output_grads[0] * 2]
def R_op(self, inputs, eval_points):
# R_op can receive None as eval_points.
# That mean there is no diferientiable path through that input
# If this imply that you cannot compute some outputs,
# return None for those.
if eval_points[0] is None:
return eval_points
return self.grad(inputs, eval_points)
doubleOp2 = DoubleOp2()
At a high level, the code fragment declares a class (e.g., DoubleOp1) and then creates one instance of it
(e.g., doubleOp1).
We often gloss over this distinction, but will be precise here: doubleOp1 (the instance) is an Op, not
DoubleOp1 (the class which is a subclass of theano.Op). You can call doubleOp1(tensor.
vector()) on a Variable to build an expression, and in the expression there will be a .op attribute
that refers to doubleOp1.
The make_node method creates a node to be included in the expression graph. It runs when we apply our Op (doubleOp1) to the Variable (x), as in doubleOp1(tensor.vector()). When an
Op has multiple inputs, their order in the inputs argument to Apply is important: Theano will call
make_node(*inputs) to copy the graph, so it is important not to change the semantics of the expression
by changing the argument order.
All the inputs and outputs arguments to Apply must be Variables. A common and easy way to ensure
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inputs are variables is to run them through as_tensor_variable. This function leaves TensorType
variables alone, raises an error for non-TensorType variables, and copies any numpy.ndarray into the
storage for a TensorType Constant. The make_node method dictates the appropriate Type for all output
variables.
The perform method implements the Op’s mathematical logic in Python. The inputs (here x) are passed
by value, but a single output is returned indirectly as the first element of single-element lists. If doubleOp1
had a second output, it would be stored in output_storage[1][0].
In some execution modes, the output storage might contain the return value of a previous call. That old
value can be reused to avoid memory re-allocation, but it must not influence the semantics of the Op output.
You can try the new Op as follows:
import theano
x = theano.tensor.matrix()
f = theano.function([x], DoubleOp1()(x))
import numpy
inp = numpy.random.rand(5, 4)
out = f(inp)
assert numpy.allclose(inp * 2, out)
print(inp)
print(out)
[[
[
[
[
[
[[
[
[
[
[
0.08257206
0.65977826
0.82358552
0.77327215
0.8452076
0.16514411
1.31955651
1.64717104
1.5465443
1.6904152
0.34308357
0.10040307
0.29502171
0.65401857
0.30500101
0.68616713
0.20080613
0.59004341
1.30803715
0.61000201
0.5288043
0.5402353
0.97387481
0.76562992
0.88430501
1.0576086
1.08047061
1.94774962
1.53125983
1.76861002
0.06582951]
0.55472296]
0.0080757 ]
0.94145702]
0.95818655]]
0.13165902]
1.10944593]
0.0161514 ]
1.88291403]
1.9163731 ]]
import theano
x = theano.tensor.matrix()
f = theano.function([x], DoubleOp2()(x))
import numpy
inp = numpy.random.rand(5, 4)
out = f(inp)
assert numpy.allclose(inp * 2, out)
print(inp)
print(out)
[[
[
[
[
[
[[
[
[
0.02443785
0.60853382
0.04427765
0.20551517
0.24082769
0.04887571
1.21706764
0.08855531
146
0.67833979
0.7770539
0.37895602
0.7419955
0.49321452
1.35667957
1.55410779
0.75791203
0.91954769
0.78163219
0.23155797
0.34500905
0.24566545
1.83909538
1.56326439
0.46311594
0.95444365]
0.92838837]
0.4934699 ]
0.49347629]
0.15351132]]
1.90888731]
1.85677674]
0.9869398 ]
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[ 0.41103034
[ 0.48165539
1.48399101
0.98642904
0.69001811
0.4913309
0.98695258]
0.30702264]]
Example: __props__ definition
We can modify the previous piece of code in order to demonstrate the usage of the __props__ attribute.
We create an Op that takes a variable x and returns a*x+b. We want to say that two such ops are equal
when their values of a and b are equal.
import theano
class AXPBOp(theano.Op):
"""
This creates an Op that takes x to a*x+b.
"""
__props__ = ("a", "b")
def __init__(self, a, b):
self.a = a
self.b = b
super(AXPBOp, self).__init__()
def make_node(self, x):
# check that the theano version has support for __props__.
assert hasattr(self, '_props'), ("Your version of theano is too"
"old to support __props__.")
x = theano.tensor.as_tensor_variable(x)
return theano.Apply(self, [x], [x.type()])
def perform(self, node, inputs, output_storage):
x = inputs[0]
z = output_storage[0]
z[0] = self.a * x + self.b
def infer_shape(self, node, i0_shapes):
return i0_shapes
def grad(self, inputs, output_grads):
return [a * output_grads[0] + b]
The use of __props__ saves the user the trouble of implementing __eq__() and __hash__() manually. It also generates a default __str__() method that prints the attribute names and their values.
We can test this by running the following segment:
mult4plus5op = AXPBOp(4, 5)
another_mult4plus5op = AXPBOp(4, 5)
mult2plus3op = AXPBOp(2, 3)
assert mult4plus5op == another_mult4plus5op
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assert mult4plus5op != mult2plus3op
x = theano.tensor.matrix()
f = theano.function([x], mult4plus5op(x))
g = theano.function([x], mult2plus3op(x))
import numpy
inp = numpy.random.rand(5, 4).astype(numpy.float32)
assert numpy.allclose(4 * inp + 5, f(inp))
assert numpy.allclose(2 * inp + 3, g(inp))
How To Test it
Theano has some functionalities to simplify testing. These help test the infer_shape, grad and R_op
methods. Put the following code in a file and execute it with the theano-nose program.
Basic Tests
Basic tests are done by you just by using the op and checking that it returns the right answer. If you
detect an error, you must raise an exception. You can use the assert keyword to automatically raise an
AssertionError.
import numpy
import theano
from theano.tests import unittest_tools as utt
from theano import config
class test_Double(utt.InferShapeTester):
def setUp(self):
super(test_Double, self).setUp()
self.op_class = DoubleOp
self.op = DoubleOp()
def test_basic(self):
x = theano.tensor.matrix()
f = theano.function([x], self.op(x))
inp = numpy.asarray(numpy.random.rand(5, 4), dtype=config.floatX)
out = f(inp)
# Compare the result computed to the expected value.
utt.assert_allclose(inp * 2, out)
We call utt.assert_allclose(expected_value, value) to compare NumPy ndarray.This
raise an error message with more information. Also, the default tolerance can be changed with the Theano
flags config.tensor.cmp_sloppy that take values in 0, 1 and 2. The defaul value do the most strict
comparison, 1 and 2 make less strict comparison.
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Testing the infer_shape
When a class inherits from the InferShapeTester class, it gets the self._compile_and_check
method that tests the op’s infer_shape method. It tests that the op gets optimized out of the graph if
only the shape of the output is needed and not the output itself. Additionally, it checks that the optimized
graph computes the correct shape, by comparing it to the actual shape of the computed output.
self._compile_and_check compiles a Theano function. It takes as parameters the lists of input and
output Theano variables, as would be provided to theano.function, and a list of real values to pass
to the compiled function. It also takes the op class as a parameter in order to verify that no instance of it
appears in the shape-optimized graph.
If there is an error, the function raises an exception. If you want to see it fail, you can implement an incorrect
infer_shape.
When testing with input values with shapes that take the same value over different dimensions (for instance,
a square matrix, or a tensor3 with shape (n, n, n), or (m, n, m)), it is not possible to detect if the output
shape was computed correctly, or if some shapes with the same value have been mixed up. For instance,
if the infer_shape uses the width of a matrix instead of its height, then testing with only square matrices
will not detect the problem. This is why the self._compile_and_check method prints a warning in
such a case. If your op works only with such matrices, you can disable the warning with the warn=False
parameter.
from theano.tests import unittest_tools as utt
from theano import config
class test_Double(utt.InferShapeTester):
# [...] as previous tests.
def test_infer_shape(self):
x = theano.tensor.matrix()
self._compile_and_check([x], # theano.function inputs
[self.op(x)], # theano.function outputs
# Always use not square matrix!
# inputs data
[numpy.asarray(numpy.random.rand(5, 4),
dtype=config.floatX)],
# Op that should be removed from the graph.
self.op_class)
Testing the gradient
The function verify_grad verifies the gradient of an op or Theano graph. It compares the analytic (symbolically computed) gradient and the numeric gradient (computed through the Finite Difference Method).
If there is an error, the function raises an exception. If you want to see it fail, you can implement an incorrect
gradient (for instance, by removing the multiplication by 2).
def test_grad(self):
theano.tests.unittest_tools.verify_grad(self.op,
[numpy.random.rand(5, 7, 2)])
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Testing the Rop
The class RopLop_checker defines the functions RopLop_checker.check_mat_rop_lop(),
RopLop_checker.check_rop_lop() and RopLop_checker.check_nondiff_rop().
These allow to test the implementation of the Rop method of a particular op.
For instance, to verify the Rop method of the DoubleOp, you can use this:
import numpy
import theano.tests
from theano.tests.test_rop import RopLop_checker
class test_DoubleRop(RopLop_checker):
def setUp(self):
super(test_DoubleRop, self).setUp()
def test_double_rop(self):
self.check_rop_lop(DoubleRop()(self.x), self.in_shape)
Testing GPU Ops
Ops to be executed on the GPU should inherit from the theano.sandbox.cuda.GpuOp and not
theano.Op. This allows Theano to distinguish them. Currently, we use this to test if the NVIDIA driver
works correctly with our sum reduction code on the GPU.
Running Your Tests
To perform your tests, you may select either one of the three following methods:
theano-nose
The method of choice to conduct tests is to run the file theano-nose. In a regular Theano installation,
the latter will be on the operating system’s path and directly accessible from any folder. Otherwise, it can
be accessed in the Theano/bin folder. The following command lines may be used for the corresponding
purposes:
• theano-nose --theano: Run every test found in Theano’s path.
• theano-nose folder_name: Run every test found in the folder folder_name.
• theano-nose test_file.py: Run every test found in the file test_file.py.
The following are particularly useful for development purposes since they call for particular classes or even
for particular tests:
• theano-nose test_file.py:test_DoubleRop: Run every test found inside the class
test_DoubleRop.
• theano-nose test_file.py:test_DoubleRop.test_double_op: Run only the test
test_double_op in the class test_DoubleRop.
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Help with the use and functionalities of theano-nose may be obtained by running it with the command
line parameter --help (-h).
nosetests
The command nosetests can also be used. Although it lacks the useful functionalities that
theano-nose provides, nosetests can be called similarly to theano-nose from any folder in
Python’s path like so:
nosetests [suffix similar to the above].
More documentation on nosetests is available here: nosetests.
In-file
One may also add a block of code similar to the following at the end of the file containing a specific test
of interest and run the file. In this example, the test test_DoubleRop in the class test_double_op would be
performed.
if __name__ == '__main__':
t = test_DoubleRop("test_double_rop")
t.setUp()
t.test_double_rop()
We recommend that when we execute a file, we run all tests in that file. This can be done by adding this at
the end of your test files:
if __name__ == '__main__':
unittest.main()
Exercise
Run the code of the DoubleOp example above.
Modify and execute to compute: x * y.
Modify and execute the example to return two outputs: x + y and x - y.
You can omit the Rop functions. Try to implement the testing apparatus described above.
(Notice that Theano’s current elemwise fusion optimization is only applicable to computations involving a
single output. Hence, to gain efficiency over the basic solution that is asked here, the two operations would
have to be jointly optimized explicitly in the code.)
Random numbers in tests
Making tests errors more reproducible is a good practice. To make your tests more reproducible, you need
a way to get the same random numbers. You can do this by seeding NumPy’s random number generator.
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For convenience, the classes InferShapeTester and RopLop_checker already do this for you. If you implement your own setUp function, don’t forget to call the parent setUp function.
For more details see Using Random Values in Test Cases.
Solution
as_op
as_op is a python decorator that converts a python function into a basic Theano op that will call the supplied
function during execution.
This isn’t the recommended way to build an op, but allows for a quick implementation.
It takes an optional infer_shape() parameter that must have this signature:
def infer_shape(node, input_shapes):
# ...
return output_shapes
- `input_shapes` and `output_shapes` are lists of tuples that
represent the shape of the corresponding inputs/outputs.
Note: Not providing the infer_shape method prevents shape-related optimizations from working with this
op. For example your_op(inputs, ...).shape will need the op to be executed just to get the shape.
Note: As no grad is defined, this means you won’t be able to differentiate paths that include this op.
Note: It converts the Python function to a callable object that takes as inputs Theano variables that were
declared.
Note: The python function wrapped by the as_op decorator needs to return a new data allocation, no views
or in place modification of the input.
as_op Example
import theano
import numpy
from theano import function
from theano.compile.ops import as_op
def infer_shape_numpy_dot(node, input_shapes):
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ashp, bshp = input_shapes
return [ashp[:-1] + bshp[-1:]]
@as_op(itypes=[theano.tensor.fmatrix, theano.tensor.fmatrix],
otypes=[theano.tensor.fmatrix], infer_shape=infer_shape_numpy_dot)
def numpy_dot(a, b):
return numpy.dot(a, b)
You can try it as follows:
x = theano.tensor.fmatrix()
y = theano.tensor.fmatrix()
f = function([x, y], numpy_dot(x, y))
inp1 = numpy.random.rand(5, 4).astype('float32')
inp2 = numpy.random.rand(4, 7).astype('float32')
out = f(inp1, inp2)
Exercise
Run the code of the numpy_dot example above.
Modify and execute to compute: numpy.add and numpy.subtract.
Modify and execute the example to return two outputs: x + y and x - y.
Documentation and Coding Style
Please always respect the Requirements for Quality Contributions or your contribution will not be accepted.
NanGuardMode and AllocEmpty
NanGuardMode help users find where in the graph NaN appear. But sometimes, we want some variables to
not be checked. For example, in the old GPU back-end, we use a float32 CudaNdarray to store the MRG
random number generator state (they are integers). So if NanGuardMode check it, it will generate false
positive. Another case is related to [Gpu]AllocEmpty or some computation on it (like done by Scan).
You can tell NanGuardMode to do not check a variable with:
variable.tag.
nan_guard_mode_check. Also, this tag automatically follow that variable during optimization.
This mean if you tag a variable that get replaced by an inplace version, it will keep that tag.
Final Note
A more extensive discussion of this section’s content may be found in the advanced tutorial Extending
Theano.
The section Other ops includes more instructions for the following specific cases:
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• Scalar/Elemwise/Reduction Ops
• SciPy Ops
• Sparse Ops
• Random ops
• OpenMP Ops
• Numba Ops
Extending Theano with a C Op
This tutorial covers how to extend Theano with an op that offers a C implementation. It does not cover
ops that run on a GPU but it does introduce many elements and concepts which are relevant for GPU ops.
This tutorial is aimed at individuals who already know how to extend Theano (see tutorial Creating a new
Op: Python implementation) by adding a new op with a Python implementation and will only cover the
additional knowledge required to also produce ops with C implementations.
Providing a Theano op with a C implementation requires to interact with Python’s C-API and Numpy’s
C-API. Thus, the first step of this tutorial is to introduce both and highlight their features which are most
relevant to the task of implementing a C op. This tutorial then introduces the most important methods that
the op needs to implement in order to provide a usable C implementation. Finally, it shows how to combine
these elements to write a simple C op for performing the simple task of multiplying every element in a vector
by a scalar.
Python C-API
Python provides a C-API to allows the manipulation of python objects from C code. In this API, all variables
that represent Python objects are of type PyObject *. All objects have a pointer to their type object and
a reference count field (that is shared with the python side). Most python methods have an equivalent C
function that can be called on the PyObject * pointer.
As such, manipulating a PyObject instance is often straight-forward but it is important to properly manage
its reference count. Failing to do so can lead to undesired behavior in the C code.
Reference counting
Reference counting is a mechanism for keeping track, for an object, of the number of references to it held by
other entities. This mechanism is often used for purposes of garbage collecting because it allows to easily
see if an object is still being used by other entities. When the reference count for an object drops to 0, it
means it is not used by anyone any longer and can be safely deleted.
PyObjects implement reference counting and the Python C-API defines a number of macros to help manage those reference counts. The definition of these macros can be found here : Python C-API Reference
Counting. Listed below are the two macros most often used in Theano C ops.
void Py_XINCREF(PyObject *o)
Increments the reference count of object o. Without effect if the object is NULL.
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void Py_XDECREF(PyObject *o)
Decrements the reference count of object o. If the reference count reaches 0, it will trigger a call of
the object’s deallocation function. Without effect if the object is NULL.
The general principle, in the reference counting paradigm, is that the owner of a reference to an object is
responsible for disposing properly of it. This can be done by decrementing the reference count once the
reference is no longer used or by transfering ownership; passing on the reference to a new owner which
becomes responsible for it.
Some functions return “borrowed references”; this means that they return a reference to an object without
transfering ownership of the reference to the caller of the function. This means that if you call a function
which returns a borrowed reference, you do not have the burden of properly disposing of that reference. You
should not call Py_XDECREF() on a borrowed reference.
Correctly managing the reference counts is important as failing to do so can lead to issues ranging from
memory leaks to segmentation faults.
NumPy C-API
The NumPy library provides a C-API to allow users to create, access and manipulate NumPy arrays from
within their own C routines. NumPy’s ndarrays are used extensively inside Theano and so extending Theano
with a C op will require interaction with the NumPy C-API.
This sections covers the API’s elements that are often required to write code for a Theano C op. The full
documentation for the API can be found here : NumPy C-API.
NumPy data types
To allow portability between platforms, the NumPy C-API defines its own data types which should be
used whenever you are manipulating a NumPy array’s internal data. The data types most commonly used
to implement C ops are the following : npy_int{8,16,32,64}, npy_uint{8,16,32,64} and
npy_float{32,64}.
You should use these data types when manipulating a NumPy array’s internal data instead of C primitives
because the size of the memory representation for C primitives can vary between platforms. For instance,
a C long can be represented in memory with 4 bytes but it can also be represented with 8. On the other
hand, the in-memory size of NumPy data types remains constant across platforms. Using them will make
your code simpler and more portable.
The full list of defined data types can be found here : NumPy C-API data types.
NumPy ndarrays
In the NumPy C-API, NumPy arrays are represented as instances of the PyArrayObject class which is a
descendant of the PyObject class. This means that, as for any other Python object that you manipulate from
C code, you need to appropriatedly manage the reference counts of PyArrayObject instances.
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Unlike in a standard multidimensionnal C array, a NumPy array’s internal data representation does not have
to occupy a continuous region in memory. In fact, it can be C-contiguous, F-contiguous or non-contiguous.
C-contiguous means that the data is not only contiguous in memory but also that it is organized such that
the index of the latest dimension changes the fastest. If the following array
x = [[1, 2, 3],
[4, 5, 6]]
is C-contiguous, it means that, in memory, the six values contained in the array x are stored in the order
[1, 2, 3, 4, 5, 6] (the first value is x[0,0], the second value is x[0,1], the third value is x[0,
2], the, fourth value is x[1,0], etc). F-contiguous (or Fortran Contiguous) also means that the data is
contiguous but that it is organized such that the index of the latest dimension changes the slowest. If the
array x is F-contiguous, it means that, in memory, the values appear in the order [1, 4, 2, 5, 3, 6]
(the first value is x[0,0], the second value is x[1,0], the third value is x[0,1], etc).
Finally, the internal data can be non-contiguous. In this case, it occupies a non-contiguous region in memory
but it is still stored in an organized fashion : the distance between the element x[i,j] and the element
x[i+1,j] of the array is constant over all valid values of i and j, just as the distance between the element
x[i,j] and the element x[i,j+1] of the array is constant over all valid values of i and j. This distance
between consecutive elements of an array over a given dimension, is called the stride of that dimension.
Accessing NumPy ndarrays’ data and properties
The following macros serve to access various attributes of NumPy ndarrays.
void* PyArray_DATA(PyArrayObject* arr)
Returns a pointer to the first element of the array’s data. The returned pointer must be cast to a pointer
of the proper Numpy C-API data type before use.
int PyArray_NDIM(PyArrayObject* arr)
Returns the number of dimensions in the the array pointed by arr
npy_intp* PyArray_DIMS(PyArrayObject* arr)
Returns a pointer on the first element of arr‘s internal array describing its dimensions. This internal
array contains as many elements as the array arr has dimensions.
The macro PyArray_SHAPE() is a synonym of PyArray_DIMS() : it has the same effect and
is used in an identical way.
npy_intp* PyArray_STRIDES(PyArrayObject* arr)
Returns a pointer on the first element of arr‘s internal array describing the stride for each of its
dimension. This array has as many elements as the number of dimensions in arr. In this array, the
strides are expressed in number of bytes.
PyArray_Descr* PyArray_DESCR(PyArrayObject* arr)
Returns a reference to the object representing the dtype of the array.
The macro PyArray_DTYPE() is a synonym of the PyArray_DESCR() : it has the same effect
and is used in an identical way.
Note This is a borrowed reference so you do not need to decrement its reference count
once you are done with it.
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int PyArray_TYPE(PyArrayObject* arr)
Returns the typenumber for the elements of the array. Like the dtype, the typenumber is a descriptor
for the type of the data in the array. However, the two are not synonyms and, as such, cannot be used
in place of the other.
npy_intp PyArray_SIZE(PyArrayObject* arr)
Returns to total number of elements in the array
bool PyArray_CHKFLAGS(PyArrayObject* arr, flags)
Returns true if the array has the specified flags. The variable flag should either be a NumPy array flag
or an integer obtained by applying bitwise or to an ensemble of flags.
The flags that can be used in with this macro are : NPY_ARRAY_C_CONTIGUOUS,
NPY_ARRAY_F_CONTIGUOUS,
NPY_ARRAY_OWNDATA,
NPY_ARRAY_ALIGNED,
NPY_ARRAY_WRITEABLE, NPY_ARRAY_UPDATEIFCOPY.
Creating NumPy ndarrays
The following functions allow the creation and copy of NumPy arrays :
PyObject* PyArray_EMPTY(int nd, npy_intp* dims, typenum dtype,
int fortran)
Constructs a new ndarray with the number of dimensions specified by nd, shape specified by dims
and data type specified by dtype. If fortran is equal to 0, the data is organized in a C-contiguous
layout, otherwise it is organized in a F-contiguous layout. The array elements are not initialized in
any way.
The function PyArray_Empty() performs the same function as the macro PyArray_EMPTY()
but the data type is given as a pointer to a PyArray_Descr object instead of a typenum.
PyObject* PyArray_ZEROS(int nd, npy_intp* dims, typenum dtype,
int fortran)
Constructs a new ndarray with the number of dimensions specified by nd, shape specified by dims
and data type specified by dtype. If fortran is equal to 0, the data is organized in a C-contiguous
layout, otherwise it is organized in a F-contiguous layout. Every element in the array is initialized to
0.
The function PyArray_Zeros() performs the same function as the macro PyArray_ZEROS()
but the data type is given as a pointer to a PyArray_Descr object instead of a typenum.
PyArrayObject* PyArray_GETCONTIGUOUS(PyObject* op)
Returns a C-contiguous and well-behaved copy of the array op. If op is already C-contiguous and
well-behaved, this function simply returns a new reference to op.
Methods the C Op needs to define
There is a key difference between an op defining a Python implementation for its computation and defining
a C implementation. In the case of a Python implementation, the op defines a function perform() which
executes the required Python code to realize the op. In the case of a C implementation, however, the op does
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not define a function that will execute the C code; it instead defines functions that will return the C code to
the caller.
This is because calling C code from Python code comes with a significant overhead. If every op was
responsible for executing its own C code, every time a Theano function was called, this overhead would
occur as many times as the number of ops with C implementations in the function’s computational graph.
To maximize performance, Theano instead requires the C ops to simply return the code needed for their
execution and takes upon itself the task of organizing, linking and compiling the code from the various ops.
Through this, Theano is able to minimize the number of times C code is called from Python code.
The following is a very simple example to illustrate how it’s possible to obtain performance gains with this
process. Suppose you need to execute, from Python code, 10 different ops, each one having a C implementation. If each op was responsible for executing its own C code, the overhead of calling C code from
Python code would occur 10 times. Consider now the case where the ops instead return the C code for their
execution. You could get the C code from each op and then define your own C module that would call the
C code from each op in succession. In this case, the overhead would only occur once; when calling your
custom module itself.
Moreover, the fact that Theano itself takes care of compiling the C code, instead of the individual ops, allows
Theano to easily cache the compiled C code. This allows for faster compilation times.
See Implementing the arithmetic Ops in C for the full documentation of the various methods of the class Op
that are related to the C implementation. Of particular interest are:
• The methods Op.c_libraries() and Op.c_lib_dirs() to allow your op to use external
libraries.
• The method Op.c_code_cleanup() to specify how the op should clean up what it has allocated
during its execution.
• The methods Op.c_init_code() and Op.c_init_code_apply() to specify code that
should be executed once when the module is initialized, before anything else is executed.
• The methods Op.c_compile_args() and Op.c_no_compile_args() to specify requirements regarding how the op’s C code should be compiled.
This section describes the methods Op.c_code(),
Op.c_support_code(),
Op.
c_support_code_apply() and Op.c_code_cache_version() because they are the ones
that are most commonly used.
c_code(node, name, input_names, output_names, sub)
This method returns a string containing the C code to perform the computation required by this op.
The node argument is an Apply node representing an application of the current Op on a list of inputs,
producing a list of outputs.
input_names is a sequence of strings which contains as many strings as the op has inputs.
Each string contains the name of the C variable to which the corresponding input has been assigned. For example, the name of the C variable representing the first input of the op is given by
input_names[0]. You should therefore use this name in your C code to interact with that variable. output_names is used identically to input_names, but for the op’s outputs.
Finally, sub is a dictionary of extras parameters to the c_code method. Among other things, it
contains sub['fail'] which is a string of C code that you should include in your C code (after
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ensuring that a Python exception is set) if it needs to raise an exception. Ex:
c_code = """
PyErr_Format(PyExc_ValueError, "X does not have the right value");
%(fail)s;
""" % {'fail' : sub['fail']}
to raise a ValueError Python exception with the specified message. The function PyErr_Format()
supports string formatting so it is possible to tailor the error message to the specifics of the error that
occured. If PyErr_Format() is called with more than two arguments, the subsequent arguments
are used to format the error message with the same behavior as the function PyString_FromFormat().
The % characters in the format characters need to be escaped since the C code itself is defined in a
string which undergoes string formatting.
c_code = """
PyErr_Format(PyExc_ValueError,
"X==%%i but it should be greater than 0", X);
%(fail)s;
""" % {'fail' : sub['fail']}
Note Your C code should not return the output of the computation but rather put the results
in the C variables whose names are contained in the output_names.
c_support_code()
Returns a string containing some support C code for this op. This code will be included at the global
scope level and can be used to define functions and structs that will be used by every apply of this op.
c_support_code_apply(node, name)
Returns a string containing some support C code for this op. This code will be included at
the global scope level and can be used to define functions and structs that will be used by
this op. The difference between this method and c_support_code() is that the C code
specified in c_support_code_apply() should be specific to each apply of the Op, while
c_support_code() is for support code that is not specific to each apply.
Both c_support_code() and c_support_code_apply () are necessary because a Theano
op can be used more than once in a given Theano function. For example, an op that adds two matrices
could be used at some point in the Theano function to add matrices of integers and, at another point,
to add matrices of doubles. Because the dtype of the inputs and outputs can change between different
applies of the op, any support code that relies on a certain dtype is specific to a given apply of the op
and should therefore be defined in c_support_code_apply().
c_code_cache_version()
Returns a tuple of integers representing the version of the C code in this op. Ex : (1, 4, 0) for version
1.4.0
This tuple is used by Theano to cache the compiled C code for this op. As such, the return value
MUST BE CHANGED every time the C code is altered or else Theano will disregard the change in
the code and simply load a previous version of the op from the cache. If you want to avoid caching of
the C code of this op, return an empty tuple or do not implement this method.
Note Theano can handle tuples of any hashable objects as return values for this function
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but, for greater readability and easier management, this function should return a tuple
of integers as previously described.
Important restrictions when implementing an Op
There are some important restrictions to remember when implementing an Op. Unless your Op correctly
defines a view_map attribute, the perform and c_code must not produce outputs whose memory is
aliased to any input (technically, if changing the output could change the input object in some sense, they
are aliased). Unless your Op correctly defines a destroy_map attribute, perform and c_code must
not modify any of the inputs.
TODO: EXPLAIN DESTROYMAP and VIEWMAP BETTER AND GIVE EXAMPLE.
When developing an Op, you should run computations in DebugMode, by using argument
mode='DebugMode' to theano.function. DebugMode is slow, but it can catch many common
violations of the Op contract.
TODO: Like what? How? Talk about Python vs. C too.
DebugMode is no silver bullet though. For example, if you modify an Op self.* during any of
make_node, perform, or c_code, you are probably doing something wrong but DebugMode will not
detect this.
TODO: jpt: I don’t understand the following sentence.
Ops and Types should usually be considered immutable – you should definitely not make a change that
would have an impact on __eq__, __hash__, or the mathematical value that would be computed by
perform or c_code.
Simple C Op example
In this section, we put together the concepts that were covered in this tutorial to generate an op which
multiplies every element in a vector by a scalar and returns the resulting vector. This is intended to be a
simple example so the methods c_support_code() and c_support_code_apply() are not used
because they are not required.
In the C code below notice how the reference count on the output variable is managed. Also take note of how
the new variables required for the op’s computation are declared in a new scope to avoid cross-initialization
errors.
Also, in the C code, it is very important to properly validate the inputs and outputs storage. Theano guarantees that the inputs exist and have the right number of dimensions but it does not guarantee their exact shape.
For instance, if an op computes the sum of two vectors, it needs to validate that its two inputs have the same
shape. In our case, we do not need to validate the exact shapes of the inputs because we don’t have a need
that they match in any way.
For the outputs, things are a little bit more subtle. Theano does not guarantee that they have been allocated
but it does guarantee that, if they have been allocated, they have the right number of dimension. Again,
Theano offers no guarantee on the exact shapes. This means that, in our example, we need to validate that
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the output storage has been allocated and has the same shape as our vector input. If it is not the case, we
allocate a new output storage with the right shape and number of dimensions.
import numpy
import theano
from theano import gof
import theano.tensor as T
class VectorTimesScalar(gof.Op):
__props__ = ()
def make_node(self, x, y):
# Validate the inputs' type
if x.type.ndim != 1:
raise TypeError('x must be a 1-d vector')
if y.type.ndim != 0:
raise TypeError('y must be a scalar')
# Create an output variable of the same type as x
output_var = x.type()
return gof.Apply(self, [x, y], [output_var])
def c_code_cache_version(self):
return (1, 0)
def c_code(self, node, name, inp, out, sub):
x, y = inp
z, = out
# Extract
# be able
# code.
dtype_x =
dtype_y =
dtype_z =
the dtypes of the inputs and outputs storage to
to declare pointers for those dtypes in the C
node.inputs[0].dtype
node.inputs[1].dtype
node.outputs[0].dtype
itemsize_x = numpy.dtype(dtype_x).itemsize
itemsize_z = numpy.dtype(dtype_z).itemsize
fail = sub['fail']
c_code = """
// Validate that the output storage exists and has the same
// dimension as x.
if (NULL == %(z)s ||
PyArray_DIMS(%(x)s)[0] != PyArray_DIMS(%(z)s)[0])
{
/* Reference received to invalid output variable.
Decrease received reference's ref count and allocate new
output variable */
Py_XDECREF(%(z)s);
%(z)s = (PyArrayObject*)PyArray_EMPTY(1,
PyArray_DIMS(%(x)s),
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PyArray_TYPE(%(x)s),
0);
if (!%(z)s) {
%(fail)s;
}
}
// Perform the vector multiplication by a scalar
{
/* The declaration of the following variables is done in a new
scope to prevent cross initialization errors */
npy_%(dtype_x)s* x_data_ptr =
(npy_%(dtype_x)s*)PyArray_DATA(%(x)s);
npy_%(dtype_z)s* z_data_ptr =
(npy_%(dtype_z)s*)PyArray_DATA(%(z)s);
npy_%(dtype_y)s y_value =
((npy_%(dtype_y)s*)PyArray_DATA(%(y)s))[0];
int x_stride = PyArray_STRIDES(%(x)s)[0] / %(itemsize_x)s;
int z_stride = PyArray_STRIDES(%(z)s)[0] / %(itemsize_z)s;
int x_dim = PyArray_DIMS(%(x)s)[0];
for(int i=0; i < x_dim; i++)
{
z_data_ptr[i * z_stride] = (x_data_ptr[i * x_stride] *
y_value);
}
}
"""
return c_code % locals()
The c_code method accepts variable names as arguments (name, inp, out, sub) and returns a C code
fragment that computes the expression output. In case of error, the %(fail)s statement cleans up and
returns properly.
More complex C Op example
This section introduces a new example, slightly more complex than the previous one, with an op to perform
an element-wise multiplication between the elements of two vectors. This new example differs from the
previous one in its use of the methods c_support_code() and c_support_code_apply() (it does
not need to use them but it does so to explain their use) and its capacity to support inputs of different dtypes.
Recall the method c_support_code() is meant to produce code that will be used for every apply of the
op. This means that the C code in this method must be valid in every setting your op supports. If the op
is meant to supports inputs of various dtypes, the C code in this method should be generic enough to work
with every supported dtype. If the op operates on inputs that can be vectors or matrices, the C code in this
method should be able to accomodate both kinds of inputs.
In our example, the method c_support_code() is used to declare a C function to validate that two
vectors have the same shape. Because our op only supports vectors as inputs, this function is allowed to rely
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on its inputs being vectors. However, our op should support multiple dtypes so this function cannot rely on
a specific dtype in its inputs.
The method c_support_code_apply(), on the other hand, is allowed to depend on the inputs to the op
because it is apply-specific. Therefore, we use it to define a function to perform the multiplication between
two vectors. Variables or functions defined in the method c_support_code_apply() will be included
at the global scale for every apply of the Op. Because of this, the names of those variables and functions
should include the name of the op, like in the example. Otherwise, using the op twice in the same graph will
give rise to conflicts as some elements will be declared more than once.
The last interesting difference occurs in the c_code() method. Because the dtype of the output is variable
and not guaranteed to be the same as any of the inputs (because of the upcast in the method make_node()),
the typenum of the output has to be obtained in the Python code and then included in the C code.
class VectorTimesVector(gof.Op):
__props__ = ()
def make_node(self, x, y):
# Validate the inputs' type
if x.type.ndim != 1:
raise TypeError('x must be a 1-d vector')
if y.type.ndim != 1:
raise TypeError('y must be a 1-d vector')
# Create an output variable of the same type as x
output_var = theano.tensor.TensorType(
dtype=theano.scalar.upcast(x.dtype, y.dtype),
broadcastable=[False])()
return gof.Apply(self, [x, y], [output_var])
def c_code_cache_version(self):
return (1, 0, 2)
def c_support_code(self):
c_support_code = """
bool vector_same_shape(PyArrayObject* arr1,
PyArrayObject* arr2)
{
return (PyArray_DIMS(arr1)[0] == PyArray_DIMS(arr2)[0]);
}
"""
return c_support_code
def c_support_code_apply(self, node, name):
dtype_x = node.inputs[0].dtype
dtype_y = node.inputs[1].dtype
dtype_z = node.outputs[0].dtype
c_support_code = """
void vector_elemwise_mult_%(name)s(npy_%(dtype_x)s* x_ptr,
int x_str, npy_%(dtype_y)s* y_ptr, int y_str,
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npy_%(dtype_z)s* z_ptr, int z_str, int nbElements)
{
for (int i=0; i < nbElements; i++){
z_ptr[i * z_str] = x_ptr[i * x_str] * y_ptr[i * y_str];
}
}
"""
return c_support_code % locals()
def c_code(self, node, name, inp, out, sub):
x, y = inp
z, = out
dtype_x = node.inputs[0].dtype
dtype_y = node.inputs[1].dtype
dtype_z = node.outputs[0].dtype
itemsize_x = numpy.dtype(dtype_x).itemsize
itemsize_y = numpy.dtype(dtype_y).itemsize
itemsize_z = numpy.dtype(dtype_z).itemsize
typenum_z = numpy.dtype(dtype_z).num
fail = sub['fail']
c_code = """
// Validate that the inputs have the same shape
if ( !vector_same_shape(%(x)s, %(y)s))
{
PyErr_Format(PyExc_ValueError, "Shape mismatch : "
"x.shape[0] and y.shape[0] should match but "
"x.shape[0] == %%i and y.shape[0] == %%i",
PyArray_DIMS(%(x)s)[0], PyArray_DIMS(%(y)s)[0]);
%(fail)s;
}
// Validate that the output storage exists and has the same
// dimension as x.
if (NULL == %(z)s || !(vector_same_shape(%(x)s, %(z)s)))
{
/* Reference received to invalid output variable.
Decrease received reference's ref count and allocate new
output variable */
Py_XDECREF(%(z)s);
%(z)s = (PyArrayObject*)PyArray_EMPTY(1,
PyArray_DIMS(%(x)s),
%(typenum_z)s,
0);
if (!%(z)s) {
%(fail)s;
}
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}
// Perform the vector elemwise multiplication
vector_elemwise_mult_%(name)s(
(npy_%(dtype_x)s*)PyArray_DATA(%(x)s),
PyArray_STRIDES(%(x)s)[0] / %(itemsize_x)s,
(npy_%(dtype_y)s*)PyArray_DATA(%(y)s),
PyArray_STRIDES(%(y)s)[0] / %(itemsize_y)s,
(npy_%(dtype_z)s*)PyArray_DATA(%(z)s),
PyArray_STRIDES(%(z)s)[0] / %(itemsize_z)s,
PyArray_DIMS(%(x)s)[0]);
"""
return c_code % locals()
Alternate way of defining C Ops
The two previous examples have covered the standard way of implementing C Ops in Theano by inheriting
from the class Op. This process is mostly simple but it still involves defining many methods as well as
mixing, in the same file, both Python and C code which tends to make the result less readable.
To help with this, Theano defines a class, COp, from which new C ops can inherit. The class COp aims to
simplify the process of implementing C ops by doing the following :
• It allows you to define the C implementation of your op in a distinct C code file. This makes it easier
to keep your Python and C code readable and well indented.
• It can automatically handle all the methods that return C code, in addition to Op.
c_code_cache_version() based on the provided external C implementation.
To illustrate how much simpler the class COp makes the process of defining a new op with a C implementation, let’s revisit the second example of this tutorial, the VectorTimesVector op. In that example,
we implemented an op to perform the task of element-wise vector-vector multiplication. The two following
blocks of code illustrate what the op would look like if it was implemented using the COp class.
The new op is defined inside a Python file with the following code :
import theano
from theano import gof
class VectorTimesVector(gof.COp):
__props__ = ()
func_file = "./vectorTimesVector.c"
func_name = "APPLY_SPECIFIC(vector_times_vector)"
def __init__(self):
super(VectorTimesVector, self).__init__(self.func_file,
self.func_name)
def make_node(self, x, y):
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# Validate the inputs' type
if x.type.ndim != 1:
raise TypeError('x must be a 1-d vector')
if y.type.ndim != 1:
raise TypeError('y must be a 1-d vector')
# Create an output variable of the same type as x
output_var = theano.tensor.TensorType(
dtype=theano.scalar.upcast(x.dtype, y.dtype),
broadcastable=[False])()
return gof.Apply(self, [x, y], [output_var])
And the following is the C implementation of the op, defined in an external C file named vectorTimesVector.c
:
#section support_code
// Support code function
bool vector_same_shape(PyArrayObject* arr1, PyArrayObject* arr2)
{
return (PyArray_DIMS(arr1)[0] == PyArray_DIMS(arr2)[0]);
}
#section support_code_apply
// Apply-specific support function
void APPLY_SPECIFIC(vector_elemwise_mult)(
DTYPE_INPUT_0* x_ptr, int x_str,
DTYPE_INPUT_1* y_ptr, int y_str,
DTYPE_OUTPUT_0* z_ptr, int z_str, int nbElements)
{
for (int i=0; i < nbElements; i++){
z_ptr[i * z_str] = x_ptr[i * x_str] * y_ptr[i * y_str];
}
}
// Apply-specific main function
int APPLY_SPECIFIC(vector_times_vector)(PyArrayObject* input0,
PyArrayObject* input1,
PyArrayObject** output0)
{
// Validate that the inputs have the same shape
if ( !vector_same_shape(input0, input1))
{
PyErr_Format(PyExc_ValueError, "Shape mismatch : "
"input0.shape[0] and input1.shape[0] should "
"match but x.shape[0] == %i and "
"y.shape[0] == %i",
PyArray_DIMS(input0)[0], PyArray_DIMS(input1)[0]);
return 1;
}
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// Validate that the output storage exists and has the same
// dimension as x.
if (NULL == *output0 || !(vector_same_shape(input0, *output0)))
{
/* Reference received to invalid output variable.
Decrease received reference's ref count and allocate new
output variable */
Py_XDECREF(*output0);
*output0 = (PyArrayObject*)PyArray_EMPTY(1,
PyArray_DIMS(input0),
TYPENUM_OUTPUT_0,
0);
if (!*output0) {
PyErr_Format(PyExc_ValueError,
"Could not allocate output storage");
return 1;
}
}
// Perform the actual vector-vector multiplication
APPLY_SPECIFIC(vector_elemwise_mult)(
(DTYPE_INPUT_0*)PyArray_DATA(input0),
PyArray_STRIDES(input0)[0] / ITEMSIZE_INPUT_0,
(DTYPE_INPUT_1*)PyArray_DATA(input1),
PyArray_STRIDES(input1)[0] / ITEMSIZE_INPUT_1,
(DTYPE_OUTPUT_0*)PyArray_DATA(*output0),
PyArray_STRIDES(*output0)[0] / ITEMSIZE_OUTPUT_0,
PyArray_DIMS(input0)[0]);
return 0;
}
As you can see from this example, the Python and C implementations are nicely decoupled which makes
them much more readable than when they were intertwined in the same file and the C code contained string
formatting markers.
Now that we have motivated the COp class, we can have a more precise look at what it does for us. For this,
we go through the various elements that make up this new version of the VectorTimesVector op :
• Parent class : instead of inheriting from the class Op, VectorTimesVector inherits from the class COp.
• Constructor : in our new op, the __init__() method has an important use; to inform the constructor
of the COp class of the location, on the filesystem of the C implementation of this op. To do this, it
gives a list of file paths containing the C code for this op. To auto-generate the c_code method with a
function call you can specify the function name as the second parameter. The paths should be given
as a relative path from the folder where the descendant of the COp class is defined.
• make_node() : the make_node() method is absolutely identical to the one in our old example.
Using the COp class doesn’t change anything here.
• External C code : the external C code implements the various functions associated with the op. Writ-
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ing this C code involves a few subtleties which deserve their own respective sections.
Main function
If you pass a function name to the __init__() method of the COp class, it must respect the following
constraints:
• It must return an int. The value of that int indicates whether the op could perform its task or not.
A value of 0 indicates success while any non-zero value will interrupt the execution of the Theano
function. When returning non-zero the function must set a python exception indicating the details of
the problem.
• It must receive one argument for each input to the op followed by one pointer to an argument for each
output of the op. The types for the argument is dependant on the Types (that is theano Types) of your
inputs and outputs.
For example, the main C function of an op that takes two TensorTypes (which has PyArrayObject * as
its C type) as inputs and returns both their sum and the difference between them would have four parameters
(two for the op’s inputs and two for its outputs) and it’s signature would look something like this :
int sumAndDiffOfScalars(PyArrayObject* in0, PyArrayObject* in1,
PyArrayObject** out0, PyArrayObject** out1)
Macros
For certain section tags, your C code can benefit from a number of pre-defined macros. These section tags
have no macros: init_code, support_code. All other tags will have the support macros discussed
below.
• APPLY_SPECIFIC(str) which will automatically append a name unique to the Apply node that
applies the Op at the end of the provided str. The use of this macro is discussed futher below.
For every input which has a dtype attribute (this means Tensors, and equivalent types on GPU), the following macros will be defined unless your Op class has an Op.check_input attribute defined to False.
In these descrptions ‘i’ refers to the position (indexed from 0) in the input array.
• DTYPE_INPUT_{i} : NumPy dtype of the data in the array. This is the variable type corresponding
to the NumPy dtype, not the string representation of the NumPy dtype. For instance, if the op’s first
input is a float32 ndarray, then the macro DTYPE_INPUT_0 corresponds to npy_float32 and can
directly be used to declare a new variable of the same dtype as the data in the array :
DTYPE_INPUT_0 myVar = someValue;
• TYPENUM_INPUT_{i} : Typenum of the data in the array
• ITEMSIZE_INPUT_{i} : Size, in bytes, of the elements in the array.
In the same way, the macros DTYPE_OUTPUT_{i},
TYPENUM_OUTPUT_{i} are defined for every output ‘i’ of the op.
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In addition to these macros, the init_code_struct, code, and code_cleanup section tags also
have the following macros:
• FAIL : Code to insert at error points. A python exception should be set prior to this code. An
invocation look like this:
if (error) {
// Set python exception
FAIL
}
You can add a semicolon after the macro if it makes your editor happy.
• PARAMS : Name of the params variable for this node. (only for Ops which have params, which is
discussed elsewhere)
Finally the tag code and code_cleanup have macros to pass the inputs and output names. These are
name INPUT_{i} and OUTPUT_{i} where i is the 0-based index position in the input and output arrays
respectively.
Support code
Certain section are limited in what you can place in them due to semantic and syntactic restrictions of the
C++ language. Most of these restrictions apply to the tags that end in _struct.
When we defined the VectorTimesVector op without using the COp class, we had to make a distinction
between two types of support_code : the support code that was apply-specific and the support code that
wasn’t. The apply-specific code was defined in the c_support_code_apply() method and the elements defined in that code (global variables and functions) had to include the name of the Apply node in
their own names to avoid conflicts between the different versions of the apply-specific code. The code that
wasn’t apply-specific was simply defined in the c_support_code() method.
To make indentifiers that include the Apply node name use the APPLY_SPECIFIC(str) macro. In
the above example, this macro is used when defining the functions vector_elemwise_mult() and
vector_times_vector() as well as when calling function vector_elemwise_mult() from inside vector_times_vector().
When using the COp class, we still have to make the distinction between C code for each of the methods of
a C class. These sections of code are separated by #section <tag> markers. The tag determines the
name of the method this C code applies to with the rule that <tag> applies to c_<tag>. Unknown tags are
an error and will be reported. Duplicate tags will be merged together in the order the appear in the C files.
The rules for knowing if where a piece of code should be put can be sometimes tricky. The key thing to
remember is that things that can be shared between instances of the op should be apply-agnostic and go into
a section which does not end in _apply or _struct. The distinction of _apply and _struct mostly
hinghes on how you want to manange the lifetime of the object. Note that to use an apply-specific object,
you have to be in a apply-specific section, so some portions of the code that might seem apply-agnostic may
still be apply-specific because of the data they use (this does not include arguments).
In the above example, the function vector_same_shape() is apply-agnostic because it uses none
of the macros defined by the class COp and it doesn’t rely on any apply-specific code. The function
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vector_elemwise_mult() is apply-specific because it uses the macros defined by COp. Finally,
the function vector_times_vector() is apply-specific because it uses those same macros and also
because it calls vector_elemwise_mult() which is an apply-specific function.
Using GDB to debug Op’s C code
When debugging C code, it can be useful to use GDB for code compiled by Theano.
For this, you must enable this Theano: cmodule.remove_gxx_opt=True. For the GPU, you must add in this
second flag nvcc.flags=-g (it slow down computation on the GPU, but it is enabled by default on the CPU).
Then you must start Python inside GDB and in it start your Python process (e.g. theano-nose):
$gdb python
(gdb)r bin/theano-nose theano/
Quick guide to GDB.
Final Note
This tutorial focuses on providing C implementations to ops that manipulate Theano tensors. For more
information about other Theano types, you can refer to the section Alternate Theano Types.
Writing an Op to work on an ndarray in C
This section walks through a non-trivial example Op that does something pretty weird and unrealistic, that
is hard to express with existing Ops. (Technically, we could use Scan to implement the Op we’re about to
describe, but we ignore that possibility for the sake of example.)
The following code works, but important error-checking has been omitted for clarity. For example, when
you write C code that assumes memory is contiguous, you should check the strides and alignment.
import theano
class Fibby(theano.Op):
"""
An arbitrarily generalized Fibbonacci sequence
"""
__props__ = ()
def make_node(self, x):
x_ = tensor.as_tensor_variable(x)
assert x_.ndim == 1
return theano.Apply(self,
inputs=[x_],
outputs=[x_.type()])
# using x_.type() is dangerous, it copies x's broadcasting behaviour
def perform(self, node, inputs, output_storage):
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x, = inputs
y = output_storage[0][0] = x.copy()
for i in range(2, len(x)):
y[i] = y[i-1] * y[i-2] + x[i]
def c_code(self, node, name, inames, onames, sub):
x, = inames
y, = onames
fail = sub['fail']
return """
Py_XDECREF(%(y)s);
%(y)s = (PyArrayObject*)PyArray_FromArray(
%(x)s, 0, NPY_ARRAY_ENSURECOPY);
if (!%(y)s)
%(fail)s;
{//New scope needed to make compilation work
dtype_%(y)s * y = (dtype_%(y)s*)PyArray_DATA(%(y)s);
dtype_%(x)s * x = (dtype_%(x)s*)PyArray_DATA(%(x)s);
for (int i = 2; i < PyArray_DIMS(%(x)s)[0]; ++i)
y[i] = y[i-1]*y[i-2] + x[i];
}
""" % locals()
def c_code_cache_version(self):
return (1,)
fibby = Fibby()
In the first two lines of the C function, we make y point to a new array with the correct size for the output.
This is essentially simulating the line y = x.copy(). The variables %(x)s and %(y)s are set up by the
TensorType to be PyArrayObject pointers. TensorType also set up dtype_%(x)s to be a typdef to the
C type for x.
Py_XDECREF(%(y)s);
%(y)s = (PyArrayObject*)PyArray_FromArray(
%(x)s, 0, NPY_ARRAY_ENSURECOPY);
The first line reduces the reference count of the data that y originally pointed to. The second line allocates
the new data and makes y point to it.
In C code for a theano op, numpy arrays are represented as PyArrayObject C structs. This is part of the
numpy/scipy C API documented at http://docs.scipy.org/doc/numpy/reference/c-api.types-and-structures.
html
TODO: NEEDS MORE EXPLANATION.
Writing an Optimization
fibby of a vector of zeros is another vector of zeros of the same size. Theano does not attempt to infer
this from the code provided via Fibby.perform or Fibby.c_code. However, we can write an optimization that makes use of this observation. This sort of local substitution of special cases is common, and
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there is a stage of optimization (specialization) devoted to such optimizations. The following optimization
(fibby_of_zero) tests whether the input is guaranteed to be all zero, and if so it returns the input itself
as a replacement for the old output.
TODO: talk about OPTIMIZATION STAGES
from theano.tensor.opt import get_scalar_constant_value,
˓→NotScalarConstantError
# Remove any fibby(zeros(...))
@theano.tensor.opt.register_specialize
@theano.gof.local_optimizer([fibby])
def fibby_of_zero(node):
if node.op == fibby:
x = node.inputs[0]
try:
if numpy.all(0 == get_scalar_constant_value(x)):
return [x]
except NotScalarConstantError:
pass
The register_specialize decorator is what activates our optimization, and tells Theano to use it
in the specialization stage. The local_optimizer decorator builds a class instance around our global
function. The [fibby] argument is a hint that our optimizer works on nodes whose .op attribute equals
fibby. The function here (fibby_of_zero) expects an Apply instance as an argument for parameter
node. It tests using function get_scalar_constant_value, which determines if a Variable (x) is
guaranteed to be a constant, and if so, what constant.
Test the optimization
Here is some code to test that the optimization is applied only when needed.
import numpy
import theano.tensor as T
from theano import function
from theano import tensor
# Test it does not apply when not needed
x = T.dvector()
f = function([x], fibby(x))
# We call the function to make sure it runs.
# If you run in DebugMode, it will compare the C and Python outputs.
f(numpy.random.rand(5))
topo = f.maker.fgraph.toposort()
assert len(topo) == 1
assert isinstance(topo[0].op, Fibby)
# Test that the optimization gets applied.
f_zero = function([], fibby(T.zeros([5])))
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# If you run in DebugMode, it will compare the output before
# and after the optimization.
f_zero()
# Check that the optimization removes the Fibby Op.
# For security, the Theano memory interface ensures that the output
# of the function is always memory not aliased to the input.
# That is why there is a DeepCopyOp op.
topo = f_zero.maker.fgraph.toposort()
assert len(topo) == 1
assert isinstance(topo[0].op, theano.compile.ops.DeepCopyOp)
Overview of the compilation pipeline
The purpose of this page is to explain each step of defining and compiling a Theano function.
Definition of the computation graph
By creating Theano Variables using theano.tensor.lscalar or theano.tensor.dmatrix or
by using Theano functions such as theano.tensor.sin or theano.tensor.log, the user builds a
computation graph. The structure of that graph and details about its components can be found in the Graph
Structures article.
Compilation of the computation graph
Once the user has built a computation graph, she can use theano.function in order to make one or
more functions that operate on real data. function takes a list of input Variables as well as a list of output
Variables that define a precise subgraph corresponding to the function(s) we want to define, compile that
subgraph and produce a callable.
Here is an overview of the various steps that are done with the computation graph in the compilation phase:
Step 1 - Create a FunctionGraph
The subgraph given by the end user is wrapped in a structure called FunctionGraph. That structure defines
several hooks on adding and removing (pruning) nodes as well as on modifying links between nodes (for
example, modifying an input of an Apply node) (see the article about fg – Graph Container [doc TODO] for
more information).
FunctionGraph provides a method to change the input of an Apply node from one Variable to another and a
more high-level method to replace a Variable with another. This is the structure that Optimizers work on.
Some relevant Features are typically added to the FunctionGraph, namely to prevent any optimization from
operating inplace on inputs declared as immutable.
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Step 2 - Execute main Optimizer
Once the FunctionGraph is made, an optimizer is produced by the mode passed to function (the Mode
basically has two important fields, linker and optimizer). That optimizer is applied on the FunctionGraph using its optimize() method.
The optimizer is typically obtained through optdb.
Step 3 - Execute linker to obtain a thunk
Once the computation graph is optimized, the linker is extracted from the Mode. It is then called with
the FunctionGraph as argument to produce a thunk, which is a function with no arguments that returns
nothing. Along with the thunk, one list of input containers (a theano.gof.Container is a sort of object that
wraps another and does type casting) and one list of output containers are produced, corresponding to the
input and output Variables as well as the updates defined for the inputs when applicable. To perform the
computations, the inputs must be placed in the input containers, the thunk must be called, and the outputs
must be retrieved from the output containers where the thunk put them.
Typically, the linker calls the toposort method in order to obtain a linear sequence of operations to
perform. How they are linked together depends on the Linker used. The CLinker produces a single block
of C code for the whole computation, whereas the OpWiseCLinker produces one thunk for each individual
operation and calls them in sequence.
The linker is where some options take effect: the strict flag of an input makes the associated input
container do type checking. The borrow flag of an output, if False, adds the output to a no_recycling
list, meaning that when the thunk is called the output containers will be cleared (if they stay there, as would
be the case if borrow was True, the thunk would be allowed to reuse (or “recycle”) the storage).
Note: Compiled libraries are stored within a specific compilation directory, which by default is set to
$HOME/.theano/compiledir_xxx, where xxx identifies the platform (under Windows the default
location is instead $LOCALAPPDATA\Theano\compiledir_xxx). It may be manually set to a different location either by setting config.compiledir or config.base_compiledir, either within
your Python script or by using one of the configuration mechanisms described in config.
The compile cache is based upon the C++ code of the graph to be compiled. So, if you change compilation configuration variables, such as config.blas.ldflags, you will need to manually remove your
compile cache, using Theano/bin/theano-cache clear
Theano also implements a lock mechanism that prevents multiple compilations within the same compilation
directory (to avoid crashes with paralell execution of some scripts). This mechanism is currently enabled by
default, but if it causes any problem it may be disabled using the function theano.gof.compilelock.
set_lock_status(..).
Step 4 - Wrap the thunk in a pretty package
The thunk returned by the linker along with input and output containers is unwieldy. function hides that
complexity away so that it can be used like a normal function with arguments and return values.
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Theano vs. C
We describe some of the patterns in Theano, and present their closest analogue in a statically typed language
such as C:
Theano
Apply
Variable
Shared Variable
Op
Type
C
function application / function call
local function data / variable
global function data / variable
operations carried out in computation / function definition
data types
For example:
int d = 0;
int main(int a) {
int b = 3;
int c = f(b)
d = b + c;
return g(a, c);
}
Based on this code snippet, we can relate f and g to Ops, a, b and c to Variables, d to Shared Variable,
g(a, c), f(b) and d = b + c (taken as meaning the action of computing f, g or + on their respective
inputs) to Applies. Lastly, int could be interpreted as the Theano Type of the Variables a, b, c and d.
Making the double type
Type’s contract
In Theano’s framework, a Type (gof.type.Type) is any object which defines the following methods.
To obtain the default methods described below, the Type should be an instance of Type or should be an
instance of a subclass of Type. If you will write all methods yourself, you need not use an instance of
Type.
Methods with default arguments must be defined with the same signature, i.e. the same default argument
names and values. If you wish to add extra arguments to any of these methods, these extra arguments must
have default values.
class PureType
filter(value, strict=False, allow_downcast=None)
This casts a value to match the Type and returns the cast value. If value is incompatible
with the Type, the method must raise an exception. If strict is True, filter must return a
reference to value (i.e. casting prohibited). If strict is False, then casting may happen, but
downcasting should only be used in two situations:
•if allow_downcast is True
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•if allow_downcast is None and the default behavior for this type allows downcasting
for the given value (this behavior is type-dependent, you may decide what your own type
does by default)
We need to define filter with three arguments. The second argument must be called strict
(Theano often calls it by keyword) and must have a default value of False. The third argument
must be called allow_downcast and must have a default value of None.
filter_inplace(value, storage, strict=False, allow_downcast=None)
If filter_inplace is defined, it will be called instead of filter() This is to allow reusing the old
allocated memory. As of this writing this is used only when we transfer new data to a shared
variable on the gpu.
storage will be the old value. i.e. The old numpy array, CudaNdarray, ...
is_valid_value(value)
Returns True iff the value is compatible with the Type. If filter(value, strict =
True) does not raise an exception, the value is compatible with the Type.
Default: True iff filter(value, strict=True) does not raise an exception.
values_eq(a, b)
Returns True iff a and b are equal.
Default: a == b
values_eq_approx(a, b)
Returns True iff a and b are approximately equal, for a definition of “approximately” which
varies from Type to Type.
Default: values_eq(a, b)
make_variable(name=None)
Makes a Variable of this Type with the specified name, if name is not None. If name is None,
then the Variable does not have a name. The Variable will have its type field set to the Type
object.
Default: there is a generic definition of this in Type. The Variable’s type will be the object that
defines this method (in other words, self).
__call__(name=None)
Syntactic shortcut to make_variable.
Default: make_variable
__eq__(other)
Used to compare Type instances themselves
Default: object.__eq__
__hash__()
Types should not be mutable, so it should be OK to define a hash function. Typically this
function should hash all of the terms involved in __eq__.
Default: id(self)
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get_shape_info(obj)
Optional. Only needed to profile the memory of this Type of object.
Return the information needed to compute the memory size of obj.
The memory size is only the data, so this excludes the container. For an ndarray, this is the data,
but not the ndarray object and other data structures such as shape and strides.
get_shape_info() and get_size() work in tandem for the memory profiler.
get_shape_info() is called during the execution of the function. So it is better that it is not
too slow.
get_size() will be called on the output of this function when printing the memory profile.
Parameters obj – The object that this Type represents during execution
Returns Python object that self.get_size() understands
get_size(shape_info)
Number of bytes taken by the object represented by shape_info.
Optional. Only needed to profile the memory of this Type of object.
Parameters shape_info – the output of the call to get_shape_info()
Returns the number of bytes taken by the object described by shape_info.
clone(dtype=None, broadcastable=None)
Optional, for TensorType-alikes.
Return a copy of the type with a possibly changed value for dtype and broadcastable (if they
aren’t None).
Parameters
• dtype – New dtype for the copy.
• broadcastable – New broadcastable tuple for the copy.
may_share_memory(a, b)
Optional to run, but mandatory for DebugMode. Return True if the Python objects a and b could
share memory. Return False otherwise. It is used to debug when Ops did not declare memory
aliasing between variables. Can be a static method. It is highly recommended to use and is
mandatory for Type in Theano as our buildbot runs in DebugMode.
For each method, the default is what Type defines for you. So, if you create an instance of Type
or an instance of a subclass of Type, you must define filter. You might want to override
values_eq_approx, as well as values_eq. The other defaults generally need not be overridden.
For more details you can go see the documentation for Type.
Additional definitions
For certain mechanisms, you can register functions and other such things to plus your type into theano’s
mechanisms. These are optional but will allow people to use you type with familiar interfaces.
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transfer()
To plug in additional options for the transfer target, define a function which takes a theano variable and
a target argument and returns eitehr a new transferred variable (which can be the same as the input if no
transfer is nessecary) or returns None if the transfer can’t be done.
Then register that function by calling register_transfer() with it as argument.
Defining double
We are going to base Type double on Python’s float. We must define filter and shall override
values_eq_approx.
filter
# Note that we shadow Python's function ``filter`` with this
# definition.
def filter(x, strict=False, allow_downcast=None):
if strict:
if isinstance(x, float):
return x
else:
raise TypeError('Expected a float!')
elif allow_downcast:
return float(x)
else:
# Covers both the False and None cases.
x_float = float(x)
if x_float == x:
return x_float
else:
raise TypeError('The double type cannot accurately represent '
'value %s (of type %s): you must explicitly '
'allow downcasting if you want to do this.'
% (x, type(x)))
If strict is True we need to return x. If strict is True and x is not a float (for example, x could
easily be an int) then it is incompatible with our Type and we must raise an exception.
If strict is False then we are allowed to cast x to a float, so if x is an int it we will
return an equivalent float. However if this cast triggers a precision loss (x != float(x)) and
allow_downcast is not True, then we also raise an exception. Note that here we decided that the
default behavior of our type (when allow_downcast is set to None) would be the same as when
allow_downcast is False, i.e. no precision loss is allowed.
values_eq_approx
def values_eq_approx(x, y, tolerance=1e-4):
return abs(x - y) / (abs(x) + abs(y)) < tolerance
The second method we define is values_eq_approx. This method allows approximate comparison between two values respecting our Type’s constraints. It might happen that an optimization changes the compu-
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tation graph in such a way that it produces slightly different variables, for example because of numerical instability like rounding errors at the end of the mantissa. For instance, a + a + a + a + a + a might
not actually produce the exact same output as 6 * a (try with a=0.1), but with values_eq_approx we
do not necessarily mind.
We added an extra tolerance argument here. Since this argument is not part of the API, it must have a
default value, which we chose to be 1e-4.
Note: values_eq is never actually used by Theano, but it might be used internally in the future. Equality
testing in DebugMode is done using values_eq_approx.
Putting them together
What we want is an object that respects the aforementioned contract. Recall that Type defines default
implementations for all required methods of the interface, except filter. One way to make the Type is to
instantiate a plain Type and set the needed fields:
from theano import gof
double = gof.Type()
double.filter = filter
double.values_eq_approx = values_eq_approx
Another way to make this Type is to make a subclass of gof.Type and define filter and
values_eq_approx in the subclass:
from theano import gof
class Double(gof.Type):
def filter(self, x, strict=False, allow_downcast=None):
# See code above.
...
def values_eq_approx(self, x, y, tolerance=1e-4):
# See code above.
...
double = Double()
double is then an instance of Type Double, which in turn is a subclass of Type.
There is a small issue with defining double this way. All instances of Double are technically the same
Type. However, different Double Type instances do not compare the same:
>>> double1 = Double()
>>> double2 = Double()
>>> double1 == double2
False
Theano compares Types using == to see if they are the same. This happens in DebugMode. Also, Ops can
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(and should) ensure that their inputs have the expected Type by checking something like if x.type ==
lvector.
There are several ways to make sure that equality testing works properly:
1. Define Double.__eq__ so that instances of type Double are equal. For example:
def __eq__(self, other):
return type(self) is Double and type(other) is Double
2. Override Double.__new__ to always return the same instance.
3. Hide the Double class and only advertise a single instance of it.
Here we will prefer the final option, because it is the simplest. Ops in the Theano code often define the
__eq__ method though.
Untangling some concepts
Initially, confusion is common on what an instance of Type is versus a subclass of Type or an instance of
Variable. Some of this confusion is syntactic. A Type is any object which has fields corresponding to the
functions defined above. The Type class provides sensible defaults for all of them except filter, so when
defining new Types it is natural to subclass Type. Therefore, we often end up with Type subclasses and it is
can be confusing what these represent semantically. Here is an attempt to clear up the confusion:
• An instance of Type (or an instance of a subclass) is a set of constraints on real data. It is akin to a
primitive type or class in C. It is a static annotation.
• An instance of Variable symbolizes data nodes in a data flow graph. If you were to parse the C
expression int x;, int would be a Type instance and x would be a Variable instance of that Type
instance. If you were to parse the C expression c = a + b;, a, b and c would all be Variable
instances.
• A subclass of Type is a way of implementing a set of Type instances that share structural similarities.
In the double example that we are doing, there is actually only one Type in that set, therefore the
subclass does not represent anything that one of its instances does not. In this case it is a singleton,
a set with one element. However, the TensorType class in Theano (which is a subclass of Type)
represents a set of types of tensors parametrized by their data type or number of dimensions. We could
say that subclassing Type builds a hierarchy of Types which is based upon structural similarity rather
than compatibility.
Final version
from theano import gof
class Double(gof.Type):
def filter(self, x, strict=False, allow_downcast=None):
if strict:
if isinstance(x, float):
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return x
else:
raise TypeError('Expected a float!')
elif allow_downcast:
return float(x)
else:
# Covers both the False and None cases.
x_float = float(x)
if x_float == x:
return x_float
else:
raise TypeError('The double type cannot accurately represent
˓→
'
'value %s (of type %s): you must explicitly '
'allow downcasting if you want to do this.'
% (x, type(x)))
def values_eq_approx(self, x, y, tolerance=1e-4):
return abs(x - y) / (abs(x) + abs(y)) < tolerance
def __str__(self):
return "double"
double = Double()
We add one utility function, __str__. That way, when we print double, it will print out something
intelligible.
Making arithmetic Ops on double
Now that we have a double type, we have yet to use it to perform computations. We’ll start by defining
multiplication.
Op’s contract
An Op is any object which inherits from gof.Op. It has to define the following methods.
make_node(*inputs)
This method is responsible for creating output Variables of a suitable symbolic Type to serve as
the outputs of this Op’s application. The Variables found in *inputs must be operated on using
Theano’s symbolic language to compute the symbolic output Variables. This method should put these
outputs into an Apply instance, and return the Apply instance.
This method creates an Apply node representing the application of the Op on the inputs provided. If
the Op cannot be applied to these inputs, it must raise an appropriate exception.
The inputs of the Apply instance returned by this call must be ordered correctly: a subsequent self.
make_node(*apply.inputs) must produce something equivalent to the first apply.
perform(node, inputs, output_storage)
This method computes the function associated to this Op. node is an Apply node created by the
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Op’s make_node method. inputs is a list of references to data to operate on using non-symbolic
statements, (i.e., statements in Python, Numpy). output_storage is a list of storage cells where
the variables of the computation must be put.
More specifically:
•node: This is a reference to an Apply node which was previously obtained via the Op‘s
make_node method. It is typically not used in simple Ops, but it contains symbolic information that could be required for complex Ops.
•inputs: This is a list of data from which the values stored in output_storage are to be
computed using non-symbolic language.
•output_storage: This is a list of storage cells where the output is to be stored. A storage cell is a one-element list. It is forbidden to change the length of the list(s) contained in
output_storage. There is one storage cell for each output of the Op.
The data put in output_storage must match the type of the symbolic output. This is a
situation where the node argument can come in handy.
A function Mode may allow output_storage elements to persist between evaluations, or
it may reset output_storage cells to hold a value of None. It can also pre-allocate some
memory for the Op to use. This feature can allow perform to reuse memory between calls, for
example. If there is something preallocated in the output_storage, it will be of the good
dtype, but can have the wrong shape and have any stride pattern.
This method must be determined by the inputs. That is to say, if it is evaluated once on inputs A and
returned B, then if ever inputs C, equal to A, are presented again, then outputs equal to B must be
returned again.
You must be careful about aliasing outputs to inputs, and making modifications to any of the inputs.
See Views and inplace operations before writing a perform implementation that does either of these
things.
Instead (or in addition to) perform() You can also provide a C implementation of For more details, refer
to the documentation for Op.
__eq__(other)
other is also an Op.
Returning True here is a promise to the optimization system that the other Op will produce exactly
the same graph effects (from perform) as this one, given identical inputs. This means it will produce
the same output values, it will destroy the same inputs (same destroy_map), and will alias outputs to
the same inputs (same view_map). For more details, see Views and inplace operations.
Note: If you set __props__, this will be automatically generated.
__hash__()
If two Op instances compare equal, then they must return the same hash value.
Equally important, this hash value must not change during the lifetime of self. Op instances should
be immutable in this sense.
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Note: If you set __props__, this will be automatically generated.
Optional methods or attributes
__props__
Default: Undefined
Must be a tuple. Lists the name of the attributes which influence the computation performed. This will
also enable the automatic generation of appropriate __eq__, __hash__ and __str__ methods. Should
be set to () if you have no attributes that are relevant to the computation to generate the methods.
New in version 0.7.
default_output
Default: None
If this member variable is an integer, then the default implementation of __call__ will return
node.outputs[self.default_output], where node was returned by make_node. Otherwise, the entire list of outputs will be returned, unless it is of length 1, where the single element will
be returned by itself.
make_thunk(node, storage_map, compute_map, no_recycling)
This function must return a thunk, that is a zero-arguments function that encapsulates the computation
to be performed by this op on the arguments of the node.
Parameters
• node – Apply instance The node for which a thunk is requested.
• storage_map – dict of lists This maps variables to a one-element lists holding
the variable’s current value. The one-element list acts as pointer to the value and
allows sharing that “pointer” with other nodes and instances.
• compute_map – dict of lists This maps variables to one-element lists holding
booleans. If the value is 0 then the variable has not been computed and the value
should not be considered valid. If the value is 1 the variable has been computed
and the value is valid. If the value is 2 the variable has been garbage-collected
and is no longer valid, but shouldn’t be required anymore for this call.
• no_recycling – WRITEME WRITEME
The returned function must ensure that is sets the computed variables as computed in the compute_map.
Defining this function removes the requirement for perform() or C code, as you will define the
thunk for the computation yourself.
__call__(*inputs, **kwargs)
By default this is a convenience function which calls make_node() with the supplied arguments
and returns the result indexed by default_output. This can be overridden by subclasses to do anything
else, but must return either a theano Variable or a list of Variables.
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If you feel the need to override __call__ to change the graph based on the arguments, you should
instead create a function that will use your Op and build the graphs that you want and call that instead
of the Op instance directly.
infer_shape(node, shapes)
This function is needed for shape optimization. shapes is a list with one tuple for each input of the
Apply node (which corresponds to the inputs of the op). Each tuple contains as many elements as the
number of dimensions of the corresponding input. The value of each element is the shape (number of
items) along the corresponding dimension of that specific input.
While this might sound complicated, it is nothing more than the shape of each input as symbolic
variables (one per dimension).
The function should return a list with one tuple for each output. Each tuple should contain the corresponding output’s computed shape.
Implementing this method will allow Theano to compute the output’s shape without computing the
output itself, potentially sparing you a costly recomputation.
flops(inputs, outputs)
It is only used to have more information printed by the memory profiler. It makes it print the mega
flops and giga flops per second for each apply node. It takes as inputs two lists: one for the inputs and
one for the outputs. They contain tuples that are the shapes of the corresponding inputs/outputs.
__str__()
This allows you to specify a more informative string representation of your Op. If an Op has parameters, it is highly recommended to have the __str__ method include the name of the op and the Op’s
parameters’ values.
Note: If you set __props__, this will be automatically generated. You can still overide it for custom
output.
do_constant_folding(node)
Default: Return True
By default when optimizations are enabled, we remove during function compilation Apply nodes
whose inputs are all constants. We replace the Apply node with a Theano constant variable. This
way, the Apply node is not executed at each function call. If you want to force the execution of an op
during the function call, make do_constant_folding return False.
As done in the Alloc op, you can return False only in some cases by analyzing the graph from the
node parameter.
debug_perform(node, inputs, output_storage)
Undefined by default.
If you define this function then it will be used instead of C code or perform() to do the computation
while debugging (currently DebugMode, but others may also use it in the future). It has the same
signature and contract as perform().
This enables ops that cause trouble with DebugMode with their normal behaviour to adopt a different
one when run under that mode. If your op doesn’t have any problems, don’t implement this.
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If you want your op to work with gradient.grad() you also need to implement the functions described below.
Gradient
These are the function required to work with gradient.grad().
grad(inputs, output_gradients)
If the Op being defined is differentiable, its gradient may be specified symbolically in this method.
Both inputs and output_gradients are lists of symbolic Theano Variables and those must
be operated on using Theano’s symbolic language. The grad method must return a list containing
one Variable for each input. Each returned Variable represents the gradient with respect to that input
computed based on the symbolic gradients with respect to each output.
If the output is not differentiable with respect to an input then this method should be defined to return
a variable of type NullType for that input. Likewise, if you have not implemented the grad computation for some input, you may return a variable of type NullType for that input. theano.gradient
contains convenience methods that can construct the variable for you: theano.gradient.
grad_undefined() and theano.gradient.grad_not_implemented(), respectively.
If an element of output_gradient is of type theano.gradient.DisconnectedType, it means that the cost
is not a function of this output. If any of the op’s inputs participate in the computation of only
disconnected outputs, then Op.grad should return DisconnectedType variables for those inputs.
If the grad method is not defined, then Theano assumes it has been forgotten. Symbolic differentiation
will fail on a graph that includes this Op.
It must be understood that the Op’s grad method is not meant to return the gradient of the Op’s output.
theano.tensor.grad computes gradients; Op.grad is a helper function that computes terms that appear
in gradients.
If an Op has a single vector-valued output y and a single vector-valued input x, then the grad method
will be passed x and a second vector z. Define J to be the Jacobian of y with respect to x. The Op’s
grad method should return dot(J.T,z). When theano.tensor.grad calls the grad method, it will set z to
be the gradient of the cost C with respect to y. If this op is the only op that acts on x, then dot(J.T,z)
is the gradient of C with respect to x. If there are other ops that act on x, theano.tensor.grad will have
to add up the terms of x’s gradient contributed by the other op’s grad method.
In practice, an op’s input and output are rarely implemented as single vectors. Even if an op’s output
consists of a list containing a scalar, a sparse matrix, and a 4D tensor, you can think of these objects
as being formed by rearranging a vector. Likewise for the input. In this view, the values computed by
the grad method still represent a Jacobian-vector product.
In practice, it is probably not a good idea to explicitly construct the Jacobian, which might be very
large and very sparse. However, the returned value should be equal to the Jacobian-vector product.
So long as you implement this product correctly, you need not understand what theano.tensor.grad is
doing, but for the curious the mathematical justification is as follows:
In essence, the grad method must simply implement through symbolic Variables and operations the
chain rule of differential calculus. The chain rule is the mathematical procedure that allows one to
calculate the total derivative 𝑑𝐶
𝑑𝑥 of the final scalar symbolic Variable C with respect to a primitive symbolic Variable x found in the list inputs. The grad method does this using output_gradients
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which provides the total derivative
𝑑𝐶
𝑑𝑓
of C with respect to a symbolic Variable that is returned by the
Op (this is provided in output_gradients), as well as the knowledge of the total derivative
of the latter with respect to the primitive Variable (this has to be computed).
𝑑𝑓
𝑑𝑥
In mathematics, the total derivative of a scalar variable (C) with respect to a vector of scalar variables
(x), i.e. the gradient, is customarily represented as the row vector of the partial derivatives, whereas the
total derivative of a vector of scalar variables (f) with respect to another (x), is customarily represented
by the matrix of the partial derivatives, i.e.the jacobian matrix. In this convenient setting, the chain rule
instructs that the gradient of the final scalar variable C with respect to the primitive scalar variables in
𝑑𝑓
𝑑𝐶
x through those in f is simply given by the matrix product: 𝑑𝐶
𝑑𝑥 = 𝑑𝑓 * 𝑑𝑥 .
Here, the chain rule must be implemented in a similar but slightly more complex setting: Theano
provides in the list output_gradients one gradient for each of the Variables returned by the Op.
Where f is one such particular Variable, the corresponding gradient found in output_gradients
and representing 𝑑𝐶
𝑑𝑓 is provided with a shape similar to f and thus not necessarily as a row vector of
scalars. Furthermore, for each Variable x of the Op’s list of input variables inputs, the returned
gradient representing 𝑑𝐶
𝑑𝑥 must have a shape similar to that of Variable x.
If the output list of the op is [𝑓1 , ...𝑓𝑛 ], then the list output_gradients is
[𝑔𝑟𝑎𝑑𝑓1 (𝐶), 𝑔𝑟𝑎𝑑𝑓2 (𝐶), ..., 𝑔𝑟𝑎𝑑𝑓𝑛 (𝐶)]. If inputs consists of the list [𝑥1 , ..., 𝑥𝑚 ], then Op.grad
𝜕𝑍
should return the list [𝑔𝑟𝑎𝑑𝑥1 (𝐶), 𝑔𝑟𝑎𝑑𝑥2 (𝐶), ..., 𝑔𝑟𝑎𝑑𝑥𝑚 (𝐶)], where (𝑔𝑟𝑎𝑑𝑦 (𝑍))𝑖 = 𝜕𝑦
(and 𝑖 can
𝑖
stand for multiple dimensions).
In other words, grad() does not return
𝑑𝐶
𝑑𝑥𝑗
chain rule:
by grad().
=
𝑑𝐶 𝑑𝑓𝑖
𝑑𝑓𝑖 · 𝑑𝑥𝑗 .
𝑑𝑓𝑖
𝑑𝑥𝑗 ,
but instead the appropriate dot product specified by the
Both the partial differentiation and the multiplication have to be performed
Theano currently imposes the following constraints on the values returned by the grad method:
1.They must be Variable instances.
2.When they are types that have dtypes, they must never have an integer dtype.
The output gradients passed to Op.grad will also obey these constraints.
Integers are a tricky subject. Integers are the main reason for having DisconnectedType, NullType or
zero gradient. When you have an integer as an argument to your grad method, recall the definition of
a derivative to help you decide what value to return:
𝑑𝑓
𝑑𝑥
= lim𝜖→0 (𝑓 (𝑥 + 𝜖) − 𝑓 (𝑥))/𝜖.
Suppose your function f has an integer-valued output. For most functions you’re likely to implement
in theano, this means your gradient should be zero, because f(x+epsilon) = f(x) for almost all x. (The
only other option is that the gradient could be undefined, if your function is discontinuous everywhere,
like the rational indicator function)
Suppose your function f has an integer-valued input. This is a little trickier, because you need to think
about what you mean mathematically when you make a variable integer-valued in theano. Most of the
time in machine learning we mean “f is a function of a real-valued x, but we are only going to pass
in integer-values of x”. In this case, f(x+epsilon) exists, so the gradient through f should be the same
whether x is an integer or a floating point variable. Sometimes what we mean is “f is a function of
an integer-valued x, and f is only defined where x is an integer.” Since f(x+epsilon) doesn’t exist, the
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gradient is undefined. Finally, many times in theano, integer valued inputs don’t actually affect the
elements of the output, only its shape.
If your function f has both an integer-valued input and an integer-valued output, then both rules have
to be combined:
•If f is defined at (x+epsilon), then the input gradient is defined. Since f(x+epsilon) would be
equal to f(x) almost everywhere, the gradient should be 0 (first rule).
•If f is only defined where x is an integer, then the gradient is undefined, regardless of what the
gradient with respect to the output is.
Examples:
1.f(x,y) = dot product between x and y. x and y are integers. Since the output is also an integer, f is a step function. Its gradient is zero almost everywhere, so Op.grad should return
zeros in the shape of x and y.
2.f(x,y) = dot product between x and y. x is floating point and y is an integer. In this case the
output is floating point. It doesn’t matter that y is an integer. We consider f to still be
defined at f(x,y+epsilon). The gradient is exactly the same as if y were floating point.
3.f(x,y) = argmax of x along axis y. The gradient with respect to y is undefined, because f(x,y)
is not defined for floating point y. How could you take an argmax along a fraActional axis?
The gradient with respect to x is 0, because f(x+epsilon, y) = f(x) almost everywhere.
4.f(x,y) = a vector with y elements, each of which taking on the value x The grad method
should return DisconnectedType()() for y, because the elements of f don’t depend
on y. Only the shape of f depends on y. You probably also want to implement a
connection_pattern method to encode this.
5.f(x) = int(x) converts float x into an int. g(y) = float(y) converts an integer y into a float. If
the final cost C = 0.5 * g(y) = 0.5 g(f(x)), then the gradient with respect to y will be 0.5,
even if y is an integer. However, the gradient with respect to x will be 0, because the output
of f is integer-valued.
connection_pattern(node):
Sometimes needed for proper operation of gradient.grad().
Returns a list of list of bools.
Op.connection_pattern[input_idx][output_idx] is true if the elements of inputs[input_idx] have an
effect on the elements of outputs[output_idx].
The node parameter is needed to determine the number of inputs. Some ops such as Subtensor take
a variable number of inputs.
If no connection_pattern is specified, gradient.grad will assume that all inputs have some elements
connected to some elements of all outputs.
This method conveys two pieces of information that are otherwise not part of the theano graph:
1.Which of the op’s inputs are truly ancestors of each of the op’s outputs. Suppose an op has two
inputs, x and y, and outputs f(x) and g(y). y is not really an ancestor of f, but it appears to be so
in the theano graph.
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2.Whether the actual elements of each input/output are relevant to a computation. For example,
the shape op does not read its input’s elements, only its shape metadata. d shape(x) / dx should
thus raise a disconnected input exception (if these exceptions are enabled). As another example,
the elements of the Alloc op’s outputs are not affected by the shape arguments to the Alloc op.
Failing to implement this function for an op that needs it can result in two types of incorrect behavior:
1.gradient.grad erroneously raising a TypeError reporting that a gradient is undefined.
2.gradient.grad failing to raise a ValueError reporting that an input is disconnected.
Even if connection_pattern is not implemented correctly, if gradient.grad returns an expression, that
expression will be numerically correct.
R_op(inputs, eval_points)
Optional, to work with gradient.R_op().
This function implements the application of the R-operator on the function represented by your op.
Let assume that function is 𝑓 , with input 𝑥, applying the R-operator means computing the Jacobian
of 𝑓 and right-multiplying it by 𝑣, the evaluation point, namely: 𝜕𝑓
𝜕𝑥 𝑣.
inputs are the symbolic variables corresponding to the value of the input where you want to evaluate
the jacobian, and eval_points are the symbolic variables corresponding to the value you want to
right multiply the jacobian with.
Same conventions as for the grad method hold. If your op is not differentiable, you can return None.
Note that in contrast to the method grad(), for R_op() you need to return the same number of
outputs as there are ouputs of the op. You can think of it in the following terms. You have all your
inputs concatenated into a single vector 𝑥. You do the same with the evaluation points (which are as
many as inputs and of the shame shape) and obtain another vector 𝑣. For each output, you reshape
it into a vector, compute the jacobian of that vector with respect to 𝑥 and multiply it by 𝑣. As a last
step you reshape each of these vectors you obtained for each outputs (that have the same shape as the
outputs) back to their corresponding shapes and return them as the output of the R_op() method.
List of op with r op support.
Defining an Op: mul
We’ll define multiplication as a binary operation, even though a multiplication Op could take an arbitrary
number of arguments.
First, we’ll instantiate a mul Op:
from theano import gof
mul = gof.Op()
make_node
This function must take as many arguments as the operation we are defining is supposed to take as inputs—
in this example that would be two. This function ensures that both inputs have the double type. Since
multiplying two doubles yields a double, this function makes an Apply node with an output Variable of type
double.
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def make_node(x, y):
if x.type != double or y.type != double:
raise TypeError('mul only works on doubles')
return gof.Apply(mul, [x, y], [double()])
mul.make_node = make_node
The first two lines make sure that both inputs are Variables of the double type that we created in the
previous section. We would not want to multiply two arbitrary types, it would not make much sense (and
we’d be screwed when we implement this in C!)
The last line is the meat of the definition. There we create an Apply node representing the application of Op
mul to inputs x and y, giving a Variable instance of type double as the output.
Note: Theano relies on the fact that if you call the make_node method of Apply’s first argument on the
inputs passed as the Apply’s second argument, the call will not fail and the returned Apply instance will be
equivalent. This is how graphs are copied.
perform
This code actually computes the function. In our example, the data in inputs will be instances of Python’s
built-in type float because this is the type that double.filter() will always return, per our own
definition. output_storage will contain a single storage cell for the multiplication’s variable.
def perform(node, inputs, output_storage):
x, y = inputs[0], inputs[1]
z = output_storage[0]
z[0] = x * y
mul.perform = perform
Here, z is a list of one element. By default, z == [None].
Note: It is possible that z does not contain None. If it contains anything else, Theano guarantees that
whatever it contains is what perform put there the last time it was called with this particular storage.
Furthermore, Theano gives you permission to do whatever you want with z‘s contents, chiefly reusing it or
the memory allocated for it. More information can be found in the Op documentation.
Warning: We gave z the Theano type double in make_node, which means that a Python float
must be put there. You should not put, say, an int in z[0] because Theano assumes Ops handle typing
properly.
Trying out our new Op
In the following code, we use our new Op:
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>>> import theano
>>> x, y = double('x'), double('y')
>>> z = mul(x, y)
>>> f = theano.function([x, y], z)
>>> f(5, 6)
30.0
>>> f(5.6, 6.7)
37.519999999999996
Note that there is an implicit call to double.filter() on each argument, so if we give integers as inputs
they are magically cast to the right type. Now, what if we try this?
>>> x = double('x')
>>> z = mul(x, 2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/u/breuleuo/hg/theano/theano/gof/op.py", line 207, in __call__
File "<stdin>", line 2, in make_node
AttributeError: 'int' object has no attribute 'type'
Automatic Constant Wrapping
Well, OK. We’d like our Op to be a bit more flexible. This can be done by modifying make_node to accept
Python int or float as x and/or y:
def make_node(x, y):
if isinstance(x, (int, float)):
x = gof.Constant(double, x)
if isinstance(y, (int, float)):
y = gof.Constant(double, y)
if x.type != double or y.type != double:
raise TypeError('mul only works on doubles')
return gof.Apply(mul, [x, y], [double()])
mul.make_node = make_node
Whenever we pass a Python int or float instead of a Variable as x or y, make_node will convert it to
Constant for us. gof.Constant is a Variable we statically know the value of.
>>> import numpy
>>> x = double('x')
>>> z = mul(x, 2)
>>> f = theano.function([x], z)
>>> f(10)
20.0
>>> numpy.allclose(f(3.4), 6.8)
True
Now the code works the way we want it to.
Note: Most Theano Ops follow this convention of up-casting literal make_node arguments to Constants.
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This makes typing expressions more natural. If you do not want a constant somewhere in your graph, you
have to pass a Variable (like double('x') here).
Final version
The above example is pedagogical. When you define other basic arithmetic operations add, sub and div,
code for make_node can be shared between these Ops. Here is revised implementation of these four
arithmetic operators:
from theano import gof
class BinaryDoubleOp(gof.Op):
__props__ = ("name", "fn")
def __init__(self, name, fn):
self.name = name
self.fn = fn
def make_node(self, x, y):
if isinstance(x, (int, float)):
x = gof.Constant(double, x)
if isinstance(y, (int, float)):
y = gof.Constant(double, y)
if x.type != double or y.type != double:
raise TypeError('%s only works on doubles' % self.name)
return gof.Apply(self, [x, y], [double()])
def perform(self, node, inp, out):
x, y = inp
z, = out
z[0] = self.fn(x, y)
def __str__(self):
return self.name
add = BinaryDoubleOp(name='add',
fn=lambda x, y: x + y)
sub = BinaryDoubleOp(name='sub',
fn=lambda x, y: x - y)
mul = BinaryDoubleOp(name='mul',
fn=lambda x, y: x * y)
div = BinaryDoubleOp(name='div',
fn=lambda x, y: x / y)
Instead of working directly on an instance of Op, we create a subclass of Op that we can parametrize. All the
operations we define are binary. They all work on two inputs with type double. They all return a single
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Variable of type double. Therefore, make_node does the same thing for all these operations, except
for the Op reference self passed as first argument to Apply. We define perform using the function fn
passed in the constructor.
This design is a flexible way to define basic operations without duplicating code. The same way a Type
subclass represents a set of structurally similar types (see previous section), an Op subclass represents a
set of structurally similar operations: operations that have the same input/output types, operations that only
differ in one small detail, etc. If you see common patterns in several Ops that you want to define, it can be
a good idea to abstract out what you can. Remember that an Op is just an object which satisfies the contract
described above on this page and that you should use all the tools at your disposal to create these objects as
efficiently as possible.
Exercise: Make a generic DoubleOp, where the number of arguments can also be given as a parameter.
Views and inplace operations
Theano allows the definition of Ops which return a view on one of their inputs or operate inplace on one or
several inputs. This allows more efficient operations on numpy’s ndarray data type than would be possible
otherwise. However, in order to work correctly, these Ops need to implement an additional interface.
Theano recognizes views and inplace operations specially. It ensures that they are used in a consistent
manner and it ensures that operations will be carried in a compatible order.
An unfortunate fact is that it is impossible to return a view on an input with the double type or to operate
inplace on it (Python floats are immutable). Therefore, we can’t make examples of these concepts out of
what we’ve just built. Nonetheless, we will present the concepts:
Views
A “view” on an object x is an object y which shares memory with x in some way. In other words, changing
x might also change y and vice versa. For example, imagine a vector structure which contains two fields:
an integer length and a pointer to a memory buffer. Suppose we have:
x = vector {length: 256,
address: 0xDEADBEEF}
y = vector {length: 224,
address: 0xDEADBEEF + 0x10}
z = vector {length: 256,
address: 0xCAFEBABE}
So x uses the memory range 0xDEADBEEF - 0xDEADBFEF, y the range 0xDEADBEFF 0xDEADBFDF and z the range 0xCAFEBABE - 0xCAFEBBBE. Since the ranges for x and y overlap,
y is considered to be a view of x and vice versa.
Suppose you had an Op which took x as input and returned y. You would need to tell Theano that y is a
view of x. For this purpose, you would set the view_map field as follows:
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myop.view_map = {0: [0]}
What this means is that the first output (position 0) is a view of the first input (position 0). Even though the
interface allows a list of inputs that are viewed by a given output, this feature is currently unsupported. Here
are more examples:
myop.view_map = {0: [0]} # first output is a view of first input
myop.view_map = {0: [1]} # first output is a view of second input
myop.view_map = {1: [0]} # second output is a view of first input
myop.view_map = {0: [0], # first output is a view of first input
1: [1]} # *AND* second output is a view of second input
myop.view_map = {0: [0], # first output is a view of first input
1: [0]} # *AND* second output is *ALSO* a view of first input
myop.view_map = {0: [0, 1]} # THIS IS NOT SUPPORTED YET! Only put a single
˓→input number in the list!
Inplace operations
An inplace operation is one that modifies one or more of its inputs. For example, the expression x += y
where x and y are numpy.ndarray instances would normally represent an inplace operation on x.
Note: Inplace operations in Theano still work in a functional setting: they need to return the modified
input. Symbolically, Theano requires one Variable standing for the input before being modified and another
Variable representing the input after being modified. Therefore, code using inplace operations would look
like this:
from theano.tensor import dscalars, log
from theano.tensor.inplace import add_inplace
x, y = dscalars('x', 'y')
r1 = log(x)
# r2 is x AFTER the add_inplace - x still represents the value before adding y
r2 = add_inplace(x, y)
# r3 is log(x) using the x from BEFORE the add_inplace
# r3 is the SAME as r1, even if we wrote this line after the add_inplace line
# Theano is actually going to compute r3 BEFORE r2
r3 = log(x)
# this is log(x) using the x from AFTER the add_inplace (so it's like log(x +
˓→y))
r4 = log(r2)
Needless to say, this goes for user-defined inplace operations as well: the modified input must figure in the
list of outputs you give to Apply in the definition of make_node.
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Also, for technical reasons but also because they are slightly confusing to use as evidenced by the previous
code, Theano does not allow the end user to use inplace operations by default. However, it does allow
optimizations to substitute them in in a later phase. Therefore, typically, if you define an inplace operation,
you will define a pure equivalent and an optimization which subsitutes one for the other. Theano will
automatically verify if it is possible to do so and will refuse the substitution if it introduces inconsistencies.
Take the previous definitions of x, y and z and suppose an Op which adds one to every byte of its input. If
we give x as an input to that Op, it can either allocate a new buffer of the same size as x (that could be z) and
set that new buffer’s bytes to the variable of the addition. That would be a normal, pure Op. Alternatively, it
could add one to each byte in the buffer x, therefore changing it. That would be an inplace Op.
Theano needs to be notified of this fact. The syntax is similar to that of view_map:
myop.destroy_map = {0: [0]}
What this means is that the first output (position 0) operates inplace on the first input (position 0).
myop.destroy_map = {0: [0]} # first output operates inplace on first input
myop.destroy_map = {0: [1]} # first output operates inplace on second input
myop.destroy_map = {1: [0]} # second output operates inplace on first input
myop.destroy_map = {0: [0], # first output operates inplace on first input
1: [1]} # *AND* second output operates inplace on second
˓→input
myop.destroy_map = {0: [0], # first output operates inplace on first input
1: [0]} # *AND* second output *ALSO* operates inplace on
˓→first input
myop.destroy_map = {0: [0, 1]} # first output operates inplace on both the
˓→first and second input
# unlike for views, the previous line is legal and supported
Destructive Operations
While some operations will operate inplace on their inputs, some might simply destroy or corrupt them. For
example, an Op could do temporary calculations right in its inputs. If that is the case, Theano also needs to
be notified. The way to notify Theano is to assume that some output operated inplace on whatever inputs are
changed or corrupted by the Op (even if the output does not technically reuse any of the input(s)’s memory).
From there, go to the previous section.
Warning:
Failure to correctly mark down views and inplace operations using view_map and
destroy_map can lead to nasty bugs. In the absence of this information, Theano might assume that
it is safe to execute an inplace operation on some inputs before doing other calculations on the previous
values of the inputs. For example, in the code: y = log(x); x2 = add_inplace(x, z) it is
imperative to do the logarithm before the addition (because after the addition, the original x that we
wanted to take the logarithm of is gone). If Theano does not know that add_inplace changes the
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value of x it might invert the order and that will certainly lead to erroneous computations.
You can often identify an incorrect view_map or destroy_map by using debugmode. Be sure to use
DebugMode when developing a new Op that uses ‘‘view_map‘‘ and/or ‘‘destroy_map‘‘.
Inplace optimization and DebugMode
It is recommended that during the graph construction, all Ops are not inplace. Then an optimization replaces
them with inplace ones. Currently DebugMode checks all optimizations that were tried even if they got
rejected. One reason an inplace optimization can get rejected is when there is another Op that is already
being applied inplace on the same input. Another reason to reject an inplace optimization is if it would
introduce a cycle into the graph.
The problem with DebugMode is that it will trigger a useless error when checking a rejected inplace
optimization, since it will lead to wrong results. In order to be able to use DebugMode in more situations, your inplace optimization can pre-check whether it will get rejected by using the theano.gof.
destroyhandler.fast_inplace_check() function, that will tell which Ops can be performed
inplace. You may then skip the optimization if it is incompatible with this check. Note however that this
check does not cover all cases where an optimization may be rejected (it will not detect cycles).
Implementing some specific Ops
This page is a guide on the implementation of some specific types of Ops, and points to some examples of
such implementations.
For the random number generating Ops, it explains different possible implementation strategies.
Scalar/Elemwise/Reduction Ops
Implementing a Theano scalar Op allows that scalar operation to be reused by our elemwise operations on
tensors. If the scalar operation has C code, the elemwise implementation will automatically have C code
too. This will enable the fusion of elemwise operations using your new scalar operation. It can also reuse
the GPU elemwise code. It is similar for reduction operations.
For examples of how to add new scalar operations, you can have a look at those 2 pull requests, that add
GammaLn and Psi and Gamma scalar Ops.
Be careful about some possible problems in the definition of the grad method, and about dependencies
that may not be available. In particular, see the following fixes: Fix to grad() methods and impl() methods
related to SciPy.
SciPy Ops
We can wrap SciPy functions in Theano. But SciPy is an optional dependency. Here is some code that
allows the Op to be optional:
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try:
import scipy.linalg
imported_scipy = True
except ImportError:
# some ops (e.g. Cholesky, Solve, A_Xinv_b) won't work
imported_scipy = False
class SomeOp(Op):
...
def make_node(self, x):
assert imported_scipy, (
"SciPy not available. SciPy is needed for the SomeOp op.")
...
from nose.plugins.skip import SkipTest
class test_SomeOp(utt.InferShapeTester):
...
def test_infer_shape(self):
if not imported_scipy:
raise SkipTest("SciPy needed for the SomeOp op.")
...
Sparse Ops
There are a few differences to keep in mind if you want to make an op that uses sparse inputs
or outputs, rather than the usual dense tensors. In particular, in the make_node() function, you
have to call theano.sparse.as_sparse_variable(x) on sparse input variables, instead of
as_tensor_variable(x).
Another difference is that you need to use SparseVariable and SparseType instead of
TensorVariable and TensorType.
Do not forget that we support only sparse matrices (so only 2 dimensions) and (like in SciPy) they do not
support broadcasting operations by default (although a few Ops do it when called manually). Also, we
support only two formats for sparse type: csr and csc. So in make_mode(), you can create output
variables like this:
out_format = inputs[0].format # or 'csr' or 'csc' if the output format is
˓→fixed
SparseType(dtype=inputs[0].dtype, format=out_format).make_variable()
See the sparse theano.sparse.basic.Cast op code for a good example of a sparse op with Python
code.
Note: From the definition of CSR and CSC formats, CSR column indices are not necessarily sorted.
Likewise for CSC row indices. Use EnsureSortedIndices if your code does not support it.
Also, there can be explicit zeros in your inputs. Use Remove0 or remove0 to make sure they aren’t
present in your input if you don’t support that.
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To remove explicit zeros and make sure indices are sorted, use clean.
Sparse Gradient
There are 2 types of gradients for sparse operations: normal gradient and structured gradient. Please
document what your op implements in its docstring. It is important that the user knows it, and it is not
always easy to infer from the code. Also make clear which inputs/outputs are sparse and which ones are
dense.
Sparse C code
Theano does not have a native C code interface for sparse matrices. The reason is simple: we use the SciPy
sparse matrix objects and they don’t have a C object. So we use a simple trick: a sparse matrix is made of
4 fields that are NumPy vector arrays: data, indices, indptr and shape. So to make an op with C
code that has sparse variables as inputs, we actually make an op that takes as input the needed fields of those
sparse variables.
You can extract the 4 fields with theano.sparse.basic.csm_properties().
You
can use theano.sparse.basic.csm_data(), theano.sparse.basic.csm_indices(),
theano.sparse.basic.csm_indptr() and theano.sparse.basic.csm_shape() to extract the individual fields.
You can look at the AddSD sparse op for an example with C code. It implements the addition of a sparse
matrix with a dense matrix.
Sparse Tests
You can reuse the test system for tensor variables. To generate the needed sparse variable and data, you can
use theano.sparse.tests.test_basic.sparse_random_inputs(). It takes many parameters, including parameters for the format (csr or csc), the shape, the dtype, whether to have explicit 0 and
whether to have unsorted indices.
Random distribution
We have 3 base random number generators. One that wraps NumPy’s random generator, one that implements
MRG31k3p and one that wraps CURAND.
The fastest, but less developed, is CURAND. It works only on CUDA-enabled GPUs. It does not work on
the CPU and it has fewer random distributions implemented.
The recommended and 2nd faster is MRG. It works on the GPU and CPU and has more implemented
distributions.
The slowest is our wrapper on NumPy’s random generator.
We explain and provide advice on 3 possibles implementations of new distributions here:
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1. Extend our wrapper around NumPy random functions. See this PR as an example.
2. Extend MRG implementation by reusing existing Theano Op. Look into the theano/sandbox/
rng_mrg.py file and grep for all code about binomial(). This distribution uses the output of the
uniform distribution and converts it to a binomial distribution with existing Theano operations. The
tests go in theano/sandbox/test_rng_mrg.py
3. Extend MRG implementation with a new Op that takes a uniform sample as input. Look in the
theano/sandbox/{rng_mrg,multinomial}.py file and its test in theano/sandbox/
test_multinomal.py. This is recommended when current Theano ops aren’t well suited to
modify the uniform to the target distribution. This can happen in particular if there is a loop or
complicated condition.
Note: In all cases, you must reuse the same interface as NumPy for compatibility.
OpenMP Ops
To allow consistent interface of Ops that support OpenMP, we have some helper code. Doing this also allows
to enable/disable OpenMP globally or per op for fine-grained control.
Your Op needs to inherit from theano.gof.OpenMPOp.
If it overrides the __init__()
method, it must have an openmp=None parameter and must call super(MyOpClass, self).
__init__(openmp=openmp).
The OpenMPOp class also implements c_compile_args and make_thunk. This makes it add the
correct g++ flags to compile with OpenMP. It also disables OpenMP and prints a warning if the version of
g++ does not support it.
The Theano flag openmp is currently False by default as we do not have code that gets sped up with it.
The only current implementation is ConvOp. It speeds up some cases, but slows down others. That is why
we disable it by default. But we have all the code to have it enabled by default if there is more than 1 core
and the environment variable OMP_NUM_THREADS is not 1. This allows Theano to respect the current
convention.
Numba Ops
Want C speed without writing C code for your new Op? You can use Numba to generate the C code for you!
Here is an example Op doing that.
Alternate Theano Types
Most ops in Theano are used to manipulate tensors. However, Theano also supports many other variable
types. The supported types are listed below, along with pointers to the relevant documentation.
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• TensorType : Theano type that represents a multidimensional array containing elements that all
have the same type. Variables of this Theano type are represented in C as objects of class PyArrayObject.
• TypedList : Theano type that represents a typed list (a list where every element in the list has the same
Theano type). Variables of this Theano type are represented in C as objects of class PyListObject.
• Scalar : Theano type that represents a C primitive type. The C type associated with this Theano type
is the represented C primitive itself.
• SparseType : Theano type used to represent sparse tensors. There is no equivalent C type for this
Theano Type but you can split a sparse variable into its parts as TensorVariables. Those can then be
used as inputs to an op with C code.
• Generic : Theano type that represents a simple Python Object. Variables of this Theano type are
represented in C as objects of class PyObject.
• CDataType : Theano type that represents a C data type. The C type associated with this Theano
type depends on the data being represented.
Implementing double in C
The previous two sections described how to define a double Type and arithmetic operations on that Type,
but all of them were implemented in pure Python. In this section we will see how to define the double type
in such a way that it can be used by operations implemented in C (which we will define in the section after
that).
How does it work?
In order to be C-compatible, a Type must provide a C interface to the Python data that satisfy the constraints
it puts forward. In other words, it must define C code that can convert a Python reference into some type
suitable for manipulation in C and it must define C code that can convert some C structure in which the C
implementation of an operation stores its variables into a reference to an object that can be used from Python
and is a valid value for the Type.
For example, in the current example, we have a Type which represents a Python float. First, we will choose
a corresponding C type. The natural choice would be the primitive double type. Then, we need to write
code that will take a PyObject*, check that it is a Python float and extract its value as a double.
Finally, we need to write code that will take a C double and will build a PyObject* of Python type
float that we can work with from Python. We will be using CPython and thus special care must be given
to making sure reference counts are updated properly!
The C code we will write makes use of CPython’s C API which you can find here.
What needs to be defined
In order to be C-compatible, a Type must define several additional methods, which all start with the c_
prefix. The complete list can be found in the documentation for gof.type.Type. Here, we’ll focus on
the most important ones:
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class CLinkerType
c_declare(name, sub, check_input=True)
This must return C code which declares variables. These variables will be available to operations
defined in C. You may also write typedefs.
c_init(name, sub)
This must return C code which initializes the variables declared in c_declare. Either this or
c_extract will be called.
c_extract(name, sub, check_input=True)
This must return C code which takes a reference to a Python object and initializes the variables
declared in c_declare to match the Python object’s data. Either this or c_init will be
called.
c_sync(name, sub)
When the computations are done, transfer the variables from the C structure we put them in to
the destination Python object. This will only be called for the outputs.
c_cleanup(name, sub)
When we are done using the data, clean up whatever we allocated and decrease the appropriate
reference counts.
c_headers([c_compiler ])
c_libraries([c_compiler ])
c_header_dirs([c_compiler ])
c_lib_dirs([c_compiler ])
Allows you to specify headers, libraries and associated directories.
These methods have two versions, one with a c_compiler argument and one without. The version
with c_compiler is tried first and if it doesn’t work, the one without is.
The c_compiler argument is the C compiler that will be used to compile the C code for the node
that uses this type.
c_compile_args([c_compiler ])
c_no_compile_args([c_compiler ])
Allows to specify special compiler arguments to add/exclude.
These methods have two versions, one with a c_compiler argument and one without. The version
with c_compiler is tried first and if it doesn’t work, the one without is.
The c_compiler argument is the C compiler that will be used to compile the C code for the node
that uses this type.
c_init_code()
Allows you to specify code that will be executed once when the module is initialized, before anything else is executed. For instance, if a type depends on NumPy’s C API, then
'import_array();' has to be among the snippets returned by c_init_code().
c_support_code()
Allows to add helper functions/structs that the Type needs.
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c_compiler()
Allows to specify a special compiler. This will force this compiler for the current compilation
block (a particular op or the full graph). This is used for the GPU code.
c_code_cache_version()
Should return a tuple of hashable objects like integers. This specifies the version of the code. It
is used to cache the compiled code. You MUST change the returned tuple for each change in the
code. If you don’t want to cache the compiled code return an empty tuple or don’t implement it.
Each of these functions take two arguments, name and sub which must be used to parameterize the C code
they return. name is a string which is chosen by the compiler to represent a Variable of the Type in such a
way that there are no name conflicts between different pieces of data. Therefore, all variables declared in
c_declare should have a name which includes name. Furthermore, the name of the variable containing
a pointer to the Python object associated to the Variable is py_<name>.
sub, on the other hand, is a dictionary containing bits of C code suitable for use in certain situations. For
instance, sub['fail'] contains code that should be inserted wherever an error is identified.
c_declare and c_extract also accept a third check_input optional argument. If you want your
type to validate its inputs, it must only do it when check_input is True.
The example code below should help you understand how everything plays out:
Warning: If some error condition occurs and you want to fail and/or raise an Exception, you must
use the fail code contained in sub['fail'] (there is an example in the definition of c_extract
below). You must NOT use the return statement anywhere, ever, nor break outside of your own
loops or goto to strange places or anything like that. Failure to comply with this restriction could
lead to erratic behavior, segfaults and/or memory leaks because Theano defines its own cleanup system
and assumes that you are not meddling with it. Furthermore, advanced operations or types might do
code transformations on your code such as inserting it in a loop – in that case they can call your codegenerating methods with custom failure code that takes into account what they are doing!
Defining the methods
c_declare
def c_declare(name, sub):
return """
double %(name)s;
""" % dict(name = name)
double.c_declare = c_declare
Very straightforward. All we need to do is write C code to declare a double. That double will be named
whatever is passed to our function in the name argument. That will usually be some mangled name like
“V0”, “V2” or “V92” depending on how many nodes there are in the computation graph and what rank the
current node has. This function will be called for all Variables whose type is double.
You can declare as many variables as you want there and you can also do typedefs. Make sure that the name
of each variable contains the name argument in order to avoid name collisions (collisions will happen if you
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don’t parameterize the variable names as indicated here). Also note that you cannot declare a variable called
py_<name> or storage_<name> because Theano already defines them.
What you declare there is basically the C interface you are giving to your Type. If you wish people to
develop operations that make use of it, it’s best to publish it somewhere.
c_init
def c_init(name, sub):
return """
%(name)s = 0.0;
""" % dict(name = name)
double.c_init = c_init
This function has to initialize the double we declared previously to a suitable value. This is useful if we
want to avoid dealing with garbage values, especially if our data type is a pointer. This is not going to be
called for all Variables with the double type. Indeed, if a Variable is an input that we pass from Python,
we will want to extract that input from a Python object, therefore it is the c_extract method that will be
called instead of c_init. You can therefore not assume, when writing c_extract, that the initialization
has been done (in fact you can assume that it hasn’t been done).
c_init will typically be called on output Variables, but in general you should only assume that either
c_init or c_extract has been called, without knowing for sure which of the two.
c_extract
def c_extract(name, sub):
return """
if (!PyFloat_Check(py_%(name)s)) {
PyErr_SetString(PyExc_TypeError, "expected a float");
%(fail)s
}
%(name)s = PyFloat_AsDouble(py_%(name)s);
""" % dict(name = name, fail = sub['fail'])
double.c_extract = c_extract
This method is slightly more sophisticated. What happens here is that we have a reference to a Python
object which Theano has placed in py_%(name)s where %(name)s must be substituted for the name
given in the inputs. This special variable is declared by Theano as PyObject* py_%(name)s where
PyObject* is a pointer to a Python object as defined by CPython’s C API. This is the reference that
corresponds, on the Python side of things, to a Variable with the double type. It is what the end user will
give and what he or she expects to get back.
In this example, the user will give a Python float. The first thing we should do is verify that what we got
is indeed a Python float. The PyFloat_Check function is provided by CPython’s C API and does this
for us. If the check fails, we set an exception and then we insert code for failure. The code for failure is in
sub["fail"] and it basically does a goto to cleanup code.
If the check passes then we convert the Python float into a double using the PyFloat_AsDouble function
(yet again provided by CPython’s C API) and we put it in our double variable that we declared previously.
c_sync
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def c_sync(name, sub):
return """
Py_XDECREF(py_%(name)s);
py_%(name)s = PyFloat_FromDouble(%(name)s);
if (!py_%(name)s) {
printf("PyFloat_FromDouble failed on: %%f\\n", %(name)s);
Py_XINCREF(Py_None);
py_%(name)s = Py_None;
}
""" % dict(name = name)
double.c_sync = c_sync
This function is probably the trickiest. What happens here is that we have computed some operation on
doubles and we have put the variable into the double variable %(name)s. Now, we need to put this data
into a Python object that we can manipulate on the Python side of things. This Python object must be put
into the py_%(name)s variable which Theano recognizes (this is the same pointer we get in c_extract).
Now, that pointer is already a pointer to a valid Python object (unless you or a careless implementer did
terribly wrong things with it). If we want to point to another object, we need to tell Python that we don’t
need the old one anymore, meaning that we need to decrease the previous object’s reference count. The
first line, Py_XDECREF(py_%(name)s) does exactly this. If it is forgotten, Python will not be able to
reclaim the data even if it is not used anymore and there will be memory leaks! This is especially important
if the data you work on is large.
Now that we have decreased the reference count, we call PyFloat_FromDouble on our double variable
in order to convert it to a Python float. This returns a new reference which we assign to py_%(name)s.
From there Theano will do the rest and the end user will happily see a Python float come out of his
computations.
The rest of the code is not absolutely necessary and it is basically “good practice”.
PyFloat_FromDouble can return NULL on failure. NULL is a pretty bad reference to have and
neither Python nor Theano like it. If this happens, we change the NULL pointer (which will cause us
problems) to a pointer to None (which is not a NULL pointer). Since None is an object like the others, we
need to increase its reference count before we can set a new pointer to it. This situation is unlikely to ever
happen, but if it ever does, better safe than sorry.
Warning: I said this already but it really needs to be emphasized that if you are going to change the
py_%(name)s pointer to point to a new reference, you must decrease the reference count of whatever
it was pointing to before you do the change. This is only valid if you change the pointer, if you are not
going to change the pointer, do NOT decrease its reference count!
c_cleanup
def c_cleanup(name, sub):
return ""
double.c_cleanup = c_cleanup
We actually have nothing to do here. We declared a double on the stack so the C language will reclaim it
for us when its scope ends. We didn’t malloc() anything so there’s nothing to free(). Furthermore,
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the py_%(name)s pointer hasn’t changed so we don’t need to do anything with it. Therefore, we have
nothing to cleanup. Sweet!
There are however two important things to keep in mind:
First, note that c_sync and c_cleanup might be called in sequence, so they need to play nice together.
In particular, let’s say that you allocate memory in c_init or c_extract for some reason. You might
want to either embed what you allocated to some Python object in c_sync or to free it in c_cleanup. If
you do the former, you don’t want to free the allocated storage so you should set the pointer to it to NULL
to avoid that c_cleanup mistakenly frees it. Another option is to declare a variable in c_declare that
you set to true in c_sync to notify c_cleanup that c_sync was called.
Second, whenever you use %(fail)s in c_extract or in the code of an operation, you can count on
c_cleanup being called right after that. Therefore, it’s important to make sure that c_cleanup doesn’t
depend on any code placed after a reference to %(fail)s. Furthermore, because of the way Theano blocks
code together, only the variables declared in c_declare will be visible in c_cleanup!
What the generated C will look like
c_init and c_extract will only be called if there is a Python object on which we want to apply computations using C code. Conversely, c_sync will only be called if we want to communicate the values we
have computed to Python, and c_cleanup will only be called when we don’t need to process the data with
C anymore. In other words, the use of these functions for a given Variable depends on the the relationship
between Python and C with respect to that Variable. For instance, imagine you define the following function
and call it:
x, y, z = double('x'), double('y'), double('z')
a = add(x, y)
b = mul(a, z)
f = function([x, y, z], b)
f(1.0, 2.0, 3.0)
Using the CLinker, the code that will be produced will look roughly like this:
// BEGIN defined by Theano
PyObject* py_x = ...;
PyObject* py_y = ...;
PyObject* py_z = ...;
PyObject* py_a = ...; // note: this reference won't actually be used for
˓→anything
PyObject* py_b = ...;
// END defined by Theano
{
double x; //c_declare for x
x = ...; //c_extract for x
{
double y; //c_declare for y
y = ...; //c_extract for y
{
double z; //c_declare for z
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z = ...; //c_extract for z
{
double a; //c_declare for a
a = 0; //c_init for a
{
double b; //c_declare for b
b = 0; //c_init for b
{
a = x + y; //c_code for add
{
b = a * z; //c_code for mul
labelmul:
//c_cleanup for mul
}
labeladd:
//c_cleanup for add
}
labelb:
py_b = ...; //c_sync for b
//c_cleanup for b
}
labela:
//c_cleanup for a
}
labelz:
//c_cleanup for z
}
labely:
//c_cleanup for y
}
labelx:
//c_cleanup for x
}
It’s not pretty, but it gives you an idea of how things work (note that the variable names won’t be x, y, z,
etc. - they will get a unique mangled name). The fail code runs a goto to the appropriate label in order
to run all cleanup that needs to be done. Note which variables get extracted (the three inputs x, y and z),
which ones only get initialized (the temporary variable a and the output b) and which one is synced (the
final output b).
The C code above is a single C block for the whole graph. Depending on which linker is used to process
the computation graph, it is possible that one such block is generated for each operation and that we transit
through Python after each operation. In that situation, a would be synced by the addition block and extracted
by the multiplication block.
Final version
from theano import gof
class Double(gof.Type):
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def filter(self, x, strict=False, allow_downcast=None):
if strict and not isinstance(x, float):
raise TypeError('Expected a float!')
return float(x)
def values_eq_approx(self, x, y, tolerance=1e-4):
return abs(x - y) / (x + y) < tolerance
def __str__(self):
return "double"
def c_declare(self, name, sub):
return """
double %(name)s;
""" % dict(name = name)
def c_init(self, name, sub):
return """
%(name)s = 0.0;
""" % dict(name = name)
def c_extract(self, name, sub):
return """
if (!PyFloat_Check(py_%(name)s)) {
PyErr_SetString(PyExc_TypeError, "expected a float");
%(fail)s
}
%(name)s = PyFloat_AsDouble(py_%(name)s);
""" % dict(sub, name = name)
def c_sync(self, name, sub):
return """
Py_XDECREF(py_%(name)s);
py_%(name)s = PyFloat_FromDouble(%(name)s);
if (!py_%(name)s) {
printf("PyFloat_FromDouble failed on: %%f\\n", %(name)s);
Py_XINCREF(Py_None);
py_%(name)s = Py_None;
}
""" % dict(name = name)
def c_cleanup(self, name, sub):
return ""
double = Double()
DeepCopyOp
We have an internal Op called DeepCopyOp. It is used to make sure we respect the user vs Theano memory
region as described in the tutorial. Theano has a Python implementation that calls the object’s copy() or
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deepcopy() method for Theano types for which it does not know how to generate C code.
You can implement c_code for this op. You register it like this:
theano.compile.ops.register_deep_copy_op_c_code(YOUR_TYPE_CLASS, THE_C_CODE,
˓→version=())
In your C code, you should use %(iname)s and %(oname)s to represent the C variable names of the
DeepCopyOp input and output respectively. See an example for the type CudaNdarrayType (GPU
array) in the file theano/sandbox/cuda/type.py. The version parameter is what is returned by DeepCopyOp.c_code_cache_version(). By default, it will recompile the c code for each process.
ViewOp
We have an internal Op called ViewOp. It is used for some verification of inplace/view Ops. Its C implementation increments and decrements Python reference counts, and thus only works with Python objects.
If your new type represents Python objects, you should tell ViewOp to generate C code when working with
this type, as otherwise it will use Python code instead. This is achieved by calling:
theano.compile.ops.register_view_op_c_code(YOUR_TYPE_CLASS, THE_C_CODE,
˓→version=())
In your C code, you should use %(iname)s and %(oname)s to represent the C variable names
of the ViewOp input and output respectively. See an example for the type CudaNdarrayType
(GPU array) in the file theano/sandbox/cuda/type.py. The version parameter is what is returned by
ViewOp.c_code_cache_version(). By default, it will recompile the c code for each process.
Shape and Shape_i
We have 2 generic Ops, Shape and Shape_i, that return the shape of any Theano Variable that has a shape
attribute (Shape_i returns only one of the elements of the shape).
theano.compile.ops.register_shape_c_code(YOUR_TYPE_CLASS, THE_C_CODE,
˓→version=())
theano.compile.ops.register_shape_i_c_code(YOUR_TYPE_CLASS, THE_C_CODE, CHECK_
˓→INPUT, version=())
The C code works as the ViewOp. Shape_i has the additional i parameter that you can use with %(i)s.
In your CHECK_INPUT, you must check that the input has enough dimensions to be able to access the i-th
one.
Implementing the arithmetic Ops in C
Now that we have set up our double type properly to allow C implementations for operations that work on
it, all we have to do now is to actually define these operations in C.
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How does it work?
Before a C Op is executed, the variables related to each of its inputs will be declared and will be filled
appropriately, either from an input provided by the end user (using c_extract) or it might simply have been
calculated by another operation. For each of the outputs, the variables associated to them will be declared
and initialized.
The operation then has to compute what it needs to using the input variables and place the variables in the
output variables.
What needs to be defined
There are less methods to define for an Op than for a Type:
class Op
c_code(node, name, input_names, output_names, sub)
This must return C code that carries the computation we want to do.
sub is a dictionary of extras parameters to the c_code method. It contains the following values:
sub['fail']
A string of code that you should execute (after ensuring that a python exception is set)
if your C code needs to raise an exception.
sub['params']
(optional) The name of the variable which holds the context for the node. This will
only appear if the op has requested a context by having a get_params() method
that return something other than None.
c_code_cleanup(node, name, input_names, output_names, sub)
This must return C code that cleans up whatever c_code allocated and that we must free.
Default: The default behavior is to do nothing.
c_headers([c_compiler ])
Returns a list of headers to include in the file. ‘Python.h’ is included by default so you don’t
need to specify it. Also all of the headers required by the Types involved (inputs and outputs)
will also be included.
The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_header_dirs([c_compiler ])
Returns a list of directories to search for headers (arguments to -I).
1
There are actually two versions of this method one with a c_compiler parameter and one without. The calling code will try the
version with c_compiler and try the version without if it does not work. Defining both versions is pointless since the one without
c_compiler will never get called.
Note that these methods are not specific to a single apply node so they may get called more than once on the same object with
different values for c_compiler.
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The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_libraries([c_compiler ])
Returns a list of library names that your op needs to link to. All ops are automatically linked
with ‘python’ and the libraries their types require. (arguments to -l)
The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_lib_dirs([c_compiler ])
Returns a list of directory to search for libraries (arguments to -L).
The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_compile_args([c_compiler ])
Allows to specify additional arbitrary arguments to the C compiler. This is not usually required.
The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_no_compile_args([c_compiler ])
Returns a list of C compiler arguments that are forbidden when compiling this Op.
The c_compiler1 parameter is the C compiler that will be used to compile the code for the node.
You may get multiple calls with different C compilers.
c_init_code()
Allows you to specify code that will be executed once when the module is initialized, before
anything else is executed. This is for code that will be executed once per Op.
c_init_code_apply(node, name)
Allows you to specify code that will be executed once when the module is initialized, before
anything else is executed and is specialized for a particular apply of an Op.
c_init_code_struct(node, name, sub)
Allows you to specify code that will be inserted in the struct constructor of the Op. This is for
code which should be executed once per thunk (Apply node, more or less).
sub is a dictionary of extras parameters to the c_code_init_code_struct method. It contains the
following values:
sub['fail']
A string of code that you should execute (after ensuring that a python exception is set)
if your C code needs to raise an exception.
sub['params']
(optional) The name of the variable which holds the context for the node. This will
only appear if the op has requested a context by having a get_params() method
that return something other than None.
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c_support_code()
Allows you to specify helper functions/structs that the Op needs. That code will be reused for
each apply of this op. It will be inserted at global scope.
c_support_code_apply(node, name)
Allows you to specify helper functions/structs specialized for a particular apply of an Op. Use
c_support_code() if the code is the same for each apply of an op. It will be inserted at
global scope.
c_support_code_struct(node, name)
Allows you to specify helper functions of variables that will be specific to one particular thunk.
These are inserted at struct scope.
Note You cannot specify CUDA kernels in the code returned by this since that isn’t
supported by CUDA. You should place your kernels in c_support_code() or
c_support_code_apply() and call them from this code.
c_cleanup_code_struct(node, name)
Allows you to specify code that will be inserted in the struct destructor of the Op. This is
for cleaninp up allocations and stuff like this when the thunk is released (when you “free” a
compiled function using this op).
infer_shape(node, (i0_shapes, i1_shapes, ...))
Allow optimizations to lift the Shape op over this op. An example of why this is good is when
we only need the shape of a variable: we will be able to obtain it without computing the variable
itself.
Must return a list where each element is a tuple representing the shape of one output.
For example, for the matrix-matrix product infer_shape will have as inputs (node, ((x0,x1),
(y0,y1))) and should return [(x0, y1)]. Both the inputs and the return value may be Theano
variables.
c_code_cache_version()
Must return a tuple of hashable objects like integers. This specifies the version of the code. It is
used to cache the compiled code. You MUST change the returned tuple for each change in the
code. If you don’t want to cache the compiled code return an empty tuple or don’t implement it.
c_code_cache_version_apply(node)
Overrides c_code_cache_version() if defined, but otherwise has the same contract.
python_constant_folding(node)
Optional. If present this method will be called before doing constant folding of a node, with
that node as a parameter. If it return True, we will not generate c code when doing constant
folding of this node. This is useful when the compilation of the c code will be longer then the
computation in python (e.g. Elemwise of scalars).
In addition, this allow to lower the number of compiled module and disk access. Particularly
useful when the file system load is high or when theano compilation directory is shared by many
process (like on a network file server on a cluster).
get_params(node)
(optional) If defined, should return the runtime params the op needs. These parameters will
be passed to the C code through the variable named in sub[’params’]. The variable is also
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available for use in the code returned by c_init_code_struct(). If it returns None this is
considered the same as if the method was not defined.
If this method is defined and does not return None, then the Op must have a params_type property
with the Type to use for the params variable.
_f16_ok
(optional) If this attribute is absent or evaluates to False, C code will be disabled for the op if
any of its inputs or outputs contains float16 data. This is added as a check to make sure we don’t
compute wrong results since there is no hardware float16 type so special care must be taken to
make sure operations are done correctly.
If you don’t intend to deal with float16 data you can leave this undefined.
This attribute is internal and may go away at any point during developpment if a better solution
is found.
The name argument is currently given an invalid value, so steer away from it. As was the case with Type,
sub['fail'] provides failure code that you must use if you want to raise an exception, after setting the
exception message.
The node argument is an Apply node representing an application of the current Op on a list of inputs,
producing a list of outputs. input_names and output_names arguments contain as many strings as
there are inputs and outputs to the application of the Op and they correspond to the name that is passed
to the type of each Variable in these lists. For example, if node.inputs[0].type == double, then
input_names[0] is the name argument passed to double.c_declare etc. when the first input is
processed by Theano.
In a nutshell, input_names and output_names parameterize the names of the inputs your operation
needs to use and the outputs it needs to put variables into. But this will be clear with the examples.
Defining the methods
We will be defining C code for the multiplication Op on doubles.
c_code
def c_code(node, name, input_names, output_names, sub):
x_name, y_name = input_names[0], input_names[1]
output_name = output_names[0]
return """
%(output_name)s = %(x_name)s * %(y_name)s;
""" % locals()
mul.c_code = c_code
And that’s it. As we enter the scope of the C code we are defining in the method above, many variables are
defined for us. Namely, the variables x_name, y_name and output_name are all of the primitive C double
type and they were declared using the C code returned by double.c_declare.
Implementing multiplication is as simple as multiplying the two input doubles and setting the output double
to what comes out of it. If you had more than one output, you would just set the variable(s) for each output
to what they should be.
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Warning: Do NOT use C’s return statement to return the variable(s) of the computations. Set the
output variables directly as shown above. Theano will pick them up for you.
c_code_cleanup
There is nothing to cleanup after multiplying two doubles. Typically, you won’t need to define this method
unless you malloc() some temporary storage (which you would free() here) or create temporary Python
objects (which you would Py_XDECREF() here).
Final version
As before, I tried to organize the code in order to minimize repetition. You can check that mul produces the
same C code in this version that it produces in the code I gave above.
from theano import gof
class BinaryDoubleOp(gof.Op):
__props__ = ("name", "fn", "ccode")
def __init__(self, name, fn, ccode):
self.name = name
self.fn = fn
self.ccode = ccode
def make_node(self, x, y):
if isinstance(x, (int, float)):
x = gof.Constant(double, x)
if isinstance(y, (int, float)):
y = gof.Constant(double, y)
if x.type != double or y.type != double:
raise TypeError('%s only works on doubles' % self.name)
return gof.Apply(self, [x, y], [double()])
def perform(self, node, inp, out):
x, y = inp
z, = out
z[0] = self.fn(x, y)
def __str__(self):
return self.name
def c_code(self, node, name, inp, out, sub):
x, y = inp
z, = out
return self.ccode % locals()
add = BinaryDoubleOp(name='add',
fn=lambda x, y: x + y,
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ccode="%(z)s = %(x)s + %(y)s;")
sub = BinaryDoubleOp(name='sub',
fn=lambda x, y: x - y,
ccode="%(z)s = %(x)s - %(y)s;")
mul = BinaryDoubleOp(name='mul',
fn=lambda x, y: x * y,
ccode="%(z)s = %(x)s * %(y)s;")
div = BinaryDoubleOp(name='div',
fn=lambda x, y: x / y,
ccode="%(z)s = %(x)s / %(y)s;")
Using Op params
The Op params is a facility to pass some runtime parameters to the code of an op without modifying it. It
can enable a single instance of C code to serve different needs and therefore reduce compilation.
The code enables you to pass a single object, but it can be a struct or python object with multiple values if
you have more than one value to pass.
We will first introduce the parts involved in actually using this functionality and then present a simple
working example.
The params type
You can either reuse an existing type such as Generic or create your own.
Using a python object for your op parameters (Generic) can be annoying to access from C code since you
would have to go through the Python-C API for all accesses.
Making a purpose-built class may require more upfront work, but can pay off if you reuse the type for a lot
of Ops, by not having to re-do all of the python manipulation.
Defining a params type
Note: This section is only relevant if you decide to create your own type.
The first thing you need to do is to define a Theano Type for your params object. It doesn’t have to be
complete type because only the following methods will be used for the type:
• filter
• __eq__
• __hash__
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• values_eq
Additionaly if you want to use your params with C code, you need the following methods:
• c_declare
• c_init
• c_extract
• c_cleanup
You can also define other convenience methods such as c_headers if you need any special things.
Registering the params with your Op
To declare that your Op uses params you have to set the class attribute params_type to an instance of
your params Type.
Note: If you want to have multiple parameters you have to bundle those inside a single object and use that
as the params type.
For example if we decide to use an int as the params the following would be appropriate:
class MyOp(Op):
params_type = Generic()
After that you need to define a get_params() method on your class with the following signature:
def get_params(self, node)
This method must return a valid object for your Type (an object that passes filter()). The node parameter is the Apply node for which we want the params. Therefore the params object can depend on the inputs
and outputs of the node.
Note: Due to implementation restrictions, None is not allowed as a params object and will be taken to mean
that the Op doesn’t have parameters.
Since this will change the expected signature of a few methods, it is strongly discouraged to have your
get_params() method return None.
Signature changes from having params
Having declared a params for your Op will affect the expected signature of perform(). The new expected
signature will have an extra parameter at the end which corresponds to the params object.
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Warning: If you do not account for this extra parameter, the code will fail at runtime if it tries to run
the python version.
Also, for the C code, the sub dictionary will contain an extra entry ‘params’ which will map to the variable
name of the params object. This is true for all methods that recieve a sub parameter, so this means that you
can use your params in the c_code and c_init_code_struct method.
A simple example
This is a simple example which uses a params object to pass a value. This Op will multiply a scalar input
by a fixed floating point value.
Since the value in this case is a python float, we chose Generic as the params type.
from theano import Op
from theano.gof.type import Generic
from theano.scalar import as_scalar
class MulOp(Op):
params_type = Generic()
__props__ = ('mul',)
def __init__(self, mul):
self.mul = float(mul)
def get_params(self, node):
return self.mul
def make_node(self, inp):
inp = as_scalar(inp)
return Apply(self, [inp], [inp.type()])
def perform(self, node, inputs, output_storage, params):
# Here params is a python float so this is ok
output_storage[0][0] = inputs[0] * params
def c_code(self, node, name, inputs, outputs, sub):
return ("%(z)s = %(x)s * PyFloat_AsDouble(%(p)s);" %
dict(z=outputs[0], x=inputs[0], p=sub['params']))
A more complex example
This is a more complex example which actually passes multiple values. It does a linear combination of two
values using floating point weights.
from theano import Op
from theano.gof.type import Generic
from theano.scalar import as_scalar
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class ab(object):
def __init__(self, alpha, beta):
self.alpha = alpha
self.beta = beta
class Mix(Op):
params_type = Generic()
__props__ = ('alpha', 'beta')
def __init__(self, alpha, beta):
self.alpha = alpha
self.beta = beta
def get_params(self, node):
return ab(alpha=self.alpha, beta=self.beta)
def make_node(self, x, y):
x = as_scalar(x)
y = as_scalar(y)
return Apply(self, [x, y], [x.type()])
def c_support_code_struct(self, node, name):
return """
double alpha_%(name)s;
double beta_%(name)s;
""" % dict(name=name)
def c_init_code_struct(self, node, name, sub):
return """{
PyObject *tmp;
tmp = PyObject_GetAttrString(%(p)s, "alpha");
if (tmp == NULL)
%(fail)s
alpha_%(name)s = PyFloat_AsDouble(tmp);
Py_DECREF(%(tmp)s);
if (PyErr_Occurred())
%(fail)s
tmp = PyObject_GetAttrString(%(p)s, "beta");
if (tmp == NULL)
%(fail)s
beta_%(name)s = PyFloat_AsDouble(tmp);
Py_DECREF(tmp);
if (PyErr_Occurred())
%(fail)s
}""" % dict(name=name, p=sub['params'], fail=sub['fail'])
def c_code(self, node, name, inputs, outputs, sub):
return """
%(z)s = alpha_%(name)s * %(x)s + beta_%(name)s * %(y)s;
""" % dict(name=name, z=outputs[0], x=inputs[0], y=inputs[1])
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Graph optimization
In this section we will define a couple optimizations on doubles.
Todo
This tutorial goes way too far under the hood, for someone who just wants to add yet another pattern to the
libraries in tensor.opt for example.
We need another tutorial that covers the decorator syntax, and explains how to register your optimization
right away. That’s what you need to get going.
Later, the rest is more useful for when that decorator syntax type thing doesn’t work. (There are optimizations that don’t fit that model).
Note: The optimization tag cxx_only is used for optimizations that insert Ops which have no Python
implementation (so they only have C code). Optimizations with this tag are skipped when there is no C++
compiler available.
Global and local optimizations
First, let’s lay out the way optimizations work in Theano. There are two types of optimizations: global
optimizations and local optimizations. A global optimization takes a FunctionGraph object (a FunctionGraph is a wrapper around a whole computation graph, you can see its documentation for more
details) and navigates through it in a suitable way, replacing some Variables by others in the process. A
local optimization, on the other hand, is defined as a function on a single Apply node and must return either
False (to mean that nothing is to be done) or a list of new Variables that we would like to replace the
node’s outputs with. A Navigator is a special kind of global optimization which navigates the computation
graph in some fashion (in topological order, reverse-topological order, random order, etc.) and applies one
or more local optimizations at each step.
Optimizations which are holistic, meaning that they must take into account dependencies that might be all
over the graph, should be global. Optimizations that can be done with a narrow perspective are better defined
as local optimizations. The majority of optimizations we want to define are local.
Global optimization
A global optimization (or optimizer) is an object which defines the following methods:
class Optimizer
apply(fgraph)
This method takes a FunctionGraph object which contains the computation graph and does modifications in line with what the optimization is meant to do. This is one of the main methods of
the optimizer.
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add_requirements(fgraph)
This method takes a FunctionGraph object and adds features to it. These features are “plugins”
that are needed for the apply method to do its job properly.
optimize(fgraph)
This is the interface function called by Theano.
Default:
this is
apply(fgraph).
defined
by
Optimizer
as
add_requirement(fgraph);
See the section about FunctionGraph to understand how to define these methods.
Local optimization
A local optimization is an object which defines the following methods:
class LocalOptimizer
transform(node)
This method takes an Apply node and returns either False to signify that no changes are to
be done or a list of Variables which matches the length of the node’s outputs list. When the
LocalOptimizer is applied by a Navigator, the outputs of the node passed as argument to the
LocalOptimizer will be replaced by the list returned.
One simplification rule
For starters, let’s define the following simplification:
𝑥𝑦
=𝑥
𝑦
We will implement it in three ways: using a global optimization, a local optimization with a Navigator and
then using the PatternSub facility.
Global optimization
Here is the code for a global optimization implementing the simplification described above:
import theano
from theano import gof
from theano.gof import toolbox
class Simplify(gof.Optimizer):
def add_requirements(self, fgraph):
fgraph.attach_feature(toolbox.ReplaceValidate())
def apply(self, fgraph):
for node in fgraph.toposort():
if node.op == true_div:
x, y = node.inputs
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z = node.outputs[0]
if x.owner and x.owner.op == mul:
a, b = x.owner.inputs
if y == a:
fgraph.replace_validate(z, b)
elif y == b:
fgraph.replace_validate(z, a)
simplify = Simplify()
Todo
What is add_requirements? Why would we know to do this? Are there other requirements we might want
to know about?
Here’s how it works: first, in add_requirements, we add the ReplaceValidate FunctionGraph
Features located in toolbox – [doc TODO]. This feature adds the replace_validate method to
fgraph, which is an enhanced version of replace that does additional checks to ensure that we are not
messing up the computation graph (note: if ReplaceValidate was already added by another optimizer,
extend will do nothing). In a nutshell, toolbox.ReplaceValidate grants access to fgraph.
replace_validate, and fgraph.replace_validate allows us to replace a Variable with another while respecting certain validation constraints. You can browse the list of FunctionGraph Feature List
and see if some of them might be useful to write optimizations with. For example, as an exercise, try to
rewrite Simplify using NodeFinder. (Hint: you want to use the method it publishes instead of the call to
toposort!)
Then, in apply we do the actual job of simplification. We start by iterating through the graph in topological
order. For each node encountered, we check if it’s a div node. If not, we have nothing to do here. If so, we
put in x, y and z the numerator, denominator and quotient (output) of the division. The simplification only
occurs when the numerator is a multiplication, so we check for that. If the numerator is a multiplication
we put the two operands in a and b, so we can now say that z == (a*b)/y. If y==a then z==b and
if y==b then z==a. When either case happens then we can replace z by either a or b using fgraph.
replace_validate - else we do nothing. You might want to check the documentation about Variable
and Apply to get a better understanding of the pointer-following game you need to get ahold of the nodes of
interest for the simplification (x, y, z, a, b, etc.).
Test time:
>>> from theano.scalar import float64, add, mul, true_div
>>> x = float64('x')
>>> y = float64('y')
>>> z = float64('z')
>>> a = add(z, mul(true_div(mul(y, x), y), true_div(z, x)))
>>> e = gof.FunctionGraph([x, y, z], [a])
>>> e
[add(z, mul(true_div(mul(y, x), y), true_div(z, x)))]
>>> simplify.optimize(e)
>>> e
[add(z, mul(x, true_div(z, x)))]
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Cool! It seems to work. You can check what happens if you put many instances of 𝑥𝑦
𝑦 in the graph. Note
that it sometimes won’t work for reasons that have nothing to do with the quality of the optimization you
wrote. For example, consider the following:
>>> x = float64('x')
>>> y = float64('y')
>>> z = float64('z')
>>> a = true_div(mul(add(y, z), x), add(y, z))
>>> e = gof.FunctionGraph([x, y, z], [a])
>>> e
[true_div(mul(add(y, z), x), add(y, z))]
>>> simplify.optimize(e)
>>> e
[true_div(mul(add(y, z), x), add(y, z))]
Nothing happened here. The reason is: add(y, z) != add(y, z). That is the case for efficiency
reasons. To fix this problem we first need to merge the parts of the graph that represent the same computation,
using the MergeOptimizer defined in theano.gof.opt.
>>> from theano.gof.opt import MergeOptimizer
>>> MergeOptimizer().optimize(e)
(0, ..., None, None, {}, 1, 0)
>>> e
[true_div(mul(*1 -> add(y, z), x), *1)]
>>> simplify.optimize(e)
>>> e
[x]
Once the merge is done, both occurrences of add(y, z) are collapsed into a single one and is used
as an input in two places. Note that add(x, y) and add(y, x) are still considered to be different
because Theano has no clue that add is commutative. You may write your own global optimizer to identify
computations that are identical with full knowledge of the rules of arithmetics that your Ops implement.
Theano might provide facilities for this somewhere in the future.
Note: FunctionGraph is a Theano structure intended for the optimization phase. It is used internally
by function and is rarely exposed to the end user. You can use it to test out optimizations, etc. if you are
comfortable with it, but it is recommended to use the function frontend and to interface optimizations with
optdb (we’ll see how to do that soon).
Local optimization
The local version of the above code would be the following:
class LocalSimplify(gof.LocalOptimizer):
def transform(self, node):
if node.op == true_div:
x, y = node.inputs
if x.owner and x.owner.op == mul:
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a, b = x.owner.inputs
if y == a:
return [b]
elif y == b:
return [a]
return False
def tracks(self):
# This should be needed for the EquilibriumOptimizer
# but it isn't now
# TODO: do this and explain it
return [] # that's not what you should do
local_simplify = LocalSimplify()
Todo
Fix up previous example... it’s bad and incomplete.
The definition of transform is the inner loop of the global optimizer, where the node is given as argument. If
no changes are to be made, False must be returned. Else, a list of what to replace the node’s outputs with
must be returned. This list must have the same length as node.ouputs. If one of node.outputs don’t have
clients(it is not used in the graph), you can put None in the returned list to remove it.
In order to apply the local optimizer we must use it in conjunction with a Navigator. Basically, a Navigator
is a global optimizer that loops through all nodes in the graph (or a well-defined subset of them) and applies
one or several local optimizers on them.
>>> x = float64('x')
>>> y = float64('y')
>>> z = float64('z')
>>> a = add(z, mul(true_div(mul(y, x), y), true_div(z, x)))
>>> e = gof.FunctionGraph([x, y, z], [a])
>>> e
[add(z, mul(true_div(mul(y, x), y), true_div(z, x)))]
>>> simplify = gof.TopoOptimizer(local_simplify)
>>> simplify.optimize(e)
(<theano.gof.opt.TopoOptimizer object at 0x...>, 1, 5, 3, ..., ..., ...)
>>> e
[add(z, mul(x, true_div(z, x)))]
OpSub, OpRemove, PatternSub
Theano defines some shortcuts to make LocalOptimizers:
OpSub(op1, op2)
Replaces all uses of op1 by op2. In other words, the outputs of all Apply involving op1 by the outputs
of Apply nodes involving op2, where their inputs are the same.
OpRemove(op)
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Removes all uses of op in the following way: if y = op(x) then y is replaced by x. op must have
as many outputs as it has inputs. The first output becomes the first input, the second output becomes
the second input, and so on.
PatternSub(pattern1, pattern2)
Replaces all occurrences of the first pattern by the second pattern. See PatternSub.
from theano.gof.opt import OpSub, OpRemove, PatternSub
# Replacing add by mul (this is not recommended for primarily
# mathematical reasons):
add_to_mul = OpSub(add, mul)
# Removing identity
remove_identity = OpRemove(identity)
# The "simplify" operation we've been defining in the past few
# sections. Note that we need two patterns to account for the
# permutations of the arguments to mul.
local_simplify_1 = PatternSub((true_div, (mul, 'x', 'y'), 'y'),
'x')
local_simplify_2 = PatternSub((true_div, (mul, 'x', 'y'), 'x'),
'y')
Note: OpSub, OpRemove and PatternSub produce local optimizers, which means that everything we
said previously about local optimizers apply: they need to be wrapped in a Navigator, etc.
Todo
wtf is a navigator?
When an optimization can be naturally expressed using OpSub, OpRemove or PatternSub, it is highly
recommended to use them.
WRITEME: more about using PatternSub (syntax for the patterns, how to use constraints, etc. - there’s some
decent doc at PatternSub for those interested)
The optimization database (optdb)
Theano exports a symbol called optdb which acts as a sort of ordered database of optimizations. When
you make a new optimization, you must insert it at the proper place in the database. Furthermore, you can
give each optimization in the database a set of tags that can serve as a basis for filtering.
The point of optdb is that you might want to apply many optimizations to a computation graph in many
unique patterns. For example, you might want to do optimization X, then optimization Y, then optimization
Z. And then maybe optimization Y is an EquilibriumOptimizer containing LocalOptimizers A, B and C
which are applied on every node of the graph until they all fail to change it. If some optimizations act up,
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we want an easy way to turn them off. Ditto if some optimizations are very CPU-intensive and we don’t
want to take the time to apply them.
The optdb system allows us to tag each optimization with a unique name as well as informative tags such as
‘stable’, ‘buggy’ or ‘cpu_intensive’, all this without compromising the structure of the optimizations.
Definition of optdb
optdb is an object which is an instance of SequenceDB, itself a subclass of DB. There exist (for now)
two types of DB, SequenceDB and EquilibriumDB. When given an appropriate Query, DB objects build an
Optimizer matching the query.
A SequenceDB contains Optimizer or DB objects. Each of them has a name, an arbitrary number of tags
and an integer representing their order in the sequence. When a Query is applied to a SequenceDB, all
Optimizers whose tags match the query are inserted in proper order in a SequenceOptimizer, which is
returned. If the SequenceDB contains DB instances, the Query will be passed to them as well and the
optimizers they return will be put in their places.
An EquilibriumDB contains LocalOptimizer or DB objects. Each of them has a name and an arbitrary
number of tags. When a Query is applied to an EquilibriumDB, all LocalOptimizers that match the query
are inserted into an EquilibriumOptimizer, which is returned. If the SequenceDB contains DB instances, the
Query will be passed to them as well and the LocalOptimizers they return will be put in their places (note
that as of yet no DB can produce LocalOptimizer objects, so this is a moot point).
Theano contains one principal DB object, optdb, which contains all of Theano’s optimizers with proper
tags. It is recommended to insert new Optimizers in it. As mentioned previously, optdb is a SequenceDB,
so, at the top level, Theano applies a sequence of global optimizations to the computation graphs.
Query
A Query is built by the following call:
theano.gof.Query(include, require=None, exclude=None, subquery=None)
class Query
include
A set of tags (a tag being a string) such that every optimization obtained through this Query must
have one of the tags listed. This field is required and basically acts as a starting point for the
search.
require
A set of tags such that every optimization obtained through this Query must have all of these
tags.
exclude
A set of tags such that every optimization obtained through this Query must have none of these
tags.
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subquery
optdb can contain sub-databases; subquery is a dictionary mapping the name of a sub-database
to a special Query. If no subquery is given for a sub-database, the original Query will be used
again.
Furthermore, a Query object includes three methods, including, requiring and excluding which
each produce a new Query object with include, require and exclude sets refined to contain the new
[WRITEME]
Examples
Here are a few examples of how to use a Query on optdb to produce an Optimizer:
from theano.gof import Query
from theano.compile import optdb
# This is how the optimizer for the fast_run mode is defined
fast_run = optdb.query(Query(include=['fast_run']))
# This is how the optimizer for the fast_compile mode is defined
fast_compile = optdb.query(Query(include=['fast_compile']))
# This is the same as fast_run but no optimizations will replace
# any operation by an inplace version. This assumes, of course,
# that all inplace operations are tagged as 'inplace' (as they
# should!)
fast_run_no_inplace = optdb.query(Query(include=['fast_run'],
exclude=['inplace']))
Registering an Optimizer
Let’s say we have a global optimizer called simplify. We can add it to optdb as follows:
# optdb.register(name, optimizer, order, *tags)
optdb.register('simplify', simplify, 0.5, 'fast_run')
Once this is done, the FAST_RUN mode will automatically include your optimization (since you gave it the
‘fast_run’ tag). Of course, already-compiled functions will see no change. The ‘order’ parameter (what it
means and how to choose it) will be explained in optdb structure below.
Registering a LocalOptimizer
LocalOptimizers may be registered in two ways:
• Wrap them in a Navigator and insert them like a global optimizer (see previous section).
• Put them in an EquilibriumDB.
Theano defines two EquilibriumDBs where you can put local optimizations:
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canonicalize()
This contains optimizations that aim to simplify the graph:
•Replace rare or esoterical operations with their equivalents using elementary operations.
•Order operations in a canonical way (any sequence of multiplications and divisions can be rewritten to contain at most one division, for example; x*x can be rewritten x**2; etc.)
•Fold constants (Constant(2)*Constant(2) becomes Constant(4))
specialize()
This contains optimizations that aim to specialize the graph:
•Replace a combination of operations with a special operation that does the same thing (but
better).
For each group, all optimizations of the group that are selected by the Query will be applied on the graph
over and over again until none of them is applicable, so keep that in mind when designing it: check carefully
that your optimization leads to a fixpoint (a point where it cannot apply anymore) at which point it returns
False to indicate its job is done. Also be careful not to undo the work of another local optimizer in the
group, because then the graph will oscillate between two or more states and nothing will get done.
optdb structure
optdb contains the following Optimizers and sub-DBs, with the given priorities and tags:
Order
0
1
2
49
49.5
100
Name
merge1
canonicalize
specialize
merge2
add_destroy_handler
merge3
Description
First merge operation
Simplify the graph
Add specialized operations
Second merge operation
Enable inplace optimizations
Third merge operation
The merge operations are meant to put together parts of the graph that represent the same computation.
Since optimizations can modify the graph in such a way that two previously different-looking parts of the
graph become similar, we merge at the beginning, in the middle and at the very end. Technically, we only
really need to do it at the end, but doing it in previous steps reduces the size of the graph and therefore
increases the efficiency of the process.
See previous section for more information about the canonicalize and specialize steps.
The add_destroy_handler step is not really an optimization. It is a marker. Basically:
Warning: Any optimization which inserts inplace operations in the computation graph must appear
after the add_destroy_handler “optimizer”. In other words, the priority of any such optimization
must be >= 50. Failure to comply by this restriction can lead to the creation of incorrect computation
graphs.
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The reason the destroy handler is not inserted at the beginning is that it is costly to run. It is cheaper to run
most optimizations under the assumption there are no inplace operations.
Navigator
WRITEME
Profiling Theano function compilation
You find that compiling a Theano function is taking too much time? You can get profiling information about
Theano optimization. The normal Theano profiler will provide you with very high-level information. The
indentation shows the included in/subset relationship between sections. The top of its output look like this:
Function profiling
==================
Message: PATH_TO_A_FILE:23
Time in 0 calls to Function.__call__: 0.000000e+00s
Total compile time: 1.131874e+01s
Number of Apply nodes: 50
Theano Optimizer time: 1.152431e+00s
Theano validate time: 2.790451e-02s
Theano Linker time (includes C, CUDA code generation/compiling): 7.
˓→893991e-02s
Import time 1.153541e-02s
Time in all call to theano.grad() 4.732513e-02s
Explanations:
• Total compile time:
1.131874e+01s gives the total time spent inside theano.function.
• Number of Apply nodes:
graph.
50 means that after optimization, there are 50 apply node in the
• Theano Optimizer time: 1.152431e+00s means that we spend 1.15s in the theano.
function phase where we optimize (modify) the graph to make it faster / more stable numerically
/ work on GPU /...
• Theano validate time: 2.790451e-02s means that we spent 2.8e-2s in the validate
subset of the optimization phase.
• Theano Linker time (includes C, CUDA code generation/compiling):
7.893991e-02s means that we spent 7.9e-2s in linker phase of theano.function.
• Import time 1.153541e-02s is a subset of the linker time where we import the compiled
module.
• Time in all call to theano.grad() 4.732513e-02s tells that we spent a total of
4.7e-2s in all calls to theano.grad. This is outside of the calls to theano.function.
The linker phase includes the generation of the C code, the time spent by g++ to compile and the time
needed by Theano to build the object we return. The C code generation and compilation is cached, so the
first time you compile a function and the following ones could take different amount of execution time.
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Detailed profiling of Theano optimizer
You can get more detailed profiling information about the Theano optimizer phase by setting to True the
Theano flags config.profile_optimizer (this require config.profile to be True as well).
This will output something like this:
Optimizer Profile
----------------SeqOptimizer OPT_FAST_RUN time 1.152s for 123/50 nodes before/after
˓→optimization
0.028s for fgraph.validate()
0.131s for callback
time
- (name, class, index) - validate time
0.751816s - ('canonicalize', 'EquilibriumOptimizer', 4) - 0.004s
EquilibriumOptimizer
canonicalize
time 0.751s for 14 passes
nb nodes (start, end, max) 108 81 117
time io_toposort 0.029s
time in local optimizers 0.687s
time in global optimizers 0.010s
0 - 0.050s 27 (0.000s in global opts, 0.002s io_toposort) - 108 nodes
˓→- ('local_dimshuffle_lift', 9) ('local_upcast_elemwise_constant_inputs', 5)
˓→('local_shape_to_shape_i', 3) ('local_fill_sink', 3) ('local_fill_to_alloc',
˓→ 2) ...
1 - 0.288s 26 (0.002s in global opts, 0.002s io_toposort) - 117 nodes
˓→- ('local_dimshuffle_lift', 8) ('local_fill_sink', 4) ('constant_folding',
˓→4) ('local_useless_elemwise', 3) ('local_subtensor_make_vector', 3) ...
2 - 0.044s 13 (0.002s in global opts, 0.003s io_toposort) - 96 nodes ˓→ ('constant_folding', 4) ('local_dimshuffle_lift', 3) ('local_fill_sink',
˓→3) ('local_useless_elemwise', 1) ('local_fill_to_alloc', 1) ...
3 - 0.045s 11 (0.000s in global opts, 0.002s io_toposort) - 91 nodes ˓→ ('constant_folding', 3) ('local_fill_to_alloc', 2) ('local_dimshuffle_lift
˓→', 2) ('local_mul_canonizer', 2) ('MergeOptimizer', 1) ...
4 - 0.035s 8 (0.002s in global opts, 0.002s io_toposort) - 93 nodes ˓→('local_fill_sink', 3) ('local_dimshuffle_lift', 2) ('local_fill_to_alloc',
˓→1) ('MergeOptimizer', 1) ('constant_folding', 1)
5 - 0.035s 6 (0.000s in global opts, 0.002s io_toposort) - 88 nodes ˓→('local_fill_sink', 2) ('local_dimshuffle_lift', 2) ('local_fill_to_alloc',
˓→1) ('local_mul_canonizer', 1)
6 - 0.038s 10 (0.001s in global opts, 0.002s io_toposort) - 95 nodes ˓→ ('local_fill_sink', 3) ('local_dimshuffle_lift', 3) ('constant_folding',
˓→2) ('local_fill_to_alloc', 1) ('MergeOptimizer', 1)
7 - 0.032s 5 (0.001s in global opts, 0.002s io_toposort) - 91 nodes ˓→('local_fill_sink', 3) ('MergeOptimizer', 1) ('local_dimshuffle_lift', 1)
8 - 0.034s 5 (0.000s in global opts, 0.002s io_toposort) - 92 nodes ˓→('local_fill_sink', 3) ('MergeOptimizer', 1) ('local_greedy_distributor', 1)
9 - 0.031s 6 (0.001s in global opts, 0.002s io_toposort) - 90 nodes ˓→('local_fill_sink', 2) ('local_fill_to_alloc', 1) ('MergeOptimizer', 1) (
˓→'local_dimshuffle_lift', 1) ('local_greedy_distributor', 1)
10 - 0.032s 5 (0.000s in global opts, 0.002s io_toposort) - 89 nodes ˓→('local_dimshuffle_lift', 2) ('local_fill_to_alloc', 1) ('MergeOptimizer',
˓→1) ('local_fill_sink', 1)
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11 - 0.030s 5 (0.000s in global opts, 0.002s io_toposort) - 88 nodes ('local_dimshuffle_lift', 2) ('local_fill_to_alloc', 1) ('MergeOptimizer',
˓→1) ('constant_folding', 1)
12 - 0.026s 1 (0.000s in global opts, 0.003s io_toposort) - 81 nodes ˓→('MergeOptimizer', 1)
13 - 0.031s 0 (0.000s in global opts, 0.003s io_toposort) - 81 nodes times - times applied - nb node created - name:
0.263s - 15 - 0 - constant_folding
0.096s - 2 - 14 - local_greedy_distributor
0.066s - 4 - 19 - local_mul_canonizer
0.046s - 28 - 57 - local_fill_sink
0.042s - 35 - 78 - local_dimshuffle_lift
0.018s - 5 - 15 - local_upcast_elemwise_constant_inputs
0.010s - 11 - 4 - MergeOptimizer
0.009s - 4 - 0 - local_useless_elemwise
0.005s - 11 - 2 - local_fill_to_alloc
0.004s - 3 - 6 - local_neg_to_mul
0.002s - 1 - 3 - local_lift_transpose_through_dot
0.002s - 3 - 4 - local_shape_to_shape_i
0.002s - 2 - 4 - local_subtensor_lift
0.001s - 3 - 0 - local_subtensor_make_vector
0.001s - 1 - 1 - local_sum_all_to_none
0.131s - in 62 optimization that where not used (display only those
˓→with a runtime > 0)
0.050s - local_add_canonizer
0.018s - local_mul_zero
0.016s - local_one_minus_erf
0.010s - local_func_inv
0.006s - local_0_dot_x
0.005s - local_track_shape_i
0.004s - local_mul_switch_sink
0.004s - local_fill_cut
0.004s - local_one_minus_erf2
0.003s - local_remove_switch_const_cond
0.003s - local_cast_cast
0.002s - local_IncSubtensor_serialize
0.001s - local_sum_div_dimshuffle
0.001s - local_div_switch_sink
0.001s - local_dimshuffle_no_inplace_at_canonicalize
0.001s - local_cut_useless_reduce
0.001s - local_reduce_join
0.000s - local_sum_sum
0.000s - local_useless_alloc
0.000s - local_reshape_chain
0.000s - local_useless_subtensor
0.000s - local_reshape_lift
0.000s - local_flatten_lift
0.000s - local_useless_slice
0.000s - local_subtensor_of_alloc
0.000s - local_subtensor_of_dot
0.000s - local_subtensor_merge
0.101733s - ('elemwise_fusion', 'SeqOptimizer', 13) - 0.000s
SeqOptimizer
elemwise_fusion time 0.102s for 78/50 nodes before/
˓→after optimization
˓→
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0.000s for fgraph.validate()
0.004s for callback
0.095307s - ('composite_elemwise_fusion', 'FusionOptimizer', 1) - 0.
˓→
000s
FusionOptimizer
nb_iter 3
nb_replacement 10
nb_inconsistency_replace 0
validate_time 0.000249624252319
callback_time 0.00316381454468
time_toposort 0.00375390052795
0.006412s - ('local_add_mul_fusion', 'FusionOptimizer', 0) - 0.000s
FusionOptimizer
nb_iter 2
nb_replacement 3
nb_inconsistency_replace 0
validate_time 6.43730163574e-05
callback_time 0.000783205032349
time_toposort 0.0035240650177
0.090089s - ('inplace_elemwise_optimizer', 'FromFunctionOptimizer', 30) ˓→0.019s
0.048993s - ('BlasOpt', 'SeqOptimizer', 8) - 0.000s
SeqOptimizer
BlasOpt time 0.049s for 81/80 nodes before/after
˓→optimization
0.000s for fgraph.validate()
0.003s for callback
0.035997s - ('gemm_optimizer', 'GemmOptimizer', 1) - 0.000s
GemmOptimizer
nb_iter 2
nb_replacement 2
nb_replacement_didn_t_remove 0
nb_inconsistency_make 0
nb_inconsistency_replace 0
time_canonicalize 0.00720071792603
time_factor_can 9.05990600586e-06
time_factor_list 0.00128507614136
time_toposort 0.00311398506165
validate_time 4.60147857666e-05
callback_time 0.00174236297607
0.004569s - ('local_dot_to_dot22', 'TopoOptimizer', 0) - 0.000s
TopoOptimizer
nb_node (start, end, changed) (81, 81, 5)
init io_toposort 0.00139284133911
loop time 0.00312399864197
callback_time 0.00172805786133
0.002283s - ('local_dot22_to_dot22scalar', 'TopoOptimizer', 2) - 0.000s
TopoOptimizer
nb_node (start, end, changed) (80, 80, 0)
init io_toposort 0.00171804428101
loop time 0.000502109527588
callback_time 0.0
0.002257s - ('local_gemm_to_gemv', 'EquilibriumOptimizer', 3) - 0.000s
EquilibriumOptimizer
local_gemm_to_gemv
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time 0.002s for 1 passes
nb nodes (start, end, max) 80 80 80
time io_toposort 0.001s
time in local optimizers 0.000s
time in global optimizers 0.000s
0 - 0.002s 0 (0.000s in global opts, 0.001s io_toposort) - 80
nodes 0.002227s - ('use_c_blas', 'TopoOptimizer', 4) - 0.000s
TopoOptimizer
nb_node (start, end, changed) (80, 80, 0)
init io_toposort 0.0014750957489
loop time 0.00068998336792
callback_time 0.0
0.001632s - ('use_scipy_ger', 'TopoOptimizer', 5) - 0.000s
TopoOptimizer
nb_node (start, end, changed) (80, 80, 0)
init io_toposort 0.00138401985168
loop time 0.000202178955078
callback_time 0.0
0.031740s - ('specialize', 'EquilibriumOptimizer', 9) - 0.000s
EquilibriumOptimizer
specialize
time 0.031s for 2 passes
nb nodes (start, end, max) 80 78 80
time io_toposort 0.003s
time in local optimizers 0.022s
time in global optimizers 0.004s
0 - 0.017s 6 (0.002s in global opts, 0.001s io_toposort) - 80 nodes ˓→('constant_folding', 2) ('local_mul_to_sqr', 1) ('local_elemwise_alloc', 1)
˓→('local_div_to_inv', 1) ('local_mul_specialize', 1)
1 - 0.014s 0 (0.002s in global opts, 0.001s io_toposort) - 78 nodes times - times applied - nb node created - name:
0.003s - 1 - 1 - local_mul_specialize
0.002s - 1 - 2 - local_elemwise_alloc
0.002s - 2 - 0 - constant_folding
0.001s - 1 - 1 - local_div_to_inv
0.001s - 1 - 1 - local_mul_to_sqr
0.016s - in 69 optimization that where not used (display only those
˓→with a runtime > 0)
0.004s - crossentropy_to_crossentropy_with_softmax_with_bias
0.002s - local_one_minus_erf
0.002s - Elemwise{sub,no_inplace}(z, Elemwise{mul,no_inplace}(alpha
˓→subject to <function <lambda> at 0x7f475e4da050>, SparseDot(x, y))) -> Usmm
˓→{no_inplace}(Elemwise{neg,no_inplace}(alpha), x, y, z)
0.002s - local_add_specialize
0.001s - local_func_inv
0.001s - local_useless_elemwise
0.001s - local_abs_merge
0.001s - local_track_shape_i
0.000s - local_one_minus_erf2
0.000s - local_sum_mul_by_scalar
0.000s - local_elemwise_sub_zeros
0.000s - local_cast_cast
0.000s - local_alloc_unary
˓→
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0.000s - Elemwise{log,no_inplace}(Softmax(x)) -> <function make_out_
pattern at 0x7f47619a8410>(x)
0.000s - local_sum_div_dimshuffle
0.000s - local_sum_alloc
0.000s - local_dimshuffle_lift
0.000s - local_reduce_broadcastable
0.000s - local_grad_log_erfc_neg
0.000s - local_advanced_indexing_crossentropy_onehot
0.000s - local_log_erfc
0.000s - local_log1p
0.000s - local_log_add
0.000s - local_useless_alloc
0.000s - local_neg_neg
0.000s - local_neg_div_neg
...
˓→
To understand this profile here is some explanation of how optimizations work:
• Optimizations are organized in an hierarchy. At the top level, there is a SeqOptimizer (Sequence
Optimizer). It contains other optimizers, and applies them in the order they were specified. Those
sub-optimizers can be of other types, but are all global optimizers.
• Each Optimizer in the hierarchy will print some stats about itself. The information that it prints
depends of the type of the optimizer.
• The SeqOptimizer will print some stats at the start:
Optimizer Profile
----------------SeqOptimizer OPT_FAST_RUN time 1.152s for 123/50 nodes
˓→before/after optimization
0.028s for fgraph.validate()
0.131s for callback
time
- (name, class, index) - validate time
Then it will print, with some additional indentation, each sub˓→optimizer's profile
information. These sub-profiles are ordered by the time they
˓→took to execute,
not by their execution order.
– OPT_FAST_RUN is the name of the optimizer
– 1.152s is the total time spent in that optimizer
– 123/50 means that before this optimization, there were 123 apply node in the function graph,
and after only 50.
– 0.028s means it spent that time calls to fgraph.validate()
– 0.131s means it spent that time for callbacks. This is a mechanism that can trigger other execution when there is a change to the FunctionGraph.
– time - (name, class, index) - validate time tells how the information for
each sub-optimizer get printed.
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– All other instances of SeqOptimizer are described like this. In particular, some suboptimizer from OPT_FAST_RUN that are also SeqOptimizer.
• The SeqOptimizer will print some stats at the start:
0.751816s - ('canonicalize', 'EquilibriumOptimizer', 4) - 0.004s
EquilibriumOptimizer
canonicalize
time 0.751s for 14 passes
nb nodes (start, end, max) 108 81 117
time io_toposort 0.029s
time in local optimizers 0.687s
time in global optimizers 0.010s
0 - 0.050s 27 (0.000s in global opts, 0.002s io_toposort) ˓→108 nodes - ('local_dimshuffle_lift', 9) ('local_upcast_
˓→elemwise_constant_inputs', 5) ('local_shape_to_shape_i', 3) (
˓→'local_fill_sink', 3) ('local_fill_to_alloc', 2) ...
1 - 0.288s 26 (0.002s in global opts, 0.002s io_toposort) ˓→117 nodes - ('local_dimshuffle_lift', 8) ('local_fill_sink',
˓→4) ('constant_folding', 4) ('local_useless_elemwise', 3) (
˓→'local_subtensor_make_vector', 3) ...
2 - 0.044s 13 (0.002s in global opts, 0.003s io_toposort) ˓→96 nodes - ('constant_folding', 4) ('local_dimshuffle_lift',
˓→3) ('local_fill_sink', 3) ('local_useless_elemwise', 1) (
˓→'local_fill_to_alloc', 1) ...
3 - 0.045s 11 (0.000s in global opts, 0.002s io_toposort) ˓→91 nodes - ('constant_folding', 3) ('local_fill_to_alloc', 2) (
˓→'local_dimshuffle_lift', 2) ('local_mul_canonizer', 2) (
˓→'MergeOptimizer', 1) ...
4 - 0.035s 8 (0.002s in global opts, 0.002s io_toposort) ˓→93 nodes - ('local_fill_sink', 3) ('local_dimshuffle_lift', 2)
˓→('local_fill_to_alloc', 1) ('MergeOptimizer', 1) ('constant_
˓→folding', 1)
5 - 0.035s 6 (0.000s in global opts, 0.002s io_toposort) ˓→88 nodes - ('local_fill_sink', 2) ('local_dimshuffle_lift', 2)
˓→('local_fill_to_alloc', 1) ('local_mul_canonizer', 1)
6 - 0.038s 10 (0.001s in global opts, 0.002s io_toposort) ˓→95 nodes - ('local_fill_sink', 3) ('local_dimshuffle_lift', 3)
˓→('constant_folding', 2) ('local_fill_to_alloc', 1) (
˓→'MergeOptimizer', 1)
7 - 0.032s 5 (0.001s in global opts, 0.002s io_toposort) ˓→91 nodes - ('local_fill_sink', 3) ('MergeOptimizer', 1) (
˓→'local_dimshuffle_lift', 1)
8 - 0.034s 5 (0.000s in global opts, 0.002s io_toposort) ˓→92 nodes - ('local_fill_sink', 3) ('MergeOptimizer', 1) (
˓→'local_greedy_distributor', 1)
9 - 0.031s 6 (0.001s in global opts, 0.002s io_toposort) ˓→90 nodes - ('local_fill_sink', 2) ('local_fill_to_alloc', 1) (
˓→'MergeOptimizer', 1) ('local_dimshuffle_lift', 1) ('local_
˓→greedy_distributor', 1)
10 - 0.032s 5 (0.000s in global opts, 0.002s io_toposort) ˓→89 nodes - ('local_dimshuffle_lift', 2) ('local_fill_to_alloc',
˓→ 1) ('MergeOptimizer', 1) ('local_fill_sink', 1)
11 - 0.030s 5 (0.000s in global opts, 0.002s io_toposort) ˓→88 nodes - ('local_dimshuffle_lift', 2) ('local_fill_to_alloc',
˓→ 1) ('MergeOptimizer', 1) ('constant_folding', 1)
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12 - 0.026s 1 (0.000s in global opts, 0.003s io_toposort) 81 nodes - ('MergeOptimizer', 1)
13 - 0.031s 0 (0.000s in global opts, 0.003s io_toposort) ˓→81 nodes times - times applied - nb node created - name:
0.263s - 15 - 0 - constant_folding
0.096s - 2 - 14 - local_greedy_distributor
0.066s - 4 - 19 - local_mul_canonizer
0.046s - 28 - 57 - local_fill_sink
0.042s - 35 - 78 - local_dimshuffle_lift
0.018s - 5 - 15 - local_upcast_elemwise_constant_inputs
0.010s - 11 - 4 - MergeOptimizer
0.009s - 4 - 0 - local_useless_elemwise
0.005s - 11 - 2 - local_fill_to_alloc
0.004s - 3 - 6 - local_neg_to_mul
0.002s - 1 - 3 - local_lift_transpose_through_dot
0.002s - 3 - 4 - local_shape_to_shape_i
0.002s - 2 - 4 - local_subtensor_lift
0.001s - 3 - 0 - local_subtensor_make_vector
0.001s - 1 - 1 - local_sum_all_to_none
0.131s - in 62 optimization that where not used (display
˓→only those with a runtime > 0)
0.050s - local_add_canonizer
0.018s - local_mul_zero
0.016s - local_one_minus_erf
0.010s - local_func_inv
0.006s - local_0_dot_x
0.005s - local_track_shape_i
0.004s - local_mul_switch_sink
0.004s - local_fill_cut
0.004s - local_one_minus_erf2
0.003s - local_remove_switch_const_cond
0.003s - local_cast_cast
0.002s - local_IncSubtensor_serialize
0.001s - local_sum_div_dimshuffle
0.001s - local_div_switch_sink
0.001s - local_dimshuffle_no_inplace_at_canonicalize
0.001s - local_cut_useless_reduce
0.001s - local_reduce_join
0.000s - local_sum_sum
0.000s - local_useless_alloc
0.000s - local_reshape_chain
0.000s - local_useless_subtensor
0.000s - local_reshape_lift
0.000s - local_flatten_lift
0.000s - local_useless_slice
0.000s - local_subtensor_of_alloc
0.000s - local_subtensor_of_dot
0.000s - local_subtensor_merge
˓→
– 0.751816s - ('canonicalize', 'EquilibriumOptimizer', 4) - 0.
004s This line is from SeqOptimizer, and indicates information related to a sub-optimizer.
It means that this sub-optimizer took a total of .7s. Its name is 'canonicalize'. It is an
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EquilibriumOptimizer. It was executed at index 4 by the SeqOptimizer. It spent
0.004s in the validate phase.
– All other lines are from the profiler of the EquilibriumOptimizer.
– An EquilibriumOptimizer does multiple passes on the Apply nodes from the graph, trying to apply local and global optimizations. Conceptually, it tries to execute all global optimizations, and to apply all local optimizations on all nodes in the graph. If no optimization got
applied during a pass, it stops. So it tries to find an equilibrium state where none of the optimizations get applied. This is useful when we do not know a fixed order for the execution of the
optimization.
– time 0.751s for 14 passes means that it took .7s and did 14 passes over the graph.
– nb nodes (start, end, max) 108 81 117 means that at the start, the graph had
108 node, at the end, it had 81 and the maximum size was 117.
– Then it prints some global timing information: it spent 0.029s in io_toposort, all local
optimizers took 0.687s together for all passes, and global optimizers took a total of 0.010s.
– Then we print the timing for each pass, the optimization that got applied, and the number of time
they got applied. For example, in pass 0, the local_dimshuffle_lift optimizer changed
the graph 9 time.
– Then we print the time spent in each optimizer, the number of times they changed the graph and
the number of nodes they introduced in the graph.
– Optimizations with that pattern local_op_lift means that a node with that op will be replaced by
another node, with the same op, but will do computation closer to the inputs of the graph. For
instance, local_op(f(x)) getting replaced by f(local_op(x)).
– Optimization with that pattern local_op_sink is the opposite of lift.
f(local_op(x)) getting replaced by local_op(f(x)).
For instance
– Local optimizers can replace any arbitrary node in the graph, not only the node it received as
input. For this, it must return a dict. The keys being nodes to replace and the values being the
corresponding replacement.
This is useful to replace a client of the node received as parameter.
Tips
Reusing outputs
WRITEME
Don’t define new Ops unless you have to
It is usually not useful to define Ops that can be easily implemented using other already existing Ops.
For example, instead of writing a “sum_square_difference” Op, you should probably just write a simple
function:
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from theano import tensor as T
def sum_square_difference(a, b):
return T.sum((a - b)**2)
Even without taking Theano’s optimizations into account, it is likely to work just as well as a custom
implementation. It also supports all data types, tensors of all dimensions as well as broadcasting, whereas a
custom implementation would probably only bother to support contiguous vectors/matrices of doubles...
Use Theano’s high order Ops when applicable
Theano provides some generic Op classes which allow you to generate a lot of Ops at a lesser effort. For
instance, Elemwise can be used to make elementwise operations easily whereas DimShuffle can be used to
make transpose-like transformations. These higher order Ops are mostly Tensor-related, as this is Theano’s
specialty.
Op Checklist
Use this list to make sure you haven’t forgotten anything when defining a new Op. It might not be exhaustive
but it covers a lot of common mistakes.
WRITEME
Unit Testing
Theano relies heavily on unit testing. Its importance cannot be stressed enough!
Unit Testing revolves around the following principles:
• ensuring correctness: making sure that your Op, Type or Optimization works in the way you intended
it to work. It is important for this testing to be as thorough as possible: test not only the obvious cases,
but more importantly the corner cases which are more likely to trigger bugs down the line.
• test all possible failure paths. This means testing that your code fails in the appropriate manner, by
raising the correct errors when in certain situations.
• sanity check: making sure that everything still runs after you’ve done your modification. If your
changes cause unit tests to start failing, it could be that you’ve changed an API on which other users
rely on. It is therefore your responsibility to either a) provide the fix or b) inform the author of your
changes and coordinate with that person to produce a fix. If this sounds like too much of a burden...
then good! APIs aren’t meant to be changed on a whim!
This page is in no way meant to replace tutorials on Python’s unittest module, for this we refer the reader to
the official documentation. We will however adress certain specificities about how unittests relate to theano.
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Unittest Primer
A unittest is a subclass of unittest.TestCase, with member functions with names that start with the
string test. For example:
import unittest
class MyTestCase(unittest.TestCase):
def test0(self):
pass
# test passes cleanly
def test1(self):
self.assertTrue(2+2 == 5)
# raises an exception, causes test to fail
def test2(self):
assert 2+2 == 5
# causes error in test (basically a failure, but counted separately)
def test2(self):
assert 2+2 == 4
# this test has the same name as a previous one,
# so this is the one that runs.
How to Run Unit Tests ?
Two options are available:
theano-nose
The easiest by far is to use theano-nose which is a command line utility that recurses through a given
directory, finds all unittests matching a specific criteria and executes them. By default, it will find & execute
tests case in test*.py files whose method name starts with ‘test’.
theano-nose is a wrapper around nosetests. You should be able to execute it if you installed Theano
using pip, or if you ran “python setup.py develop” after the installation. If theano-nose is not found by
your shell, you will need to add Theano/bin to your PATH environment variable.
Note: In Theano versions <= 0.5, theano-nose was not included. If you are working with such a
version, you can call nosetests instead of theano-nose in all the examples below.
Running all unit tests
cd Theano/
theano-nose
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Running unit tests with standard out
theano-nose -s
Running unit tests contained in a specific .py file
theano-nose <filename>.py
Running a specific unit test
theano-nose <filename>.py:<classname>.<method_name>
Using unittest module
To launch tests cases from within python, you can also use the functionality offered by the unittest
module. The simplest thing is to run all the tests in a file using unittest.main(). Python’s built-in
unittest module uses metaclasses to know about all the unittest.TestCase classes you have created.
This call will run them all, printing ‘.’ for passed tests, and a stack trace for exceptions. The standard footer
code in theano’s test files is:
if __name__ == '__main__':
unittest.main()
You can also choose to run a subset of the full test suite.
To run all the tests in one or more TestCase subclasses:
suite = unittest.TestLoader()
suite = suite.loadTestsFromTestCase(MyTestCase0)
suite = suite.loadTestsFromTestCase(MyTestCase1)
...
unittest.TextTestRunner(verbosity=2).run(suite)
To run just a single MyTestCase member test function called test0:
MyTestCase('test0').debug()
Folder Layout
“tests” directories are scattered throughout theano. Each tests subfolder is meant to contain the unittests
which validate the .py files in the parent folder.
Files containing unittests should be prefixed with the word “test”.
Optimally every python module should have a unittest file associated with it, as shown below. Unittests
testing functionality of module <module>.py should therefore be stored in tests/test_<module>.py:
Theano/theano/tensor/basic.py
Theano/theano/tensor/elemwise.py
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Theano/theano/tensor/tests/test_basic.py
Theano/theano/tensor/tests/test_elemwise.py
How to Write a Unittest
Test Cases and Methods
Unittests should be grouped “logically” into test cases, which are meant to group all unittests operating
on the same element and/or concept. Test cases are implemented as Python classes which inherit from
unittest.TestCase
Test cases contain multiple test methods. These should be prefixed with the word “test”.
Test methods should be as specific as possible and cover a particular aspect of the problem. For example,
when testing the TensorDot Op, one test method could check for validity, while another could verify that the
proper errors are raised when inputs have invalid dimensions.
Test method names should be as explicit as possible, so that users can see at first glance, what functionality
is being tested and what tests need to be added.
Example:
import unittest
class TestTensorDot(unittest.TestCase):
def test_validity(self):
# do stuff
...
def test_invalid_dims(self):
# do more stuff
...
Test cases can define a special setUp method, which will get called before each test method is executed. This
is a good place to put functionality which is shared amongst all test methods in the test case (i.e initializing
data, parameters, seeding random number generators – more on this later)
import unittest
class TestTensorDot(unittest.TestCase):
def setUp(self):
# data which will be used in various test methods
self.avals = numpy.array([[1,5,3],[2,4,1]])
self.bvals = numpy.array([[2,3,1,8],[4,2,1,1],[1,4,8,5]])
Similarly, test cases can define a tearDown method, which will be implicitely called at the end of each test
method.
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Checking for correctness
When checking for correctness of mathematical expressions, the user should preferably compare theano’s
output to the equivalent numpy implementation.
Example:
class TestTensorDot(unittest.TestCase):
def setUp(self):
...
def test_validity(self):
a = T.dmatrix('a')
b = T.dmatrix('b')
c = T.dot(a, b)
f = theano.function([a, b], [c])
cmp = f(self.avals, self.bvals) == numpy.dot(self.avals, self.bvals)
self.assertTrue(numpy.all(cmp))
Avoid hard-coding variables, as in the following case:
self.assertTrue(numpy.all(f(self.avals, self.bvals) == numpy.array([[25, 25,
˓→30, 28], [21, 18, 14, 25]])))
This makes the test case less manageable and forces the user to update the variables each time the input is
changed or possibly when the module being tested changes (after a bug fix for example). It also constrains
the test case to specific input/output data pairs. The section on random values covers why this might not be
such a good idea.
Here is a list of useful functions, as defined by TestCase:
• checking the state of boolean variables: assert, assertTrue, assertFalse
• checking for (in)equality constraints: assertEqual, assertNotEqual
• checking for (in)equality constraints up to a given precision (very useful in theano): assertAlmostEqual, assertNotAlmostEqual
Checking for errors
On top of verifying that your code provides the correct output, it is equally important to test that it fails in
the appropriate manner, raising the appropriate exceptions, etc. Silent failures are deadly, as they can go
unnoticed for a long time and a hard to detect “after-the-fact”.
Example:
import unittest
class TestTensorDot(unittest.TestCase):
...
def test_3D_dot_fail(self):
def func():
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a = T.TensorType('float64', (False,False,False)) # create 3d
˓→
tensor
b = T.dmatrix()
c = T.dot(a,b) # we expect this to fail
# above should fail as dot operates on 2D tensors only
self.assertRaises(TypeError, func)
Useful function, as defined by TestCase:
• assertRaises
Test Cases and Theano Modes
When compiling theano functions or modules, a mode parameter can be given to specify which linker and
optimizer to use.
Example:
from theano import function
f = function([a,b],[c],mode='FAST_RUN')
Whenever possible, unit tests should omit this parameter. Leaving out the mode will ensure that unit tests
use the default mode. This default mode is set to the configuration variable config.mode, which defaults
to ‘FAST_RUN’, and can be set by various mechanisms (see config).
In particular, the enviromnment variable THEANO_FLAGS allows the user to easily switch the mode in
which unittests are run. For example to run all tests in all modes from a BASH script, type this:
THEANO_FLAGS='mode=FAST_COMPILE' theano-nose
THEANO_FLAGS='mode=FAST_RUN' theano-nose
THEANO_FLAGS='mode=DebugMode' theano-nose
Using Random Values in Test Cases
numpy.random is often used in unit tests to initialize large data structures, for use as inputs to the function
or module being tested. When doing this, it is imperative that the random number generator be seeded at the
be beginning of each unit test. This will ensure that unittest behaviour is consistent from one execution to
another (i.e always pass or always fail).
Instead of using numpy.random.seed to do this, we encourage users to do the following:
from theano.tests import unittest_tools
class TestTensorDot(unittest.TestCase):
def setUp(self):
unittest_tools.seed_rng()
# OR ... call with an explicit seed
unittest_tools.seed_rng(234234) #use only if really necessary!
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The behaviour of seed_rng is as follows:
• If an explicit seed is given, it will be used for seeding numpy’s rng.
• If not, it will use config.unittests.rseed (its default value is 666).
• If config.unittests.rseed is set to “random”, it will seed the rng with None, which is equivalent to
seeding with a random seed.
The main advantage of using unittest_tools.seed_rng is that it allows us to change the seed used in the
unitests, without having to manually edit all the files. For example, this allows the nightly build to run
theano-nose repeatedly, changing the seed on every run (hence achieving a higher confidence that the variables are correct), while still making sure unittests are deterministic.
Users who prefer their unittests to be random (when run on their local machine) can simply set config.
unittests.rseed to ‘random’ (see config).
Similarly, to provide a seed to numpy.random.RandomState, simply use:
import numpy
rng = numpy.random.RandomState(unittest_tools.fetch_seed())
# OR providing an explicit seed
rng = numpy.random.RandomState(unittest_tools.fetch_seed(1231)) #again not
˓→recommended
Note that the ability to change the seed from one nosetest to another, is incompatible with the method of
hard-coding the baseline variables (against which we compare the theano outputs). These must then be
determined “algorithmically”. Although this represents more work, the test suite will be better because of
it.
Creating an Op UnitTest
A few tools have been developed to help automate the development of unitests for Theano Ops.
Validating the Gradient
The verify_grad function can be used to validate that the grad function of your Op is properly implemented. verify_grad is based on the Finite Difference Method where the derivative of function f at
point x is approximated as:
𝜕𝑓
𝑓 (𝑥 + ∆) − 𝑓 (𝑥 − ∆)
= 𝑙𝑖𝑚Δ→0
𝜕𝑥
2∆
verify_grad performs the following steps:
• approximates the gradient numerically using the Finite Difference Method
• calculate the gradient using the symbolic expression provided in the grad function
• compares the two values. The tests passes if they are equal to within a certain tolerance.
Here is the prototype for the verify_grad function.
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def verify_grad(fun, pt, n_tests=2, rng=None, eps=1.0e-7, abs_tol=0.0001, rel_
˓→tol=0.0001):
verify_grad raises an Exception if the difference between the analytic gradient and numerical gradient
(computed through the Finite Difference Method) of a random projection of the fun’s output to a scalar
exceeds both the given absolute and relative tolerances.
The parameters are as follows:
• fun: a Python function that takes Theano variables as inputs, and returns a Theano variable. For
instance, an Op instance with a single output is such a function. It can also be a Python function that
calls an op with some of its inputs being fixed to specific values, or that combine multiple ops.
• pt: the list of numpy.ndarrays to use as input values
• n_tests: number of times to run the test
• rng: random number generator used to generate a random vector u, we check the gradient of
sum(u*fn) at pt
• eps: stepsize used in the Finite Difference Method
• abs_tol: absolute tolerance used as threshold for gradient comparison
• rel_tol: relative tolerance used as threshold for gradient comparison
In the general case, you can define fun as you want, as long as it takes as inputs Theano symbolic variables
and returns a sinble Theano symbolic variable:
def test_verify_exprgrad():
def fun(x,y,z):
return (x + tensor.cos(y)) / (4 * z)**2
x_val
y_val
z_val
rng =
= numpy.asarray([[1], [1.1], [1.2]])
= numpy.asarray([0.1, 0.2])
= numpy.asarray(2)
numpy.random.RandomState(42)
tensor.verify_grad(fun, [x_val, y_val, z_val], rng=rng)
Here is an example showing how to use verify_grad on an Op instance:
def test_flatten_outdimNone():
# Testing gradient w.r.t. all inputs of an op (in this example the op
# being used is Flatten(), which takes a single input).
a_val = numpy.asarray([[0,1,2],[3,4,5]], dtype='float64')
rng = numpy.random.RandomState(42)
tensor.verify_grad(tensor.Flatten(), [a_val], rng=rng)
Here is another example, showing how to verify the gradient w.r.t. a subset of an Op’s inputs. This is useful
in particular when the gradient w.r.t. some of the inputs cannot be computed by finite difference (e.g. for
discrete inputs), which would cause verify_grad to crash.
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def test_crossentropy_softmax_grad():
op = tensor.nnet.crossentropy_softmax_argmax_1hot_with_bias
def op_with_fixed_y_idx(x, b):
# Input `y_idx` of this Op takes integer values, so we fix them
# to some constant array.
# Although this op has multiple outputs, we can return only one.
# Here, we return the first output only.
return op(x, b, y_idx=numpy.asarray([0, 2]))[0]
x_val = numpy.asarray([[-1, 0, 1], [3, 2, 1]], dtype='float64')
b_val = numpy.asarray([1, 2, 3], dtype='float64')
rng = numpy.random.RandomState(42)
tensor.verify_grad(op_with_fixed_y_idx, [x_val, b_val], rng=rng)
Note: Although verify_grad is defined in theano.tensor.basic, unittests should use the version
of verify_grad defined in theano.tests.unittest_tools. This is simply a wrapper function
which takes care of seeding the random number generator appropriately before calling theano.tensor.
basic.verify_grad
makeTester and makeBroadcastTester
Most Op unittests perform the same function. All such tests must verify that the op generates the proper
output, that the gradient is valid, that the Op fails in known/expected ways. Because so much of this is common, two helper functions exists to make your lives easier: makeTester and makeBroadcastTester
(defined in module theano.tensor.tests.test_basic).
Here is an example of makeTester generating testcases for the Dot product op:
from numpy import dot
from numpy.random import rand
from theano.tensor.tests.test_basic import makeTester
DotTester = makeTester(name = 'DotTester',
op = dot,
expected = lambda x, y: numpy.dot(x, y),
checks = {},
good = dict(correct1 = (rand(5, 7), rand(7, 5)),
correct2 = (rand(5, 7), rand(7, 9)),
correct3 = (rand(5, 7), rand(7))),
bad_build = dict(),
bad_runtime = dict(bad1 = (rand(5, 7), rand(5, 7)),
bad2 = (rand(5, 7), rand(8,3))),
grad = dict())
In the above example, we provide a name and a reference to the op we want to test. We then provide in the
expected field, a function which makeTester can use to compute the correct values. The following
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five parameters are dictionaries which contain:
• checks: dictionary of validation functions (dictionary key is a description of what each function
does). Each function accepts two parameters and performs some sort of validation check on each
op-input/op-output value pairs. If the function returns False, an Exception is raised containing the
check’s description.
• good: contains valid input values, for which the output should match the expected output. Unittest
will fail if this is not the case.
• bad_build: invalid parameters which should generate an Exception when attempting to build the graph
(call to make_node should fail). Fails unless an Exception is raised.
• bad_runtime: invalid parameters which should generate an Exception at runtime, when trying to compute the actual output values (call to perform should fail). Fails unless an Exception is raised.
• grad: dictionary containing input values which will be used in the call to verify_grad
makeBroadcastTester is a wrapper function for makeTester. If an inplace=True parameter is
passed to it, it will take care of adding an entry to the checks dictionary. This check will ensure that inputs
and outputs are equal, after the Op’s perform function has been applied.
Extending Theano: FAQ and Troubleshooting
I wrote a new Op/Type, and weird stuff is happening...
First, check the Op’s contract and the Type’s contract and make sure you’re following the rules. Then try
running your program in Using DebugMode. DebugMode might catch something that you’re not seeing.
I wrote a new optimization, but it’s not getting used...
Remember that you have to register optimizations with the The optimization database (optdb) for them to
get used by the normal modes like FAST_COMPILE, FAST_RUN, and DebugMode.
I wrote a new optimization, and it changed my results even though I’m pretty sure it is
correct.
First, check the Op’s contract and make sure you’re following the rules. Then try running your program in
Using DebugMode. DebugMode might catch something that you’re not seeing.
6.2.6 Developer Start Guide
Contributing
You want to contribute to Theano? That is great! This page explain our workflow and some resource for
doing so.
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Looking for an idea for a first contribution? Check the github issues with a label easy fix. They are
good starter. It is recommanded that you write on the issue you want to work on it. This help make sure it is
up to date and see if nobody else is working on it. Also, we can sometimes provides more information about
it. There is also the label NeedSomeoneToFinish that is interesting to check. The difficulty level is variable.
Resources
See Community for a list of Theano resources. The following groups/mailing-lists are especially useful to
Theano contributors: theano-dev, theano-buildbot, and theano-github.
To get up to speed, you’ll need to
• Learn some non-basic Python to understand what’s going on in some of the trickier files (like tensor.py).
• Go through the NumPy documentation.
• Learn to write reStructuredText for Sphinx.
• Learn about how unittest and nose work
Requirements for Quality Contributions
• All the code should be properly tested.
• The code should be compatible with Python 2.6 and above, as well as Python 3.3 and above (using six
if needed).
• All the code should respect the PEP8 Code Style Guide.
• The docstrings of all the classes and functions should respect the PEP257 rules and follow the Numpy
docstring standard.
Each point will be referred to more in detail in the following.
Unit tests
When you submit a pull request, your changes will automatically be tested via Travis-CI. This will post the
results of the tests with a little icon next to your commit. A yellow circle means the tests are running. A red
X means the tests failed and a green circle means the tests passed.
Just because the tests run automatically does not mean you shouldn’t run them yourself to make sure everything is all right. You can run only the portion you are modifying to go faster and have travis to make sure
there are no global impacts.
Also, if you are changing GPU code, travis doesn’t test that, because there are no GPUs on the test nodes.
To run the test suite with the default options, you can follow the instructions of Testing your installation.
Each night we execute all the unit tests automatically, with several sets of options. The result is sent by
email to the theano-buildbot mailing list.
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For more detail, see The nightly build/tests process.
To run all the tests with the same configuration as the buildbot, run this script:
theano/misc/do_nightly_build
This script accepts arguments that it forwards to nosetests. You can run only some tests or enable pdb by
giving the equivalent nosetests parameters.
Setting up your Editor for PEP8
Here are instructions for Vim and Emacs. If you have similar instructions for other text editors or IDE, please
let us know and we will update this documentation.
Vim
Detection of warnings and errors is done by the pep8 script (or flake8, that also checks for other things, like
syntax errors). Syntax highlighting and general integration into Vim is done by the Syntastic plugin for Vim.
To setup VIM:
1. Install flake8 (if not already installed) with:
pip install flake8
Note: You can use easy_install instead of pip, and pep8 instead of flake8 if you prefer.
The important thing is that the flake8 or pep8 executable ends up in your $PATH.
2. Install vundle with:
git clone https://github.com/VundleVim/Vundle.vim.git ~/.vim/bundle/
˓→Vundle.vim
3. Edit ~/.vimrc and add the lines:
set nocompatible
" be iMproved, required
filetype off
" required
" set the runtime path to include Vundle and initialize
set rtp+=~/.vim/bundle/Vundle.vim
call vundle#begin()
Plugin 'gmarik/Vundle.vim' " let Vundle manage Vundle (required!)
Plugin 'scrooloose/syntastic'
Plugin 'jimf/vim-pep8-text-width'
call vundle#end()
" Syntastic settings
" You can run checkers explicitly by calling :SyntasticCheck
˓→<checker
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let g:syntastic_python_checkers = ['flake8'] "use one of the
˓→following checkers:
" flake8, pyflakes,
˓→pylint, python (native checker)
let g:syntastic_enable_highlighting = 1 "highlight errors and
˓→warnings
let g:syntastic_style_error_symbol = ">>" "error symbol
let g:syntastic_warning_symbol = ">>" "warning symbol
let g:syntastic_check_on_open = 1
let g:syntastic_auto_jump = 0 "do not jump to errors when
˓→detected
4. Open a new vim and run :PluginInstall to automatically install the plugins. When the installation is done, close the installation “window” with :q. From now on Vim will check for PEP8 errors
and highlight them whenever a file is saved.
A few useful commands
• Open the list of errors: :lopen, that can be abbreviated in :lop (denoted :lop[en]).
• Close that list: :lcl[ose].
• Next error: :lne[xt].
• Previous error: :lp[revious].
Once you fix errors, messages and highlighting will still appear in the fixed file until you save it again.
We can also configure the ~/.vimrc to make it easier to work with Syntastic. For instance, to add a
summary in the status bar, you can add:
set statusline+=%{SyntasticStatuslineFlag()}
To bind F2 and F3 to navigate to previous and next error, you can add:
map <F2> :lprevious<CR>
map <F3> :lnext<CR>
You can prefix those by autocmd FileType python if you want these bindings to work only on
Python files.
Emacs
There is an excellent system to configure emacs for Python: emacs-for-python. It gathers many emacs
config into one, and modifies them to behave together nicely. You can use it to check for pep8 compliance
and for Python syntax errors.
To install it on Linux, you can do like this:
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cd
git clone https://github.com/gabrielelanaro/emacs-for-python.git ~/.emacs.d/
˓→emacs-for-python
Then in your ~/.emacs file, add this:
;; Mandatory
(load-file "~/.emacs.d/emacs-for-python/epy-init.el")
(add-to-list 'load-path "~/.emacs.d/emacs-for-python/") ;; tell where to load
˓→the various files
;; Each of them enables different parts of the system.
;; Only the first two are needed for pep8, syntax check.
(require 'epy-setup) ;; It will setup other loads, it is required!
(require 'epy-python) ;; If you want the python facilities [optional]
(require 'epy-completion) ;; If you want the autocompletion settings
˓→[optional]
(require 'epy-editing) ;; For configurations related to editing [optional]
;; [newer version of emacs-for-python]
(require 'epy-nose) ;; For shortcut to call nosetests [optional]
;; Define f10 to previous error
;; Define f11 to next error
(require 'epy-bindings) ;; For my suggested keybindings [optional]
;; Some shortcut that do not collide with gnome-terminal,
;; otherwise, "epy-bindings" define f10 and f11 for them.
(global-set-key [f2] 'flymake-goto-prev-error)
(global-set-key [f3] 'flymake-goto-next-error)
;; Next two lines are the checks to do. You can add more if you wish.
(epy-setup-checker "pyflakes %f") ;; For python syntax check
(epy-setup-checker "pep8 -r %f") ;; For pep8 check
Note: The script highlights problematic lines. This can make part of the line not readable depending on the
background. To replace the line highlight by an underline, add this to your emacs configuration file:
;; Make lines readable when there is an warning [optional] (custom-set-faces ‘(flymake-errline ((((class
color)) (:underline “red”)))) ‘(flymake-warnline ((((class color)) (:underline “yellow”)))))
Documentation and docstrings
• The documentation and the API documentation are generated using Sphinx.
• The documentation should be written in reStructuredText and the docstrings of all the classes and
functions should respect the PEP257 rules and follow the Numpy docstring standard.
• Split the docstrings in sections, according to the Allowed docstring sections in Napoleon
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• To cross-reference other objects (e.g. reference other classes or methods) in the docstrings, use the
cross-referencing objects syntax. :py can be omitted, see e.g. this stackoverflow answer.
• See Documentation Documentation AKA Meta-Documentation, for some information on how to generate the documentation.
A Docstring Example
Here is an example on how to add a docstring to a class.
import theano
class DoubleOp(theano.Op):
"""
Double each element of a tensor.
Parameters
---------x : tensor
Input tensor
Returns
------tensor
a tensor of the same shape and dtype as the input with all
values doubled.
Notes
----this is a test note
See Also
-------:class:`~theano.tensor.elemwise.Elemwise` : You can use this to replace
this example. Just execute `x * 2` with x being a Theano variable.
.. versionadded:: 0.6
"""
This is how it will show up for files that we auto-list in the library documentation:
class theano.misc.doubleop.DoubleOp(use_c_code=’/usr/bin/g++’)
Double each element of a tensor.
Parameters x (tensor) – Input tensor
Returns a tensor of the same shape and dtype as the input with all values doubled.
Return type tensor
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Notes
this is a test note
See also:
Elemwise : You can use this to replace this example. Just execute x * 2 with x being a Theano
variable.
New in version 0.6.
Installation and configuration
To obtain developer access: register with GitHub and create a fork of Theano.
This will create your own Theano project on GitHub, referred later as “YourProfile/Theano”, or “origin”,
from which you will be able to contribute to the original Theano/Theano, also called “central”.
Create a local copy
Clone your fork locally with
git clone [email protected]:YOUR_GITHUB_LOGIN/Theano.git
For this URL to work, you must set your public ssh keys inside your github account setting.
From your local repository, your own fork on GitHub will be called “origin”.
Then, add a reference to the original (“central”) Theano repository with
git remote add central git://github.com/Theano/Theano.git
You can choose another name than “central” to reference Theano/Theano (for instance, NumPy uses “upstream”), but this documentation will stick to “central.”
You can then test your installation of Theano by following the steps of Testing your installation.
Using your local copy
To update your library to the latest revision, you should have a local branch that tracks central/master. You
can add one (named “trunk” here) with:
git fetch central
git branch trunk central/master
Once you have such a branch, in order to update it, do:
git checkout trunk
git pull
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Keep in mind that this branch should be “read-only”: if you want to patch Theano, you should work in
another branch, like described in the Development Workflow section below.
Configure Git
On your local machine, you need to configure git with basic informations:
git config --global user.email [email protected]
git config --global user.name "Your Name Comes Here"
You can also instruct git to use color in diff. For this, you need to add those lines in the file ~/.gitconfig
[color]
branch = auto
diff = auto
interactive = auto
status = auto
Development Workflow
Start a new local branch
When working on a new feature in your own fork, start from an up-to-date copy of the master branch (the
principal one) of the central repository (Theano/Theano on GitHub):
git fetch central
git checkout -b my_shiny_feature central/master
Note: This last line is a shortcut for:
git branch my_shiny_feature central/master
git checkout my_shiny_feature
Submit your changes to the central repository
Once your code is ready for others to review, you need to commit all the changes and then push your branch
to your github fork first:
git commit -a -m "your message here"
git push -u origin my_shiny_feature
Then, go to your fork’s github page on the github website, select your feature branch and hit the “Pull
Request” button in the top right corner. This will signal the maintainers that you wish to submit your
changes for inclusion in central/master. If you don’t get any feedback, bug us on the theano-dev mailing list.
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Address reviewer comments
Your pull request will be reviewed by members of the core development team. If your branch is not directly
accepted, the reviewers will use GitHub’s system to add “notes”, either general (on the entire commit), or
“line notes”, relative to a particular line of code. In order to have the pull request accepted, you may have to
answer the reviewer’s questions, you can do that on GitHub.
You may also have to edit your code to address their concerns. Some of the usual requests include fixing
typos in comments, adding or correcting comments, adding unit tests in the test suite. In order to do that,
you should continue your edits in the same branch you used (in this example, “my_shiny_feature”). For
instance, if you changed your working branch, you should first:
git checkout my_shiny_feature
Then, edit your code, and test it appropriately (see Requirements for Quality Contributions below), and push
it again to your GitHub fork, like the first time (except the -u option is only needed the first time):
git push origin my_shiny_feature
The pull request to the central repository will then be automatically updated by GitHub. However, the
reviewers will not be automatically notified of your revision, so it is advised to reply to the comments on
GitHub, to let them know that you have submitted a fix.
More Advanced Git Usage
You can find information and tips in the numpy development page. Here are a few.
Cleaning up branches
When your pull request has been merged, you can delete the branch from your GitHub fork’s list of branches.
This is useful to avoid having too many branches staying there. Deleting this remote branch is achieved with:
git push origin :my_shiny_feature
This lines pushes to the “origin” repository (your fork of Theano on GitHub), into the branch
“my_shiny_feature”, an empty content (that’s why there is nothing before the colon), effectively removing it.
The branch will still be present in your local clone of the repository. If you want to delete it from there, too,
you can run:
git branch -d my_shiny_feature
Amending a submitted pull request
If you want to fix a commit already submitted within a pull request (e.g. to fix a small typo), before the pull
request is accepted, you can do it like this to keep history clean:
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git checkout my_shiny_feature
git commit --amend
git push origin my_shiny_feature:my_shiny_feature
Do not abuse that command, and please use it only when there are only small issues to be taken care of.
Otherwise, it becomes difficult to match the comments made by reviewers with the new modifications. In
the general case, you should stick with the approach described above.
Cleaning up history
Sometimes you may have commits in your feature branch that are not needed in the final pull request. There
is a page that talks about this. In summary:
• Commits to the trunk should be a lot cleaner than commits to your feature branch; not just for ease of
reviewing but also because intermediate commits can break blame (the bisecting tool).
• git merge –squash will put all of the commits from your feature branch into one commit.
• There are other tools that are useful if your branch is too big for one squash.
Add another distant repository
To collaborate with another user on some feature he is developing, and that is not ready for inclusion in
central, the easiest way is to use a branch of their Theano fork (usually on GitHub).
Just like we added Theano/Theano as a remote repository, named “central”, you can add (on your local
machine) a reference to their fork as a new remote repository. REPO_NAME is the name you choose to
name this fork, and GIT_REPO_PATH is the URL of the fork in question.
git remote add REPO_NAME GIT_REPO_PATH
Then, you can create a new local branch (LOCAL_BRANCH_NAME) based on a specific branch (REMOTE_BRANCH_NAME) from the remote repository (REPO_NAME):
git checkout -b LOCAL_BRANCH_NAME REPO_NAME/REMOTE_BRANCH_NAME
Other tools that can help you
• cProfile: time profiler that work at function level.
• Yep: A module for profiling compiled extensions.
• autopep8: A tool that automatically formats Python code to conform to the PEP 8 style guide.
• line_profiler: Line-by-line profiler.
• memory_profiler: memory profiler
• runsnake: Gui for cProfile(time profiler) and Meliae(memory profiler)
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• Guppy: Supports object and heap memory sizing, profiling and debugging.
• hub: A tool that adds github commands to the git command line.
• git pull-requests: Another tool for git/github command line.
6.2.7 Optimizations
Theano applies many kinds of graph optimizations, with different objectives:
• simplifying and standardizing the form of the expression graph (e.g. merge, add canonicalization ),
• reducing the maximum memory footprint (e.g. inplace_elemwise),
• increasing execution speed (e.g. constant folding).
The optimizations are listed in roughly chronological order. The table below gives a quick summary of the
optimizations included in the default modes. The descriptions are brief and point to further reading.
If you would like to add an additional optimization, refer to Graph optimization in the guide to extending
Theano.
Note: This list is partial.
The print_summary method allows several OpDBs and optimizers to list the executed optimizations. This
makes it possible to have an up-to-date list.
python -c ‘import theano; theano.compile.FAST_RUN.optimizer.print_summary()’
python -c ‘import theano; theano.compile.FAST_COMPILE.optimizer.print_summary()’
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Optimization
merge
constant folding
shape promotion
fill cut
inc_subtensor srlz.
reshape_chain
const. elimination
add canonical.
mul canonical.
dot22
sparse_dot
sum_scalar_mul
neg_neg
neg_div_neg
add specialize
mul specialize
pow specialize
inplace_setsubtensor
gemm
inplace_elemwise
inplace_random
elemwise fusion
GPU transfer
local_log_softmax
local_remove_all_assert
FAST_RUN
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
FAST_COMPILE
x
x
Stabilization
x
merge A simple optimization in which redundant Apply nodes are combined. For example, in
function([x,y], [(x+y)*2, (x+y)*3]) the merge optimization will ensure that x and
y are only added once.
This optimization is very useful because it frees users to write highly redundant mathematical code.
Theano will make sure to compute just what is necessary.
See MergeOptimizer.
constant folding When all the inputs to an expression are constant, then the expression can be precomputed at compile-time.
See opt.constant_folding()
shape promotion Theano often knows how to infer the shape of an output from the shape of its inputs.
Without this optimization, it would otherwise have to compute things (e.g. log(x)) just to find out
the shape of it!
See opt.local_shape_lift_*()
fill cut Fill(a,b) means to make a tensor of the shape of a full of the value b. Often when fills are used
with elementwise operations (e.g. f) they are un-necessary: * f(fill(a,b), c) -> f(b, c)
* f(fill(a, b), fill(c, d), e) -> fill(a, fill(c, f(b, d, e)))
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See opt.local_fill_cut(), opt.local_fill_sink()
inc_subtensor serialization Incrementing a small subregion of a large tensor can be done quickly using
an inplace operation, but if two increments are being done on the same large tensor, then only one of
them can be done inplace. This optimization reorders such graphs so that all increments can be done
inplace.
inc_subensor(a,b,idx) + inc_subtensor(a,c,idx) ->
inc_subtensor(inc_subtensor(a,b,idx),c,idx)
See local_IncSubtensor_serialize()
reshape_chain This optimizes graphs like reshape(reshape(x, shape1), shape2) ->
reshape(x, shape2)
See local_reshape_chain()
constant elimination Many constants indicate special cases, such as pow(x,1) -> x. Theano recognizes many of these special cases.
See local_mul_specialize(), local_mul_specialize(),:func:local_mul_specialize
add canonicalization Rearrange expressions of additions and subtractions to a canonical form:
(𝑎 + 𝑏 + 𝑐 + ...) − (𝑧 + 𝑥 + 𝑦 + ....)
See Canonizer, local_add_canonizer
mul canonicalization Rearrange expressions of multiplication and division to a canonical form:
𝑎 * 𝑏 * 𝑐 * ...
𝑧 * 𝑥 * 𝑦 * ....
See Canonizer, local_mul_canonizer
dot22 This simple optimization replaces dot(matrix, matrix) with a special dot22 op that only works for
matrix multiplication. This op is implemented with a call to GEMM, and sometimes replaced entirely
by the gemm optimization.
See local_dot_to_dot22()
sparse_dot Theano has a sparse matrix multiplication algorithm that is faster in many cases than scipy’s
(for dense matrix output). This optimization swaps scipy’s algorithm for ours.
See local_structured_dot()
sum_scalar_mul
This
sum(tensor)
optimizes
graphs
like
sum(scalar * tensor)
->
scalar *
See local_sum_mul_by_scalar()
neg_neg Composition of two negatives can be cancelled out.
See local_neg_neg()
neg_div_neg Matching negatives in both the numerator and denominator can both be removed.
See local_neg_div_neg()
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add specialization This optimization simplifies expressions involving the addition of zero.
See local_add_specialize()
mul specialization Several special cases of mul() exist, and this optimization tries to recognize them. Some
examples include: * mul(x,x) -> x**2 * mul(x,0) -> zeros_like(x) * mul(x, -1) ->
neg(x)
See local_mul_specialize()
pow specialization Several special cases of pow() exist, and this optimization tries to recognize them.
Some examples include: * pow(x,2) -> x**2 * pow(x,0) -> ones_like(x) * pow(x, -0.
5) -> inv(sqrt(x))
See local_pow_specialize()
inplace_setsubtensor In order to be a pure Op, setsubtensor must copy its entire input, and modify just
the subtensor in question (possibly a single element). It is much more efficient to modify that element
inplace.
See local_inplace_setsubtensor()
gemm Numerical libraries such as MKL and ATLAS implement the BLAS-level-3 interface, and provide
a function GEMM that implements 𝑍 ← 𝛼𝐴 · 𝐵 + 𝛽𝑍, for matrices A, B and Z, and scalars 𝛼, 𝛽.
This optimization tries to rearrange a variety of linear algebra expressions into one or more instances
of this motif, and replace them each with a single Gemm Op.
See GemmOptimizer
inplace_elemwise When one of the inputs to an elementwise expression has the same type and shape as
the output, and is no longer needed for computation after the elemwise expression is evaluated, then
we can reuse the storage of the input to store the output.
See insert_inplace_optimizer()
inplace_random Typically when a graph uses random numbers, the RandomState is stored in a shared
variable, used once per call and, updated after each function call. In this common case, it makes sense
to update the random number generator in-place.
See random_make_inplace()
elemwise fusion This optimization compresses subgraphs of computationally cheap elementwise operations into a single Op that does the whole job in a single pass over the inputs (like loop fusion). This
is a win when transfer from main memory to the CPU (or from graphics memory to the GPU) is a
bottleneck.
See FusionOptimizer
GPU transfer The current strategy for choosing which expressions to evaluate on the CPU and which to
evaluate on the GPU is a greedy one. There are a number of Ops *TODO* with GPU implementations
and whenever we find a graph copying data from GPU to CPU in order to evaluate an expression that
could have been evaluated on the GPU, we substitute the GPU version of that Op for the CPU version.
Likewise if we are copying the output of a Op with a GPU implementation to the GPU, then we
substitute the GPU version for the CPU version. In this way, if all goes well, this procedure will result
in a graph with the following form:
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1. copy non-shared inputs to GPU
2. carry out most/all computations on the GPU
3. copy output back to CPU
When using a GPU, shared() will default to GPU storage for ‘float32’ ndarray arguments, and
these shared variables act as seeds for the greedy algorithm.
See theano.sandbox.cuda.opt.*().
local_log_softmax This is a stabilization optimization. It can happen due to rounding errors that the
softmax probability of one value gets to 0. Taking the log of 0 would generate -inf that will probably
generate NaN later. We return a closer answer.
local_remove_all_assert This is an unsafe optimization. For the fastest possible Theano, this optimization
can be enabled by setting optimizer_including=local_remove_all_assert which will
remove all assertions in the graph for checking user inputs are valid. Use this optimization if you are
sure everthing is valid in your graph.
See unsafe_optimization
6.2.8 API Documentation
This documentation covers Theano module-wise. This is suited to finding the Types and Ops that you can
use to build and compile expression graphs.
compile – Transforming Expression Graphs to Functions
shared - defines theano.shared
class theano.compile.sharedvalue.SharedVariable
Variable with Storage that is shared between functions that it appears in. These variables are meant to
be created by registered shared constructors (see shared_constructor()).
The user-friendly constructor is shared()
value
Read/write access to the [non-symbolic] value/data associated with this SharedVariable.
Changes to this value will be visible to all functions using this SharedVariable.
__init__(self, name, type, value, strict, container=None)
Parameters
• name (None or str) – The name for this variable.
• type – The Type for this Variable.
• value – A value to associate with this variable (a new container will be created).
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• strict – True -> assignments to self.value will not be casted or copied,
so they must have the correct type or an exception will be raised.
• container – The container to use for this variable. This should instead of the
value parameter. Using both is an error.
container
A container to use for this SharedVariable when it is an implicit function parameter.
Type class:Container
theano.compile.sharedvalue.shared(value,
name=None,
strict=False,
low_downcast=None, **kwargs)
Return a SharedVariable Variable, initialized with a copy or reference of value.
al-
This function iterates over constructor functions to find a suitable SharedVariable subclass. The
suitable one is the first constructor that accept the given value. See the documentation of
shared_constructor() for the definition of a contructor function.
This function is meant as a convenient default. If you want to use a specific shared variable constructor, consider calling it directly.
theano.shared is a shortcut to this function.
theano.compile.sharedvalue.constructors
A list of shared variable constructors that will be tried in reverse order.
Notes
By passing kwargs, you effectively limit the set of potential constructors to those that can accept those
kwargs.
Some shared variable have borrow as extra kwargs. See for details.
Some shared variable have broadcastable as extra kwargs. As shared variable shapes can change,
all dimensions default to not being broadcastable, even if value has a shape of 1 along some dimension. This parameter allows you to create for example a row or column 2d tensor.
theano.compile.sharedvalue.shared_constructor(ctor)
Append ctor to the list of shared constructors (see shared()).
Each registered constructor ctor will be called like this:
ctor(value, name=name, strict=strict, **kwargs)
If it do not support given value, it must raise a TypeError.
function - defines theano.function
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Guide
This module provides function(), commonly accessed as theano.function, the interface for compiling
graphs into callable objects.
You’ve already seen example usage in the basic tutorial... something like this:
>>> import theano
>>> x = theano.tensor.dscalar()
>>> f = theano.function([x], 2*x)
>>> f(4)
array(8.0)
The idea here is that we’ve compiled the symbolic graph (2*x) into a function that can be called on a
number and will do some computations.
The behaviour of function can be controlled in several ways, such as In, Out, mode, updates, and
givens. These are covered in the tutorial examples and tutorial on modes.
Reference
class theano.compile.function.In
A class for attaching information to function inputs.
variable
A variable in an expression graph to use as a compiled-function parameter
name
A string to identify an argument for this parameter in keyword arguments.
value
The default value to use at call-time (can also be a Container where the function will find a value
at call-time.)
update
An expression which indicates updates to the Value after each function call.
mutable
True means the compiled-function is allowed to modify this argument. False means it is not
allowed.
borrow
True indicates that a reference to internal storage may be returned, and that the caller is aware
that subsequent function evaluations might overwrite this memory.
strict
If False, a function argument may be copied or cast to match the type required by the parameter
variable. If True, a function argument must exactly match the type required by variable.
allow_downcast
True indicates that the value you pass for this input can be silently downcasted to fit the right
type, which may lose precision. (Only applies when strict is False.)
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autoname
True means that the name is set to variable.name.
implicit
True means that the input is implicit in the sense that the user is not allowed to provide a value
for it. Requires ‘value’ to be set. False means that the user can provide a value for this input.
__init__(self, variable, name=None, value=None, update=None, mutable=None,
strict=False, allow_downcast=None, autoname=True, implicit=None, borrow=None, shared=False)
Initialize attributes from arguments.
class theano.compile.function.Out
A class for attaching information to function outputs
variable
A variable in an expression graph to use as a compiled-function output
borrow
True indicates that a reference to internal storage may be returned, and that the caller is aware
that subsequent function evaluations might overwrite this memory.
__init__(variable, borrow=False)
Initialize attributes from arguments.
theano.compile.function.function(inputs, outputs, mode=None, updates=None,
givens=None,
no_default_updates=False,
accept_inplace=False,
name=None,
rebuild_strict=True, allow_input_downcast=None,
profile=None, on_unused_input=’raise’)
Return a callable object that will calculate outputs from inputs.
Parameters
• params
(list of either Variable or In instances, but
not shared variables.) – the returned Function instance will have
parameters for these variables.
• outputs (list of Variables or Out instances) – expressions to
compute.
• mode (None, string or Mode instance.) – compilation mode
• updates
(iterable over pairs (shared_variable,
new_expression) List, tuple or dict.) – expressions for new
SharedVariable values
• givens (iterable over pairs (Var1, Var2) of Variables.
List, tuple or dict. The Var1 and Var2 in each pair
must have the same Type.) – specific substitutions to make in the
computation graph (Var2 replaces Var1).
• no_default_updates (either bool or list of Variables) – if
True, do not perform any automatic update on Variables. If False (default), per-
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form them all. Else, perform automatic updates on all Variables that are neither in
updates nor in no_default_updates.
• name – an optional name for this function. The profile mode will print the time
spent in this function.
• rebuild_strict – True (Default) is the safer and better tested setting, in
which case givens must substitute new variables with the same Type as the variables they replace. False is a you-better-know-what-you-are-doing setting, that
permits givens to replace variables with new variables of any Type. The consequence of changing a Type is that all results depending on that variable may have
a different Type too (the graph is rebuilt from inputs to outputs). If one of the new
types does not make sense for one of the Ops in the graph, an Exception will be
raised.
• allow_input_downcast (Boolean or None) – True means that the values passed as inputs when calling the function can be silently downcasted to fit the
dtype of the corresponding Variable, which may lose precision. False means that
it will only be cast to a more general, or precise, type. None (default) is almost
like False, but allows downcasting of Python float scalars to floatX.
• profile (None, True, or ProfileStats instance) – accumulate
profiling information into a given ProfileStats instance. If argument is True then a
new ProfileStats instance will be used. This profiling object will be available via
self.profile.
• on_unused_input – What to do if a variable in the ‘inputs’ list is not used in
the graph. Possible values are ‘raise’, ‘warn’, and ‘ignore’.
Return type Function instance
Returns a callable object that will compute the outputs (given the inputs) and update the
implicit function arguments according to the updates.
Inputs can be given as variables or In instances. In instances also have a variable, but they attach
some extra information about how call-time arguments corresponding to that variable should be used.
Similarly, Out instances can attach information about how output variables should be returned.
The default is typically ‘FAST_RUN’ but this can be changed in theano.config. The mode argument
controls the sort of optimizations that will be applied to the graph, and the way the optimized graph
will be evaluated.
After each function evaluation, the updates mechanism can replace the value of any SharedVariable
[implicit] inputs with new values computed from the expressions in the updates list. An exception
will be raised if you give two update expressions for the same SharedVariable input (that doesn’t
make sense).
If a SharedVariable is not given an update expression, but has a default_update member
containing an expression, this expression will be used as the update expression for this variable.
Passing no_default_updates=True to function disables this behavior entirely, passing
no_default_updates=[sharedvar1, sharedvar2] disables it for the mentioned variables.
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Regarding givens: Be careful to make sure that these substitutions are independent, because behaviour
when Var1 of one pair appears in the graph leading to Var2 in another expression is undefined (e.g.
with {a: x, b: a + 1}). Replacements specified with givens are different from optimizations in that Var2 is not expected to be equivalent to Var1.
theano.compile.function.function_dump(filename,
inputs,
outputs=None,
mode=None, updates=None, givens=None,
no_default_updates=False,
accept_inplace=False,
name=None,
rebuild_strict=True,
allow_input_downcast=None,
profile=None,
on_unused_input=None,
extra_tag_to_remove=None)
This is helpful to make a reproducable case for problem during Theano compilation.
Ex:
replace theano.function(...) by theano.function_dump(‘filename.pkl’, ...).
If you see this, you where probably asked to use this function to help debug a particular case during the compilation of a Theano function. function_dump allows to easily reproduce your compilation without asking any code. It pickle all the objects and parameters needed to reproduce a call
to theano.function(). This include shared variables and there values. If you do not want that, you
can set to replace shared variables values by zeros by calling set_value(...) on them before calling
function_dump.
To load such a dump and do the compilation:
>>>
>>>
>>>
>>>
from six.moves import cPickle
import theano
d = cPickle.load(open("func_dump.bin", "rb"))
f = theano.function(**d)
Note: The parameter extra_tag_to_remove, is passed to the StripPickler used. To pickle graph made
by Blocks, it must be: [’annotations’, ‘replacement_of’, ‘aggregation_scheme’, ‘roles’]
class theano.compile.function_module.Function(fn, input_storage, output_storage,
indices, outputs, defaults, unpack_single, return_none, output_keys, maker)
Type of the functions returned by theano.function or theano.FunctionMaker.create.
Function is the callable object that does computation. It has the storage of inputs and outputs, performs
the packing and unpacking of inputs and return values. It implements the square-bracket indexing so
that you can look up the value of a symbolic node.
Functions are copyable via {{{fn.copy()}}} and {{{copy.copy(fn)}}}. When a function is copied, this
instance is duplicated. Contrast with self.maker (instance of FunctionMaker) that is shared between
copies. The meaning of copying a function is that the containers and their current values will all be
duplicated. This requires that mutable inputs be copied, whereas immutable inputs may be shared
between copies.
A Function instance is hashable, on the basis of its memory address (its id).
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A Function instance is only equal to itself.
A Function instance may be serialized using the pickle or cPickle modules. This will save all default
inputs, the graph, and WRITEME to the pickle file.
A Function instance have a trust_input field that default to False. When True, we don’t do extra
check of the input to give better error message. In some case, python code will still return the good
results if you pass a python or numpy scalar instead of a numpy tensor. C code should raise an error
if you pass an object of the wrong type.
finder
inv_finder
copy(share_memory=False, swap=None, delete_updates=False, name=None, profile=None)
Copy this function. Copied function will have separated maker and fgraph with original function.
User can choose whether to separate storage by changing the share_memory arguments.
Parameters
• share_memory (boolean) – When True, two function share intermediate
storages(storages except input and output storages). Otherwise two functions
will only share partial storages and same maker. If two functions share memory
and allow_gc=False, this will increase executing speed and save memory.
• swap (dict) – Dictionary that map old SharedVariables to new SharedVariables. Default is None. NOTE: The shared variable swap in only done in the
new returned function, not in the user graph.
• delete_updates (boolean) – If True, Copied function will not have updates.
• name (string) – If provided, will be the name of the new Function. Otherwise, it will be old + ” copy”
• profile – as theano.function profile parameter
Returns
Return type Copied theano.Function
free()
When allow_gc = False, clear the Variables in storage_map
Note: *TODO* Freshen up this old documentation
io - defines theano.function [TODO]
Inputs
The inputs argument to theano.function is a list, containing the Variable instances for which
values will be specified at the time of the function call. But inputs can be more than just Variables. In
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instances let us attach properties to Variables to tell function more about how to use them.
class theano.compile.io.In(object)
__init__(variable, name=None, value=None, update=None, mutable=False, strict=False,
autoname=True, implicit=None)
variable: a Variable instance. This will be assigned a value before running the function, not
computed from its owner.
name: Any type. (If autoname_input==True, defaults to variable.name). If name
is a valid Python identifier, this input can be set by kwarg, and its value can be accessed by
self.<name>. The default value is None.
value: literal or Container. The initial/default value for this input.
If update is‘‘
None‘‘, this input acts just like an argument with a default value in Python. If update is
not None, changes to this value will “stick around”, whether due to an update or a user’s
explicit action.
update: Variable instance. This expression Variable will replace value after each function
call. The default value is None, indicating that no update is to be done.
mutable: Bool (requires value). If True, permit the compiled function to modify the Python
object being used as the default value. The default value is False.
strict: Bool (default: False ). True means that the value you pass for this input must have
exactly the right type. Otherwise, it may be cast automatically to the proper type.
autoname: Bool. If set to True, if name is None and the Variable has a name, it will be
taken as the input’s name. If autoname is set to False, the name is the exact value passed as
the name parameter (possibly None).
implicit: Bool or None (default: None) True: This input is implicit in the sense that the
user is not allowed to provide a value for it. Requires value to be set.
False: The user can provide a value for this input. Be careful when value is a container,
because providing an input value will overwrite the content of this container.
None: Automatically choose between True or False depending on the situation. It will
be set to False in all cases except if value is a container (so that there is less risk of
accidentally overwriting its content without being aware of it).
Value: initial and default values
A non-None value argument makes an In() instance an optional parameter of the compiled function. For
example, in the following code we are defining an arity-2 function inc.
>>>
>>>
>>>
>>>
>>>
import theano.tensor as T
from theano import function
from theano.compile.io import In
u, x, s = T.scalars('u', 'x', 's')
inc = function([u, In(x, value=3), In(s, update=(s+x*u), value=10.0)], [])
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Since we provided a value for s and x, we can call it with just a value for u like this:
>>> inc(5)
[]
>>> print(inc[s])
25.0
# update s with 10+3*5
The effect of this call is to increment the storage associated to s in inc by 15.
If we pass two arguments to inc, then we override the value associated to x, but only for this one function
call.
>>> inc(3, 4)
[]
>>> print(inc[s])
37.0
>>> print(inc[x])
3.0
# update s with 25 + 3*4
# the override value of 4 was only temporary
If we pass three arguments to inc, then we override the value associated with x and u and s. Since s‘s
value is updated on every call, the old value of s will be ignored and then replaced.
>>> inc(3, 4, 7)
[]
>>> print(inc[s])
19.0
# update s with 7 + 3*4
We can also assign to inc[s] directly:
>>> inc[s] = 10
>>> inc[s]
array(10.0)
Input Argument Restrictions
The following restrictions apply to the inputs to theano.function:
• Every input list element must be a valid In instance, or must be upgradable to a valid In instance.
See the shortcut rules below.
• The same restrictions apply as in Python function definitions: default arguments and keyword arguments must come at the end of the list. Un-named mandatory arguments must come at the beginning
of the list.
• Names have to be unique within an input list. If multiple inputs have the same name, then the function
will raise an exception. [*Which exception?]
• Two In instances may not name the same Variable. I.e. you cannot give the same parameter multiple
times.
If no name is specified explicitly for an In instance, then its name will be taken from the Variable’s name.
Note that this feature can cause harmless-looking input lists to not satisfy the two conditions above. In such
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cases, Inputs should be named explicitly to avoid problems such as duplicate names, and named arguments
preceding unnamed ones. This automatic naming feature can be disabled by instantiating an In instance
explicitly with the autoname flag set to False.
Access to function values and containers
For each input, theano.function will create a Container if value was not already a Container
(or if implicit was False). At the time of a function call, each of these containers must be filled with
a value. Each input (but especially ones with a default value or an update expression) may have a value
between calls. The function interface defines a way to get at both the current value associated with an input,
as well as the container which will contain all future values:
• The value property accesses the current values. It is both readable and writable, but assignments
(writes) may be implemented by an internal copy and/or casts.
• The container property accesses the corresponding container. This property accesses is a readonly dictionary-like interface. It is useful for fetching the container associated with a particular input
to share containers between functions, or to have a sort of pointer to an always up-to-date value.
Both value and container properties provide dictionary-like access based on three types of keys:
• integer keys: you can look up a value/container by its position in the input list;
• name keys: you can look up a value/container by its name;
• Variable keys: you can look up a value/container by the Variable it corresponds to.
In addition to these access mechanisms, there is an even more convenient method to access values by indexing a Function directly by typing fn[<name>], as in the examples above.
To show some examples of these access methods...
>>>
>>>
>>>
>>>
from theano import tensor as T, function
a, b, c = T.scalars('xys') # set the internal names of graph nodes
# Note that the name of c is 's', not 'c'!
fn = function([a, b, ((c, c+a+b), 10.0)], [])
>>> # the value associated with c is accessible in 3 ways
>>> fn['s'] is fn.value[c]
True
>>> fn['s'] is fn.container[c].value
True
>>> fn['s']
array(10.0)
>>> fn(1, 2)
[]
>>> fn['s']
array(13.0)
>>> fn['s'] = 99.0
>>> fn(1, 0)
[]
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>>> fn['s']
array(100.0)
>>> fn.value[c] = 99.0
>>> fn(1,0)
[]
>>> fn['s']
array(100.0)
>>> fn['s'] == fn.value[c]
True
>>> fn['s'] == fn.container[c].value
True
Input Shortcuts
Every element of the inputs list will be upgraded to an In instance if necessary.
• a Variable instance r will be upgraded like In(r)
• a tuple (name, r) will be In(r, name=name)
• a tuple (r, val) will be In(r, value=value, autoname=True)
• a tuple ((r,up), val) will be In(r, value=value, update=up, autoname=True)
• a tuple (name, r, val) will be In(r, name=name, value=value)
• a tuple (name, (r,up), val) will be In(r, name=name, value=val, update=up,
autoname=True)
Example:
>>>
>>>
>>>
>>>
>>>
>>>
>>>
import theano
from theano import tensor as T
from theano.compile.io import In
x = T.scalar()
y = T.scalar('y')
z = T.scalar('z')
w = T.scalar('w')
>>>
...
>>>
>>>
>>>
>>>
fn = theano.function(inputs=[x, y, In(z, value=42), ((w, w+x), 0)],
outputs=x + y + z)
# the first two arguments are required and the last two are
# optional and initialized to 42 and 0, respectively.
# The last argument, w, is updated with w + x each time the
# function is called.
>>> fn(1)
# illegal because there are two required arguments
Traceback (most recent call last):
...
TypeError: Missing required input: y
>>> fn(1, 2)
# legal, z is 42, w goes 0 -> 1 (because w <- w + x)
array(45.0)
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>>> fn(1, y=2)
# legal, z is 42, w goes 1 -> 2
array(45.0)
>>> fn(x=1, y=2)
# illegal because x was not named
Traceback (most recent call last):
...
TypeError: Unknown input or state: x. The function has 3 named inputs (y, z,
˓→w), and 1 unnamed input which thus cannot be accessed through keyword
˓→argument (use 'name=...' in a variable's constructor to give it a name).
>>> fn(1, 2, 3)
# legal, z is 3, w goes 2 -> 3
array(6.0)
>>> fn(1, z=3, y=2) # legal, z is 3, w goes 3 -> 4
array(6.0)
>>> fn(1, 2, w=400)
# legal, z is 42 again, w goes 400 -> 401
array(45.0)
>>> fn(1, 2)
# legal, z is 42, w goes 401 -> 402
array(45.0)
In the example above, z has value 42 when no value is explicitly given. This default value is potentially
used at every function invocation, because z has no update or storage associated with it.
Outputs
The outputs argument to function can be one of
• None, or
• a Variable or Out instance, or
• a list of Variables or Out instances.
An Out instance is a structure that lets us attach options to individual output Variable instances, similarly
to how In lets us attach options to individual input Variable instances.
Out(variable, borrow=False) returns an Out instance:
• borrow
If True, a reference to function’s internal storage is OK. A value returned for this output might be
clobbered by running the function again, but the function might be faster.
Default: False
If a single Variable or Out instance is given as argument, then the compiled function will return a single
value.
If a list of Variable or Out instances is given as argument, then the compiled function will return a list
of their values.
>>> import numpy
>>> from theano.compile.io import Out
>>> x, y, s = T.matrices('xys')
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>>> # print a list of 2 ndarrays
>>> fn1 = theano.function([x], [x+x, Out((x+x).T, borrow=True)])
>>> fn1(numpy.asarray([[1,0],[0,1]]))
[array([[ 2., 0.],
[ 0., 2.]]), array([[ 2., 0.],
[ 0., 2.]])]
>>> # print a list of 1 ndarray
>>> fn2 = theano.function([x], [x+x])
>>> fn2(numpy.asarray([[1,0],[0,1]]))
[array([[ 2., 0.],
[ 0., 2.]])]
>>> # print an ndarray
>>> fn3 = theano.function([x], outputs=x+x)
>>> fn3(numpy.asarray([[1,0],[0,1]]))
array([[ 2., 0.],
[ 0., 2.]])
ops – Some Common Ops and extra Ops stuff
This file contains auxiliary Ops, used during the compilation phase and Ops building class
(FromFunctionOp) and decorator (as_op()) that help make new Ops more rapidly.
class theano.compile.ops.FromFunctionOp(fn, itypes, otypes, infer_shape)
Build a basic Theano Op around a function.
Since the resulting Op is very basic and is missing most of the optional functionalities, some optimizations may not apply. If you want to help, you can supply an infer_shape function that computes
the shapes of the output given the shapes of the inputs.
Also the gradient is undefined in the resulting op and Theano will raise an error if you attempt to get
the gradient of a graph containing this op.
class theano.compile.ops.OutputGuard(use_c_code=’/usr/bin/g++’)
This op is used only internally by Theano.
Only the AddDestroyHandler optimizer tries to insert them in the graph.
This Op is declared as destructive while it is not destroying anything. It returns a view. This is used
to prevent destruction of the output variables of a Theano function.
There is a mechanism in Theano that should prevent this, but the use of OutputGuard adds a safeguard:
it may be possible for some optimization run before the add_destroy_handler phase to bypass this
mechanism, by making in-place optimizations.
TODO: find a current full explanation.
class theano.compile.ops.Rebroadcast(*axis)
Change the input’s broadcastable fields in some predetermined way.
See also:
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unbroadcast, addbroadcast, patternbroadcast
Notes
Works inplace and works for CudaNdarrayType.
Example
Rebroadcast((0, True), (1, False))(x) would make x broadcastable in axis 0 and not broadcastable in
axis 1.
class theano.compile.ops.Shape(use_c_code=’/usr/bin/g++’)
L{Op} to return the shape of a matrix.
Notes
Non-differentiable.
class theano.compile.ops.Shape_i(i)
L{Op} to return the shape of a matrix.
Notes
Non-differentiable.
class theano.compile.ops.SpecifyShape(use_c_code=’/usr/bin/g++’)
L{Op} that puts into the graph the user-provided shape.
In the case where this op stays in the final graph, we assert the shape. For this the output of this op
must be used in the graph. This is not the case most of the time if we only take the shape of the output.
Maybe there are other optimizations that will mess with this.
Notes
Maybe in the future we will never do the assert!
We currently don’t support specifying partial shape information.
TODO : test this op with sparse and cuda ndarray. Do C code for them too.
class theano.compile.ops.ViewOp(use_c_code=’/usr/bin/g++’)
Returns an inplace view of the input. Used internally by Theano.
theano.compile.ops.as_op(itypes, otypes, infer_shape=None)
Decorator that converts a function into a basic Theano op that will call the supplied function as its
implementation.
It takes an optional infer_shape parameter that should be a callable with this signature:
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def infer_shape(node, input_shapes): ... return output_shapes
Here input_shapes and output_shapes are lists of tuples that represent the shape of the corresponding
inputs/outputs.
This should not be used when performance is a concern since the very basic nature of the resulting
Op may interfere with certain graph optimizations.
Examples
@as_op(itypes=[theano.tensor.fmatrix, theano.tensor.fmatrix], otypes=[theano.tensor.fmatrix])
def numpy_dot(a, b): return numpy.dot(a, b)
theano.compile.ops.register_deep_copy_op_c_code(typ, code, version=())
Tell DeepCopyOp how to generate C code for a Theano Type.
Parameters
• typ (Theano type) – It must be the Theano class itself and not an instance of
the class.
• code (C code) – Deep copies the Theano type ‘typ’. Use %(iname)s and %(oname)s for the input and output C variable names respectively.
• version – A number indicating the version of the code, for cache.
theano.compile.ops.register_rebroadcast_c_code(typ, code, version=())
Tell Rebroadcast how to generate C code for a Theano Type.
typ [Theano type] It must be the Theano class itself and not an instance of the class.
code [C code] That checks if the dimension %(axis)s is of shape 1 for the Theano type ‘typ’. Use
%(iname)s and %(oname)s for the input and output C variable names respectively, and %(axis)s
for the axis that we need to check. This code is put in a loop for all axes.
version A number indicating the version of the code, for cache.
theano.compile.ops.register_shape_c_code(type, code, version=())
Tell Shape Op how to generate C code for a Theano Type.
Parameters
• typ (Theano type) – It must be the Theano class itself and not an instance of
the class.
• code (C code) – Returns a vector representing the shape for the Theano type
‘typ’. Use %(iname)s and %(oname)s for the input and output C variable names
respectively.
• version – A number indicating the version of the code, for cache.
theano.compile.ops.register_shape_i_c_code(typ, code, check_input, version=())
Tell Shape_i how to generate C code for a Theano Type.
Parameters
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• typ (Theano type) – It must be the Theano class itself and not an instance of
the class.
• code (C code) – Gets the shape of dimensions %(i)s for the Theano type ‘typ’.
Use %(iname)s and %(oname)s for the input and output C variable names respectively.
• version – A number indicating the version of the code, for cache.
theano.compile.ops.register_specify_shape_c_code(typ, code, version=(),
c_support_code_apply=None)
Tell SpecifyShape how to generate C code for a Theano Type.
Parameters
• typ (Theano type) – It must be the Theano class itself and not an instance of
the class.
• code (C code) – Checks the shape and returns a view for the Theano type
‘typ’. Use %(iname)s and %(oname)s for the input and output C variable names
respectively. %(shape)s is the vector of shape of %(iname)s. Check that its length
is good.
• version – A number indicating the version of the code, for cache.
• c_support_code_apply – Extra code.
theano.compile.ops.register_view_op_c_code(type, code, version=())
Tell ViewOp how to generate C code for a Theano Type.
Parameters
• type (Theano type) – It must be the Theano class itself and not an instance
of the class.
• code (C code) – Returns a view for the Theano type ‘type’. Use %(iname)s
and %(oname)s for the input and output C variable names respectively.
• version – A number indicating the version of the code, for cache.
theano.compile.ops.shape_i(var, i, fgraph=None)
Equivalent of var.shape[i], but apply if possible the shape feature optimization.
This is useful in optimization that need to get the shape. This remove the need of the following
shape_feature optimization that convert it. So this speed up optimization and remove Equilibrium
max iteration problems.
Parameters
• var – The variable we want to take the shape of.
• i – The shape dimensions we want
• fgraph (optional) – If var.fgraph do not exist, the fgraph that have the
shape_feature to introduce var in to get the optimized shape.
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mode – controlling compilation
Guide
The mode parameter to theano.function() controls how the inputs-to-outputs graph is transformed
into a callable object.
Theano defines the following modes by name:
• 'FAST_COMPILE': Apply just a few graph optimizations and only use Python implementations.
• 'FAST_RUN': Apply all optimizations, and use C implementations where possible.
• 'DebugMode': A mode for debugging. See DebugMode for details.
• 'ProfileMode': Deprecated, use the Theano flag config.profile.
• 'NanGuardMode: Nan detector
• 'DEBUG_MODE': Deprecated. Use the string DebugMode.
• 'PROFILE_MODE': Deprecated, use the Theano flag config.profile.
The default mode is typically FAST_RUN, but it can be controlled via the configuration variable config.
mode, which can be overridden by passing the keyword argument to theano.function().
Todo
For a finer level of control over which optimizations are applied, and whether C or Python implementations
are used, read.... what exactly?
Reference
theano.compile.mode.FAST_COMPILE
theano.compile.mode.FAST_RUN
class theano.compile.mode.Mode(object)
Compilation is controlled by two attributes: the optimizer controls how an expression graph will be
transformed; the linker controls how the optimized expression graph will be evaluated.
optimizer
An optimizer instance.
linker
A linker instance.
including(*tags)
Return a new Mode instance like this one, but with an optimizer modified by including the given
tags.
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excluding(*tags)
Return a new Mode instance like this one, but with an optimizer modified by excluding the given
tags.
requiring(*tags)
Return a new Mode instance like this one, but with an optimizer modified by requiring the given
tags.
debugmode
Guide
The DebugMode evaluation mode includes a number of self-checks and assertions that can help to diagnose
several kinds of programmer errors that can lead to incorrect output.
It is much slower to evaluate a function or method with DebugMode than it would be in 'FAST_RUN' or
even 'FAST_COMPILE'. We recommended you use DebugMode during development, but not when you
launch 1000 processes on a cluster.
DebugMode can be used as follows:
import theano
from theano import tensor
from theano.compile.debugmode import DebugMode
x = tensor.dscalar('x')
f = theano.function([x], 10*x, mode='DebugMode')
f(5)
f(0)
f(7)
It can also be used by setting the configuration variable config.mode. It can also be used by passing a
DebugMode instance as the mode, as in
>>> f = theano.function([x], 10*x, mode=DebugMode(check_c_code=False))
If any problem is detected, DebugMode will raise an exception according to what went wrong, either at
call time (f(5)) or compile time ( f = theano.function(x, 10*x, mode='DebugMode')).
These exceptions should not be ignored; talk to your local Theano guru or email the users list if you cannot
make the exception go away.
Some kinds of errors can only be detected for certain input value combinations. In the example above, there
is no way to guarantee that a future call to say, f(-1) won’t cause a problem. DebugMode is not a silver
bullet.
If you instantiate DebugMode using the constructor compile.DebugMode rather than the keyword
DebugMode you can configure its behaviour via constructor arguments.
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Reference
class theano.compile.debugmode.DebugMode(Mode)
Evaluation Mode that detects internal theano errors.
This mode catches several kinds of internal error:
•inconsistent outputs when calling the same Op twice with the same inputs, for instance if c_code
and perform implementations, are inconsistent, or in case of incorrect handling of output memory (see BadThunkOutput)
•a variable replacing another when their runtime values don’t match. This is a symptom of an
incorrect optimization step, or faulty Op implementation (raises BadOptimization)
•stochastic optimization ordering (raises StochasticOrder)
•incomplete destroy_map specification (raises BadDestroyMap)
•an op that returns an illegal value not matching the output Variable Type (raises InvalidValueError)
Each of these exceptions inherits from the more generic DebugModeError.
If there are no internal errors, this mode behaves like FAST_RUN or FAST_COMPILE, but takes a
little longer and uses more memory.
If there are internal errors, this mode will raise an DebugModeError exception.
stability_patience = config.DebugMode.patience
When checking for the stability of optimization, recompile the graph this many times. Default
10.
check_c_code = config.DebugMode.check_c
Should we evaluate (and check) the c_code implementations?
True -> yes, False -> no.
Default yes.
check_py_code = config.DebugMode.check_py
Should we evaluate (and check) the perform implementations?
True -> yes, False -> no.
Default yes.
check_isfinite = config.DebugMode.check_finite
Should we check for (and complain about) NaN/Inf ndarray elements?
True -> yes, False -> no.
Default yes.
require_matching_strides = config.DebugMode.check_strides
Check for (and complain about) Ops whose python and C outputs are ndarrays with different
strides. (This can catch bugs, but is generally overly strict.)
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0 -> no check, 1 -> warn, 2 -> err.
Default warn.
__init__(self, optimizer=’fast_run’, stability_patience=None, check_c_code=None,
check_py_code=None, check_isfinite=None, require_matching_strides=None,
linker=None)
Initialize member variables.
If any of these arguments (except optimizer) is not None, it overrides the class default. The
linker arguments is not used. It is set their to allow Mode.requiring() and some other fct to work
with DebugMode too.
The keyword version of DebugMode (which you get by using mode='DebugMode) is quite strict, and can
raise several different Exception types. There following are DebugMode exceptions you might encounter:
class theano.compile.debugmode.DebugModeError(Exception)
This is a generic error. All the other exceptions inherit from this one. This error is typically not raised
directly. However, you can use except DebugModeError: ... to catch any of the more
specific types of Exception.
class theano.compile.debugmode.BadThunkOutput(DebugModeError)
This exception means that different calls to the same Op with the same inputs did not compute
the same thing like they were supposed to. For instance, it can happen if the python (perform)
and c (c_code) implementations of the Op are inconsistent (the problem might be a bug in either
perform or c_code (or both)). It can also happen if perform or c_code does not handle correctly output memory that has been preallocated (for instance, if it did not clear the memory before
accumulating into it, or if it assumed the memory layout was C-contiguous even if it is not).
class theano.compile.debugmode.BadOptimization(DebugModeError)
This exception indicates that an Optimization replaced one variable (say V1) with another one (say
V2) but at runtime, the values for V1 and V2 were different. This is something that optimizations are
not supposed to do.
It can be tricky to identify the one-true-cause of an optimization error, but this exception provides a
lot of guidance. Most of the time, the exception object will indicate which optimization was at fault.
The exception object also contains information such as a snapshot of the before/after graph where the
optimization introduced the error.
class theano.compile.debugmode.BadDestroyMap(DebugModeError)
This happens when an Op’s perform() or c_code() modifies an input that it wasn’t supposed
to. If either the perform or c_code implementation of an Op might modify any input, it has to
advertise that fact via the destroy_map attribute.
For detailed documentation on the destroy_map attribute, see Inplace operations.
class theano.compile.debugmode.BadViewMap(DebugModeError)
This happens when an Op’s perform() or c_code() creates an alias or alias-like dependency between
an input and an output... and it didn’t warn the optimization system via the view_map attribute.
For detailed documentation on the view_map attribute, see Views.
class theano.compile.debugmode.StochasticOrder(DebugModeError)
This happens when an optimization does not perform the same graph operations in the same order
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when run several times in a row. This can happen if any steps are ordered by id(object) somehow,
such as via the default object hash function. A Stochastic optimization invalidates the pattern of work
whereby we debug in DebugMode and then run the full-size jobs in FAST_RUN.
class theano.compile.debugmode.InvalidValueError(DebugModeError)
This happens when some Op’s perform or c_code implementation computes an output that is
invalid with respect to the type of the corresponding output variable. Like if it returned a complexvalued ndarray for a dscalar Type.
This can also be triggered when floating-point values such as NaN and Inf are introduced into the
computations. It indicates which Op created the first NaN. These floating-point values can be allowed
by passing the check_isfinite=False argument to DebugMode.
profilemode – profiling Theano functions
Guide
Note: ProfileMode is deprecated. Use config.profile instead.
To profile a Theano graph, a special mode called ProfileMode, must be passed as an argument when compiling your graph. Using ProfileMode is a three-step process.
Creating a ProfileMode Instance
First create a ProfileMode instance.
>>> import theano
>>> from theano import ProfileMode
>>> profmode = theano.ProfileMode(optimizer='fast_run', linker=theano.gof.
˓→OpWiseCLinker())
The ProfileMode constructor takes as input an optimizer and a linker. Which optimizer and linker to use will
depend on the application. For example, a user wanting to profile the Python implementation only, should
use the gof.PerformLinker (or “py” for short). On the other hand, a user wanting to profile his graph using
C implementations wherever possible should use the gof.OpWiseCLinker (or “c|py”).
In the same manner, modifying which optimizer is passed to ProfileMode will decide which optimizations
are applied to the graph, prior to profiling. Changing the optimizer should be especially useful when developing new graph optimizations, in order to evaluate their impact on performance. Also keep in mind that
optimizations might change the computation graph a lot, meaning that you might not recognize some of the
operations that are profiled (you did not use them explicitly but an optimizer decided to use it to improve
performance or numerical stability). If you cannot easily relate the output of ProfileMode with the computations you defined, you might want to try setting optimizer to None (but keep in mind the computations will
be slower than if they were optimized).
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Note that most users will want to use ProfileMode to optimize their graph and find where most of the
computation time is being spent. In this context, ‘fast_run’ optimizer and gof.OpWiseCLinker are the
most appropriate choices.
Compiling your Graph with ProfileMode
Once the ProfileMode instance is created, simply compile your graph as you would normally, by specifying
the mode parameter.
>>> # with functions
>>> f = theano.function([input1,input2],[output1], mode=profmode)
Retrieving Timing Information
Once your graph is compiled, simply run the program or operation you wish to profile, then call
profmode.print_summary(). This will provide you with the desired timing information, indicating where your graph is spending most of its time.
This is best shown through an example. Lets use the example of logistic regression. (Code for this example
is in the file benchmark/regression/regression.py.)
Compiling the module with ProfileMode and calling profmode.print_summary() generates the following output:
"""
ProfileMode.print_summary()
--------------------------local_time 0.0749197006226 (Time spent running thunks)
Apply-wise summary: <fraction of local_time spent at this position> (<Apply
˓→position>, <Apply Op name>)
0.069
15
_dot22
0.064
1
_dot22
0.053
0
InplaceDimShuffle{x,0}
0.049
2
InplaceDimShuffle{1,0}
0.049
10
mul
0.049
6
Elemwise{ScalarSigmoid{output_types_preference=
˓→<theano.scalar.basic.transfer_type object at 0x171e650>}}[(0, 0)]
0.049
3
InplaceDimShuffle{x}
0.049
4
InplaceDimShuffle{x,x}
0.048
14
Sum{0}
0.047
7
sub
0.046
17
mul
0.045
9
sqr
0.045
8
Elemwise{sub}
0.045
16
Sum
0.044
18
mul
... (remaining 6 Apply instances account for 0.25 of the runtime)
Op-wise summary: <fraction of local_time spent on this kind of Op> <Op name>
0.139
* mul
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0.134
* _dot22
0.092
* sub
0.085
* Elemwise{Sub{output_types_preference=<theano.scalar.basic.
˓→transfer_type object at 0x1779f10>}}[(0, 0)]
0.053
* InplaceDimShuffle{x,0}
0.049
* InplaceDimShuffle{1,0}
0.049
* Elemwise{ScalarSigmoid{output_types_preference=<theano.
˓→scalar.basic.transfer_type object at 0x171e650>}}[(0, 0)]
0.049
* InplaceDimShuffle{x}
0.049
* InplaceDimShuffle{x,x}
0.048
* Sum{0}
0.045
* sqr
0.045
* Sum
0.043
* Sum{1}
0.042
* Elemwise{Mul{output_types_preference=<theano.scalar.basic.
˓→transfer_type object at 0x17a0f50>}}[(0, 1)]
0.041
* Elemwise{Add{output_types_preference=<theano.scalar.basic.
˓→transfer_type object at 0x1736a50>}}[(0, 0)]
0.039
* Elemwise{Second{output_types_preference=<theano.scalar.
˓→basic.transfer_type object at 0x1736d90>}}[(0, 1)]
... (remaining 0 Ops account for 0.00 of the runtime)
(*) Op is running a c implementation
"""
Note: *TODO*
The following text was recovered from a recent version of the source file... hopefully things haven’t gotten
too out-of-sync!
The first show an Apply-wise summary, the second show an Op-wise summary, the third show an type-Opwise summary.
The Apply-wise summary print the timing information for the worst offending Apply nodes. This corresponds to individual Op applications within your graph which take the longest to execute (so if you use dot
twice, you will see two entries there).
The Op-wise summary print the execution time of all Apply nodes executing the same Op are grouped
together and the total execution time per Op is shown (so if you use dot twice, you will see only one entry
there corresponding to the sum of the time spent in each of them). If two Op have different hash value, they
will be separate.
The type-Op-wise summary group the result by type of op. So event if two Op have different hash value,
they will be merged.
Their is an hack with the Op-wise summary. Go see it if you want to know more.
The summary has two components to it. In the first section called the Apply-wise summary, timing information is provided for the worst offending Apply nodes. This corresponds to individual Op applications within
your graph which take the longest to execute (so if you use dot twice, you will see two entries there). In
the second portion, the Op-wise summary, the execution time of all Apply nodes executing the same Op are
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grouped together and the total execution time per Op is shown (so if you use dot twice, you will see only
one entry there corresponding to the sum of the time spent in each of them).
Note that the ProfileMode also shows which Ops were running a c implementation.
Developers wishing to optimize the performance of their graph should focus on the worst offending Ops and
Apply nodes – either by optimizing an implementation, providing a missing C implementation, or by writing
a graph optimization that eliminates the offending Op altogether. You should strongly consider emailing one
of our lists about your issue before spending too much time on this.
Reference
class theano.compile.profilemode.ProfileMode(Mode)
print_summary(n_apply_to_print=None, n_ops_to_print=None)
Print three summaries to stdout that show where cpu time is spent during theano function executions (for all functions using this object instance).
Parameters
• n_apply_to_print – the number of apply nodes to print. The default 15, but can be configured via ProfileMode.n_ops_to_print in
THEANO_FLAGS.
• n_ops_to_print – the number of ops to print. Default 20, or but can be
configured via ProfileMode.n_apply_to_print in THEANO_FLAGS.
Returns None
print_diff_summary(self, other, n_apply_to_print=None, n_ops_to_print=None):
""" As print_summary, but print the difference on two different profile mode.
TODO: Also we don't print the Apply-wise summary as it don't work for now.
TODO: make comparaison with gpu code.
Parameters
• other – the other instance of ProfileMode that we want to be compared to.
• n_apply_to_print – the number of apply nodes to print. The default 15, but can be configured via ProfileMode.n_ops_to_print in
THEANO_FLAGS.
• n_ops_to_print – the number of ops to print. Default 20, or but can be
configured via ProfileMode.n_apply_to_print in THEANO_FLAGS.
Returns None
nanguardmode
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Guide
The NanGuardMode aims to prevent the model from outputing NaNs or Infs. It has a number of self-checks,
which can help to find out which apply node is generating those incorrect outputs. It provides automatic
detection of 3 types of abnormal values: NaNs, Infs, and abnormally big values.
NanGuardMode can be used as follows:
import numpy
import theano
import theano.tensor as T
from theano.compile.nanguardmode import NanGuardMode
x =
w =
y =
fun
T.matrix()
theano.shared(numpy.random.randn(5, 7).astype(theano.config.floatX))
T.dot(x, w)
= theano.function(
[x], y,
mode=NanGuardMode(nan_is_error=True, inf_is_error=True, big_is_error=True)
)
While using the theano function fun, it will monitor the values of each input and output variable of each
node. When abnormal values are detected, it raises an error to indicate which node yields the NaNs. For
example, if we pass the following values to fun:
infa = numpy.tile(
(numpy.asarray(100.) ** 1000000).astype(theano.config.floatX), (3, 5))
fun(infa)
It will raise an AssertionError indicating that Inf value is detected while executing the function.
You can also set the three parameters in NanGuardMode() to indicate which kind of abnormal values to
monitor. nan_is_error and inf_is_error has no default values, so they need to be set explicitly,
but big_is_error is set to be True by default.
Note: NanGuardMode significantly slows down computations; only enable as needed.
Reference
class theano.compile.nanguardmode.NanGuardMode(nan_is_error=None,
inf_is_error=None,
big_is_error=None,
optimizer=’default’, linker=None)
A Theano compilation Mode that makes the compiled function automatically detect NaNs and Infs
and detect an error if they occur.
Parameters
• nan_is_error (bool) – If True, raise an error anytime a NaN is encountered.
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• inf_is_error (bool) – If True, raise an error anytime an Inf is encountered.
Note that some pylearn2 modules currently use np.inf as a default value (e.g.
mlp.max_pool) and these will cause an error if inf_is_error is True.
• big_is_error (bool) – If True, raise an error when a value greater than 1e10
is encountered.
Note: We ignore the linker parameter
config – Theano Configuration
Guide
The config module contains many attributes that modify Theano’s behavior. Many of these attributes
are consulted during the import of the theano module and many are assumed to be read-only.
As a rule, the attributes in this module should not be modified by user code.
Theano’s code comes with default values for these attributes, but you can override them from your .theanorc
file, and override those values in turn by the THEANO_FLAGS environment variable.
The order of precedence is:
1. an assignment to theano.config.<property>
2. an assignment in THEANO_FLAGS
3. an assignment in the .theanorc file (or the file indicated in THEANORC)
You can print out the current/effective configuration at any time by printing theano.config. For example, to see a list of all active configuration variables, type this from the command-line:
python -c 'import theano; print(theano.config)' | less
Environment Variables
THEANO_FLAGS
This is a list of comma-delimited key=value pairs that control Theano’s behavior.
For example, in bash, you can override your THEANORC defaults for <myscript>.py by typing this:
THEANO_FLAGS='floatX=float32,device=gpu0,lib.cnmem=1'
˓→py
python <myscript>.
If a value is defined several times in THEANO_FLAGS, the right-most definition is used. So, for
instance, if THEANO_FLAGS='device=cpu,device=gpu0', then gpu0 will be used.
THEANORC
The location[s] of the .theanorc file[s] in ConfigParser format. It defaults to $HOME/.theanorc.
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On Windows, it defaults to $HOME/.theanorc:$HOME/.theanorc.txt to make Windows
users’ life easier.
Here is the .theanorc equivalent to the THEANO_FLAGS in the example above:
[global]
floatX = float32
device = gpu0
[lib]
cnmem = 1
Configuration attributes that are available directly in config (e.g. config.device, config.
mode) should be defined in the [global] section. Attributes from a subsection of config (e.g.
config.lib.cnmem, config.dnn.conv.algo_fwd) should be defined in their corresponding section (e.g. [nvcc], [dnn.conv]).
Multiple configuration files can be specified by separating them with ‘:’ characters (as in $PATH).
Multiple configuration files will be merged, with later (right-most) files taking priority over earlier
files in the case that multiple files specify values for a common configuration option. For example, to override system-wide settings with personal ones, set THEANORC=/etc/theanorc:~/.
theanorc.
Config Attributes
The list below describes some of the more common and important flags that you might want to use. For the
complete list (including documentation), import theano and print the config variable, as in:
python -c 'import theano; print(theano.config)' | less
config.device
String value: either 'cpu', 'gpu', 'gpu0', 'gpu1', 'gpu2', or 'gpu3'
Default device for computations. If gpu*, change the default to try to move computation to it and
to put shared variable of float32 on it. Choose the default compute device for theano graphs. Setting
this to a gpu* string will make theano to try by default to move computation to it. Also it will make
theano put by default shared variable of float32 on it. 'gpu' lets the driver select the GPU to use,
while 'gpu?' makes Theano try to use a specific device. If we are not able to use the GPU, either
we fall back on the CPU, or an error is raised, depending on the force_device flag.
This flag’s value cannot be modified during the program execution.
Do not use upper case letters, only lower case even if NVIDIA use capital letters.
config.force_device
Bool value: either True or False
Default: False
If True and device=gpu*, we raise an error if we cannot use the specified device. If True
and device=cpu, we disable the GPU. If False and device=gpu*, and if the specified device
cannot be used, we warn and fall back to the CPU.
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This is useful to run Theano’s tests on a computer with a GPU, but without running the GPU tests.
This flag’s value cannot be modified during the program execution.
config.init_gpu_device
String value: either '', 'gpu', 'gpu0', 'gpu1', 'gpu2', or 'gpu3'
Initialize the gpu device to use. When its value is gpu*, the theano flag device must be "cpu".
Unlike device, setting this flag to a specific GPU will not try to use this device by default, in
particular it will not move computations, nor shared variables, to the specified GPU.
This flag is useful to run GPU-specific tests on a particular GPU, instead of using the default one.
This flag’s value cannot be modified during the program execution.
config.pycuda.init
Bool value: either True or False
Default: False
If True, always initialize PyCUDA when Theano want to initialize the GPU. With PyCUDA version
2011.2.2 or earlier, PyCUDA must initialize the GPU before Theano does it. Setting this flag to True,
ensure that, but always import PyCUDA. It can be done manually by importing theano.misc.
pycuda_init before Theano initialize the GPU device. Newer version of PyCUDA (currently
only in the trunk) don’t have this restriction.
config.print_active_device
Bool value: either True or False
Default: True
Print active device at when the GPU device is initialized.
config.enable_initial_driver_test
Bool value: either True or False
Default: True
Tests the nvidia driver when a GPU device is initialized.
config.floatX
String value: 'float64', 'float32', or 'float16' (with limited support)
Default: 'float64'
This sets the default dtype returned by tensor.matrix(), tensor.vector(), and similar
functions. It also sets the default Theano bit width for arguments passed as Python floating-point
numbers.
config.warn_float64
String value: either 'ignore', 'warn', 'raise', or 'pdb'
Default: 'ignore'
When creating a TensorVariable with dtype float64, what should be done? This is useful to help find
upcast to float64 in user code.
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config.allow_gc
Bool value: either True or False
Default: True
This sets the default for the use of the Theano garbage collector for intermediate results. To use
less memory, Theano frees the intermediate results as soon as they are no longer needed. Disabling
Theano garbage collection allows Theano to reuse buffers for intermediate results between function
calls. This speeds up Theano by no longer spending time reallocating space. This gives significant
speed up on functions with many ops that are fast to execute, but this increases Theano’s memory
usage.
config.scan.allow_output_prealloc
Bool value, either True or False
Default: True
This enables, or not, an optimization in Scan in which it tries to pre-allocate memory for its outputs.
Enabling the optimization can give a significant speed up with Scan at the cost of slightly increased
memory usage.
config.scan.allow_gc
Bool value, either True or False
Default: False
Allow/disallow gc inside of Scan.
If config.allow_gc is True, but config.scan.allow_gc is False, then we will gc the
inner of scan after all iterations. This is the default.
config.openmp
Bool value: either True or False
Default: True if the environment variable OMP_NUM_THREADS!=1 or if we detect more
than 1 CPU core. Otherwise False.
Enable or not parallel computation on the CPU with OpenMP. It is the default value used when creating an Op that support it. The best is to define it via Theano configuration file or with the environment
variable THEANO_FLAGS.
config.openmp_elemwise_minsize
Positive int value, default: 200000.
This specifies the vectors minimum size for which elemwise ops use openmp, if openmp is enabled.
config.cast_policy
String value: either 'numpy+floatX' or 'custom'
Default: 'custom'
This specifies how data types are implicitly figured out in Theano, e.g. for constants or in the
results of arithmetic operations. The ‘custom’ value corresponds to a set of custom rules originally used in Theano (which can be partially customized, see e.g. the in-code help of tensor.
NumpyAutocaster), and will be deprecated in the future. The ‘numpy+floatX’ setting attempts
to mimic the numpy casting rules, although it prefers to use float32 numbers instead of float64 when
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config.floatX is set to ‘float32’ and the user uses data that is not explicitly typed as float64
(e.g. regular Python floats). Note that ‘numpy+floatX’ is not currently behaving exactly as planned
(it is a work-in-progress), and thus you should consider it as experimental. At the moment it behaves
differently from numpy in the following situations:
•Depending on the value of config.int_division, the resulting type of a division of integer types with the / operator may not match that of numpy.
•On mixed scalar / array operations, numpy tries to prevent the scalar from upcasting the array’s
type unless it is of a fundamentally different type. Theano does not attempt to do the same at
this point, so you should be careful that scalars may upcast arrays when they would not when
using numpy. This behavior should change in the near future.
config.int_division
String value: either 'int', 'floatX', or 'raise'
Default: 'int'
Specifies what to do when one tries to compute x / y, where both x and y are of integer types
(possibly unsigned). ‘int’ means an integer is returned (as in Python 2.X), but this behavior is deprecated. ‘floatX’ returns a number of type given by config.floatX. ‘raise’ is the safest choice (and
will become default in a future release of Theano) and raises an error when one tries to do such an
operation, enforcing the use of the integer division operator (//) (if a float result is intended, either
cast one of the arguments to a float, or use x.__truediv__(y)).
config.mode
String value: 'Mode', 'ProfileMode' (deprecated), 'DebugMode', 'FAST_RUN',
'FAST_COMPILE'
Default: 'Mode'
This sets the default compilation mode for theano functions. By default the mode Mode is equivalent
to FAST_RUN. See Config attribute linker and optimizer.
config.profile
Bool value: either True or False
Default: False
Do the vm/cvm linkers profile the execution time of Theano functions?
See Profiling Theano function for examples.
config.profile_memory
Bool value: either True or False
Default: False
Do the vm/cvm linkers profile the memory usage of Theano functions? It only works when profile=True.
config.profile_optimizer
Bool value: either True or False
Default: False
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Do the vm/cvm linkers profile the optimization phase when compiling a Theano function? It only
works when profile=True.
config.profiling.n_apply
Positive int value, default: 20.
The number of Apply nodes to print in the profiler output
config.profiling.n_ops
Positive int value, default: 20.
The number of Ops to print in the profiler output
config.profiling.min_memory_size
Positive int value, default: 1024.
For the memory profile, do not print Apply nodes if the size of their outputs (in bytes) is lower than
this.
config.profiling.min_peak_memory
Bool value: either True or False
Default: False
Does the memory profile print the min peak memory usage? It only works when profile=True, profile_memory=True
config.profiling.destination
String value: 'stderr', 'stdout', or a name of a file to be created
Default: 'stderr'
Name of the destination file for the profiling output. The profiling output can be either directed to
stderr (default), or stdout or an arbitrary file.
config.profiling.debugprint
Bool value: either True or False
Default: False
Do a debugprint of the profiled functions
config.lib.amdlibm
Bool value: either True or False
Default: False
This makes the compilation use the amdlibm library, which is faster than the standard libm.
config.lib.cnmem
Float value: >= 0
Controls the use of CNMeM (a faster CUDA memory allocator). In Theano dev version until 0.8 is
released.
The CNMeM library is included in Theano and does not need to be separately installed.
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The value represents the start size (either in MB or the fraction of total GPU memory) of the memory pool. If more memory is needed, Theano will try to obtain more, but this can cause memory
fragmentation.
•0: not enabled.
•0 < N <= 1: use this fraction of the total GPU memory (clipped to .95 for driver memory).
•> 1: use this number in megabytes (MB) of memory.
Default: 0 (but should change later)
Note: This could cause memory fragmentation. So if you have a memory error while using CNMeM,
try to allocate more memory at the start or disable it. If you try this, report your result on :ref‘theanodev‘.
Note: The clipping at 95% can be bypassed by specifing the exact number of megabytes. If more
then 95% are needed, it will try automatically to get more memory. But this can cause fragmentation,
see note above.
config.linker
String value: 'c|py', 'py', 'c', 'c|py_nogc'
Default: 'c|py'
When the mode is Mode, it sets the default linker used. See Configuration Settings and Compiling
Modes for a comparison of the different linkers.
config.optimizer
String value: 'fast_run', 'merge', 'fast_compile', 'None'
Default: 'fast_run'
When the mode is Mode, it sets the default optimizer used.
config.on_opt_error
String value: 'warn', 'raise', 'pdb' or 'ignore'
Default: 'warn'
When a crash occurs while trying to apply some optimization, either warn the user and skip
this optimization (‘warn’), raise the exception (‘raise’), fall into the pdb debugger (‘pdb’)
or ignore it (‘ignore’). We suggest to never use ‘ignore’ except in tests.
If you encounter a warning, report it on theano-dev.
config.assert_no_cpu_op
String value: 'ignore' or 'warn' or 'raise' or 'pdb'
Default: 'ignore'
If there is a CPU op in the computational graph, depending on its value; this flag can either raise a
warning, an exception or stop the compilation with pdb.
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config.on_shape_error
String value: 'warn' or 'raise'
Default: 'warn'
When an exception is raised when inferring the shape of some apply node, either warn the user and
use a default value (‘warn’), or raise the exception (‘raise’).
config.warn.ignore_bug_before
String value: 'None', 'all', '0.3', '0.4', '0.4.1', '0.5', '0.6', '0.7', '0.8', '0.
8.1', '0.8.2'
Default: '0.7'
When we fix a Theano bug that generated bad results under some circumstances, we also make Theano
raise a warning when it encounters the same circumstances again. This helps to detect if said bug had
affected your past experiments, as you only need to run your experiment again with the new version,
and you do not have to understand the Theano internal that triggered the bug. A better way to detect
this will be implemented. See this ticket.
This flag allows new users not to get warnings about old bugs, that were fixed before their first checkout of Theano. You can set its value to the first version of Theano that you used (probably 0.3 or
higher)
'None' means that all warnings will be displayed. 'all' means all warnings will be ignored.
It is recommended that you put a version, so that you will see future warnings. It is also recommended
you put this into your .theanorc, so this setting will always be used.
This flag’s value cannot be modified during the program execution.
config.base_compiledir
Default: On Windows: $LOCALAPPDATA\Theano if $LOCALAPPDATA is defined, otherwise and
on other systems: ~/.theano.
This directory stores the platform-dependent compilation directories.
This flag’s value cannot be modified during the program execution.
config.compiledir_format
Default: "compiledir_%(platform)s-%(processor)s-%(python_version)s-%(python_bitwid
This is a Python format string that specifies the subdirectory of config.base_compiledir
in which to store platform-dependent compiled modules. To see a list of all available substitution
keys, run python -c "import theano; print(theano.config)", and look for compiledir_format.
This flag’s value cannot be modified during the program execution.
config.compiledir
Default: config.base_compiledir/config.compiledir_format
This directory stores dynamically-compiled modules for a particular platform.
This flag’s value cannot be modified during the program execution.
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config.blas.ldflags
Default: '-lblas'
Link arguments to link against a (Fortran) level-3 blas implementation. The default will test if
'-lblas' works. If not, we will disable our C code for BLAS.
config.experimental.local_alloc_elemwise_assert
Bool value: either True or False
Default: True
When the local_alloc_optimization is applied, add an assert to highlight shape errors.
Without such asserts this optimization could hide errors in the user code. We add the assert only if
we can’t infer that the shapes are equivalent. As such this optimization does not always introduce an
assert in the graph. Removing the assert could speed up execution.
config.cuda.root
Default: $CUDA_ROOT or failing that, "/usr/local/cuda"
A directory with bin/, lib/, include/ folders containing cuda utilities.
config.dnn.enabled
String value: 'auto', 'True', 'False'
Default: 'auto'
If 'auto', automatically detect and use cuDNN if it is available. If cuDNN is unavailable, raise no
error.
If 'True', require the use of cuDNN. If cuDNN is unavailable, raise an error.
If 'False', do not use cuDNN or check if it is available.
config.dnn.conv.workmem
Deprecated, use config.dnn.conv.algo_fwd.
config.dnn.conv.workmem_bwd
Deprecated, use config.dnn.conv.algo_bwd_filter
algo_bwd_data instead.
and
config.dnn.conv.
config.dnn.conv.algo_fwd
String
value:
'small',
'none',
'large',
'fft',
'winograd',
'guess_once',
'guess_on_shape_change',
'time_on_shape_change'.
'fft_tiling',
'time_once',
Default: 'small'
3d
convolution
only
support
'none',
'winograd',
'guess_once',
'guess_on_shape_change', 'time_once', 'time_on_shape_change'.
config.dnn.conv.algo_bwd
Deprecated, use config.dnn.conv.algo_bwd_filter
algo_bwd_data instead.
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config.dnn.conv.
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config.dnn.conv.algo_bwd_filter
String value:
'none', 'deterministic', 'fft', 'small', 'guess_once',
'guess_on_shape_change', 'time_once', 'time_on_shape_change'.
Default: 'none'
3d convolution only supports 'none', 'guess_once', 'guess_on_shape_change',
'time_once', 'time_on_shape_change'.
config.dnn.conv.algo_bwd_data
String
value:
'none',
'deterministic',
'fft',
'winograd',
'guess_once',
'guess_on_shape_change',
'time_on_shape_change'.
'fft_tiling',
'time_once',
Default: 'none'
3d
convolution
only
support
'none',
'winograd',
'guess_once',
'guess_on_shape_change', 'time_once', 'time_on_shape_change'.
config.gcc.cxxflags
Default: ""
Extra parameters to pass to gcc when compiling. Extra include paths, library paths, configuration
options, etc.
config.cxx
Default: Full path to g++ if g++ is present. Empty string otherwise.
Indicates which C++ compiler to use. If empty, no C++ code is compiled. Theano automatically
detects whether g++ is present and disables C++ compilation when it is not. On darwin systems (Mac
OS X), it preferably looks for clang++ and uses that if available.
We print a warning if we detect that no compiler is present. It is recommended to run with C++
compilation as Theano will be much slower otherwise.
This can be any compiler binary (full path or not) but things may break if the interface is not g++compatible to some degree.
config.nvcc.fastmath
Bool value, default: False
If true, this will enable fastmath (--use-fast-math) mode for compiled cuda code which makes
div and sqrt faster at the cost of precision. This also disables support for denormal numbers. This can
cause NaN. So if you have NaN and use this flag, try to disable it.
config.optimizer_excluding
Default: ""
A list of optimizer tags that we don’t want included in the default Mode. If multiple tags, separate them by ‘:’. Ex: to remove the elemwise inplace optimizer(slow for big graph), use the flags:
optimizer_excluding:inplace_opt, where inplace_opt is the name of that optimization.
This flag’s value cannot be modified during the program execution.
config.optimizer_including
Default: ""
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A list of optimizer tags that we want included in the default Mode. If multiple tags, separate them by
‘:’.
This flag’s value cannot be modified during the program execution.
config.optimizer_requiring
Default: ""
A list of optimizer tags that we require for optimizer in the default Mode. If multiple tags, separate
them by ‘:’.
This flag’s value cannot be modified during the program execution.
config.optimizer_verbose
Bool value: either True or False
Default: False
When True, we print on the stdout the optimization applied.
config.nocleanup
Bool value: either True or False
Default: False
If False, source code files are removed when they are not needed anymore. This means files whose
compilation failed are deleted. Set to True to keep those files in order to debug compilation errors.
config.compile
This section contains attributes which influence the compilation of C code for ops. Due to historical
reasons many attributes outside of this section also have an influence over compilation, most notably
‘cxx’. This is not expected to change any time soon.
config.compile.timeout
Positive int value, default: compile.wait * 24
Time to wait before an unrefreshed lock is broken and stolen. This is in place to avoid manual cleanup
of locks in case a process crashed and left a lock in place.
The refresh time is automatically set to half the timeout value.
config.compile.wait
Positive int value, default: 5
Time to wait between attempts at grabbing the lock if the first attempt is not successful. The actual
time will be between compile.wait and compile.wait * 2 to avoid a crowding effect on lock.
config.DebugMode
This section contains various attributes configuring the behaviour of mode DebugMode. See directly
this section for the documentation of more configuration options.
config.DebugMode.check_preallocated_output
Default: ''
A list of kinds of preallocated memory to use as output buffers for each Op’s computations, separated
by :. Implemented modes are:
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•"initial": initial storage present in storage map (for instance, it can happen in the inner
function of Scan),
•"previous": reuse previously-returned memory,
•"c_contiguous": newly-allocated C-contiguous memory,
•"f_contiguous": newly-allocated Fortran-contiguous memory,
•"strided": non-contiguous memory with various stride patterns,
•"wrong_size": memory with bigger or smaller dimensions,
•"ALL": placeholder for all of the above.
In order not to test with preallocated memory, use an empty string, "".
config.DebugMode.check_preallocated_output_ndim
Positive int value, default: 4.
When testing with “strided” preallocated output memory, test all combinations of strides over that
number of (inner-most) dimensions. You may want to reduce that number to reduce memory or time
usage, but it is advised to keep a minimum of 2.
config.DebugMode.warn_input_not_reused
Bool value, default: True
Generate a warning when the destroy_map or view_map tell that an op work inplace, but the op did
not reuse the input for its output.
config.NanGuardMode.nan_is_error
Bool value, default: True
Controls whether NanGuardMode generates an error when it sees a nan.
config.NanGuardMode.inf_is_error
Bool value, default: True
Controls whether NanGuardMode generates an error when it sees an inf.
config.NanGuardMode.nan_is_error
Bool value, default: True
Controls whether NanGuardMode generates an error when it sees a big value (>1e10).
config.numpy
This section contains different attributes for configuring NumPy’s behaviour, described by
numpy.seterr.
config.numpy.seterr_all
String Value: 'ignore', 'warn', 'raise', 'call', 'print', 'log', 'None'
Default: 'ignore'
Set the default behaviour described by numpy.seterr.
'None' means that numpy’s default behaviour will not be changed (unless one of the other config.
numpy.seterr_* overrides it), but this behaviour can change between numpy releases.
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This flag sets the default behaviour for all kinds of floating-pont errors, and it can be overriden for
specific errors by setting one (or more) of the flags below.
This flag’s value cannot be modified during the program execution.
config.numpy.seterr_divide
String Value: 'None', 'ignore', 'warn', 'raise', 'call', 'print', 'log'
Default: 'None'
Sets numpy’s behavior for division by zero. 'None' means using the default, defined by config.numpy.seterr_all.
This flag’s value cannot be modified during the program execution.
config.numpy.seterr_over
String Value: 'None', 'ignore', 'warn', 'raise', 'call', 'print', 'log'
Default: 'None'
Sets numpy’s behavior for floating-point overflow. 'None' means using the default, defined by
config.numpy.seterr_all.
This flag’s value cannot be modified during the program execution.
config.numpy.seterr_under
String Value: 'None', 'ignore', 'warn', 'raise', 'call', 'print', 'log'
Default: 'None'
Sets numpy’s behavior for floating-point underflow. 'None' means using the default, defined by
config.numpy.seterr_all.
This flag’s value cannot be modified during the program execution.
config.numpy.seterr_invalid
String Value: 'None', 'ignore', 'warn', 'raise', 'call', 'print', 'log'
Default: 'None'
Sets numpy’s behavior for invalid floating-point operation. 'None' means using the default, defined
by config.numpy.seterr_all.
This flag’s value cannot be modified during the program execution.
config.compute_test_value
String Value: 'off', 'ignore', 'warn', 'raise'.
Default: 'off'
Setting this attribute to something other than 'off' activates a debugging mechanism, where Theano
executes the graph on-the-fly, as it is being built. This allows the user to spot errors early on (such as
dimension mis-match), before optimizations are applied.
Theano will execute the graph using the Constants and/or shared variables provided by the user.
Purely symbolic variables (e.g. x = T.dmatrix()) can be augmented with test values, by writing to their 'tag.test_value' attribute (e.g. x.tag.test_value = numpy.random.
rand(5, 4)).
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When not 'off', the value of this option dictates what happens when an Op’s inputs do not provide
appropriate test values:
•'ignore' will silently skip the debug mechanism for this Op
•'warn' will raise a UserWarning and skip the debug mechanism for this Op
•'raise' will raise an Exception
config.compute_test_value_opt
As compute_test_value, but it is the value used during Theano optimization phase. Theano
user’s do not need to use this. This is to help debug shape error in Theano optimization.
config.print_test_value
Bool value, default: False
If 'True', Theano will override the __str__ method of its variables to also print the tag.test_value
when this is available.
config.reoptimize_unpickled_function
Bool value, default: False (changed in master after Theano 0.7 release)
Theano users can use the standard python pickle tools to save a compiled theano function. When
pickling, both graph before and after the optimization are saved, including shared variables. When set
to True, the graph is reoptimized when being unpickled. Otherwise, skip the graph optimization and
use directly the optimized graph.
config.exception_verbosity
String Value: 'low', 'high'.
Default: 'low'
If 'low', the text of exceptions will generally refer to apply nodes with short names such as
'Elemwise{add_no_inplace}'. If 'high', some exceptions will also refer to apply nodes
with long descriptions like:
A. Elemwise{add_no_inplace}
B. log_likelihood_v_given_h
C. log_likelihood_h
config.cmodule.warn_no_version
Bool value, default: False
If True, will print a warning when compiling one or more Op with C code that can’t be cached because
there is no c_code_cache_version() function associated to at least one of those Ops.
config.cmodule.mac_framework_link
Bool value, default: False
If set to True, breaks certain MacOS installations with the infamous Bus Error.
config.cmodule.remove_gxx_opt
Bool value, default: False
If True, will remove the -O* parameter passed to g++. This is useful to debug in gdb modules
compiled by Theano. The parameter -g is passed by default to g++.
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config.cmodule.compilation_warning
Bool value, default: False
If True, will print compilation warnings.
config.cmodule.preload_cache
Bool value, default: False
If set to True, will preload the C module cache at import time
config.traceback.limit
Int value, default: 8
The number of user stack level to keep for variables.
d3viz – d3viz: Interactive visualization of Theano compute graphs
Guide
Requirements
d3viz requires the pydot package. pydot-ng fork is better maintained, and it works both in Python 2.x and
3.x. Install it with pip:
pip install pydot-ng
Like Theano’s printing module, d3viz requires graphviz binary to be available.
Overview
d3viz extends Theano’s printing module to interactively visualize compute graphs. Instead of creating a
static picture, it creates an HTML file, which can be opened with current web-browsers. d3viz allows
• to zoom to different regions and to move graphs via drag and drop,
• to position nodes both manually and automatically,
• to retrieve additional information about nodes and edges such as their data type or definition in the
source code,
• to edit node labels,
• to visualizing profiling information, and
• to explore nested graphs such as OpFromGraph nodes.
Note: This userguide is also avaible as IPython notebook.
As an example, consider the following multilayer perceptron with one hidden layer and a softmax output
layer.
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import theano as th
import theano.tensor as T
import numpy as np
ninputs = 1000
nfeatures = 100
noutputs = 10
nhiddens = 50
rng = np.random.RandomState(0)
x = T.dmatrix('x')
wh = th.shared(rng.normal(0, 1, (nfeatures, nhiddens)), borrow=True)
bh = th.shared(np.zeros(nhiddens), borrow=True)
h = T.nnet.sigmoid(T.dot(x, wh) + bh)
wy = th.shared(rng.normal(0, 1, (nhiddens, noutputs)))
by = th.shared(np.zeros(noutputs), borrow=True)
y = T.nnet.softmax(T.dot(h, wy) + by)
predict = th.function([x], y)
The function predict outputs the probability of 10 classes.
printing.pydotprint() as follows:
You can visualize it with theano.
from theano.printing import pydotprint
import os
if not os.path.exists('examples'):
os.makedirs('examples')
pydotprint(predict, 'examples/mlp.png')
The output file is available at examples/mlp.png
from IPython.display import Image
Image('./examples/mlp.png', width='80%')
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To visualize it interactively, import theano.d3viz.d3viz.d3viz() from the the theano.d3viz.
d3viz module, which can be called as before:
import theano.d3viz as d3v
d3v.d3viz(predict, 'examples/mlp.html')
Open visualization!
When you open the output file mlp.html in your web-browser, you will see an interactive visualization
of the compute graph. You can move the whole graph or single nodes via drag and drop, and zoom via the
mouse wheel. When you move the mouse cursor over a node, a window will pop up that displays detailed
information about the node, such as its data type or definition in the source code. When you left-click on a
node and select Edit, you can change the predefined node label. If you are dealing with a complex graph
with many nodes, the default node layout may not be perfect. In this case, you can press the Release
node button in the top-left corner to automatically arrange nodes. To reset nodes to their default position,
press the Reset nodes button.
You can also display the interactive graph inline in IPython using IPython.display.IFrame:
from IPython.display import IFrame
d3v.d3viz(predict, 'examples/mlp.html')
IFrame('examples/mlp.html', width=700, height=500)
Currently if you use display.IFrame you still have to create a file, and this file can’t be outside notebooks
root (e.g. usually it can’t be in /tmp/).
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Profiling
Theano allows function profiling via the profile=True flag. After at least one function call, the compute
time of each node can be printed in text form with debugprint. However, analyzing complex graphs in
this way can be cumbersome.
d3viz can visualize the same timing information graphically, and hence help to spot bottlenecks in the
compute graph more easily! To begin with, we will redefine the predict function, this time by using
profile=True flag. Afterwards, we capture the runtime on random data:
predict_profiled = th.function([x], y, profile=True)
x_val = rng.normal(0, 1, (ninputs, nfeatures))
y_val = predict_profiled(x_val)
d3v.d3viz(predict_profiled, 'examples/mlp2.html')
Open visualization!
When you open the HTML file in your browser, you will find an additional Toggle profile colors
button in the menu bar. By clicking on it, nodes will be colored by their compute time, where red corresponds
to a high compute time. You can read out the exact timing information of a node by moving the cursor over
it.
Different output formats
Internally, d3viz represents a compute graph in the Graphviz DOT language, using the pydot package, and
defines a front-end based on the d3.js library to visualize it. However, any other Graphviz front-end can be
used, which allows to export graphs to different formats.
formatter = d3v.formatting.PyDotFormatter()
pydot_graph = formatter(predict_profiled)
pydot_graph.write_png('examples/mlp2.png');
pydot_graph.write_png('examples/mlp2.pdf');
Image('./examples/mlp2.png')
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Here, we used the theano.d3viz.formatting.PyDotFormatter class to convert the compute
graph into a pydot graph, and created a PNG and PDF file. You can find all output formats supported by
Graphviz here.
OpFromGraph nodes
An OpFromGraph node defines a new operation, which can be called with different inputs at different
places in the compute graph. Each OpFromGraph node defines a nested graph, which will be visualized
accordingly by d3viz.
x, y, z = T.scalars('xyz')
e = T.nnet.sigmoid((x + y + z)**2)
op = th.OpFromGraph([x, y, z], [e])
e2 = op(x, y, z) + op(z, y, x)
f = th.function([x, y, z], e2)
d3v.d3viz(f, 'examples/ofg.html')
Open visualization!
In this example, an operation with three inputs is defined, which is used to build a function that calls this
operations twice, each time with different input arguments.
In the d3viz visualization, you will find two OpFromGraph nodes, which correspond to the two OpFromGraph calls. When you double click on one of them, the nested graph appears with the correct mapping
of its input arguments. You can move it around by drag and drop in the shaded area, and close it again by
double-click.
An OpFromGraph operation can be composed of further OpFromGraph operations, which will be visualized
as nested graphs as you can see in the following example.
x, y, z = T.scalars('xyz')
e = x * y
op = th.OpFromGraph([x, y], [e])
e2 = op(x, y) + z
op2 = th.OpFromGraph([x, y, z], [e2])
e3 = op2(x, y, z) + z
f = th.function([x, y, z], [e3])
d3v.d3viz(f, 'examples/ofg2.html')
Open visualization!
Feedback
If you have any problems or great ideas on how to improve d3viz, please let me know!
• Christof Angermueller
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• [email protected]
• https://cangermueller.com
References
d3viz module
Dynamic visualization of Theano graphs.
Author: Christof Angermueller <[email protected]>
theano.d3viz.d3viz.d3viz(fct, outfile, copy_deps=True, *args, **kwargs)
Create HTML file with dynamic visualizing of a Theano function graph.
In the HTML file, the whole graph or single nodes can be moved by drag and drop. Zooming is
possible via the mouse wheel. Detailed information about nodes and edges are displayed via mouseover events. Node labels can be edited by selecting Edit from the context menu.
Input nodes are colored in green, output nodes in blue. Apply nodes are ellipses, and colored depending on the type of operation they perform. Red ellipses are transfers from/to the GPU (ops with names
GpuFromHost, HostFromGpu).
Edges are black by default. If a node returns a view of an input, the input edge will be blue. If it
returns a destroyed input, the edge will be red.
Parameters
• fct (theano.compile.function_module.Function) – A compiled
Theano function, variable, apply or a list of variables.
• outfile (str) – Path to output HTML file.
• copy_deps (bool, optional) – Copy javascript and CSS dependencies to
output directory.
Notes
This function accepts extra parameters which will be forwarded to theano.d3viz.
formatting.PyDotFormatter.
theano.d3viz.d3viz.d3write(fct, path, *args, **kwargs)
Convert Theano graph to pydot graph and write to dot file.
Parameters
• fct (theano.compile.function_module.Function) – A compiled
Theano function, variable, apply or a list of variables.
• path (str) – Path to output file
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Notes
This function accepts extra parameters which will be forwarded to theano.d3viz.
formatting.PyDotFormatter.
theano.d3viz.d3viz.escape_quotes(s)
Escape quotes in string.
Parameters s (str) – String on which function is applied
theano.d3viz.d3viz.replace_patterns(x, replace)
Replace replace in string x.
Parameters
• s (str) – String on which function is applied
• replace (dict) – key, value pairs where key is a regular expression and value
a string by which key is replaced
PyDotFormatter
class theano.d3viz.formatting.PyDotFormatter(compact=True)
Create pydot graph object from Theano function.
Parameters compact (bool) – if True, will remove intermediate variables without
name.
node_colors
dict – Color table of node types.
apply_colors
dict – Color table of apply nodes.
shapes
dict – Shape table of node types.
__call__(fct, graph=None)
Create pydot graph from function.
Parameters
• fct (theano.compile.function_module.Function) – A compiled
Theano function, variable, apply or a list of variables.
• graph (pydot.Dot) – pydot graph to which nodes are added. Creates new
one if undefined.
Returns Pydot graph of fct
Return type pydot.Dot
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gof – Theano Internals [doc TODO]
graph – Interface for the Theano graph
Reference
Node classes (Apply, Variable) and expression graph algorithms.
class theano.gof.graph.Apply(op, inputs, outputs)
An Apply instance is a node in an expression graph which represents the application of an Op to some
input Variable nodes, producing some output Variable nodes.
This class is typically instantiated by an Op’s make_node() function, which is typically called by that
Op’s __call__() function.
An Apply instance serves as a simple structure with three important attributes:
•inputs : a list of Variable nodes that represent the arguments of the expression,
•outputs : a list of Variable nodes that represent the variable of the expression, and
•op : an Op instance that determines the nature of the expression being applied.
The driver compile.function uses Apply’s inputs attribute together with Variable’s owner attribute
to search the expression graph and determine which inputs are necessary to compute the function’s
outputs.
A Linker uses the Apply instance’s op field to compute the variables.
Comparing with the Python language, an Apply instance is theano’s version of a function call (or
expression instance) whereas Op is theano’s version of a function definition.
Parameters
• op (Op instance) –
• inputs (list of Variable instances) –
• outputs (list of Variable instances) –
Notes
The owner field of each output in the outputs list will be set to self.
If an output element has an owner that is neither None nor self, then a ValueError exception will be
raised.
clone()
Duplicate this Apply instance with inputs = self.inputs.
Returns A new Apply instance (or subclass instance) with new outputs.
Return type object
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Notes
Tags are copied from self to the returned instance.
clone_with_new_inputs(inputs, strict=True)
Duplicate this Apply instance in a new graph.
Parameters
• inputs – List of Variable instances to use as inputs.
• strict (bool) – If True, the type fields of all the inputs must be equal to the
current ones (or compatible, for instance Tensor / CudaNdarray of the same
dtype and broadcastable patterns, in which case they will be converted into
current Type), and returned outputs are guaranteed to have the same types as
self.outputs. If False, then there’s no guarantee that the clone’s outputs will
have the same types as self.outputs, and cloning may not even be possible (it
depends on the Op).
Returns An Apply instance with the same op but different outputs.
Return type object
default_output()
Returns the default output for this node.
Returns An element of self.outputs, typically self.outputs[0].
Return type Variable instance
Notes
May raise AttributeError self.op.default_output is out of range, or if there are multiple outputs
and self.op.default_output does not exist.
nin
Property – Number of inputs.
nout
Property – Number of outputs.
out
Alias for self.default_output().
params_type
type to use for the params
run_params()
Returns the params for the node, or NoParams if no params is set.
class theano.gof.graph.Constant(type, data, name=None)
A Constant is a Variable with a value field that cannot be changed at runtime.
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Constant nodes make eligible numerous optimizations: constant inlining in C code, constant folding,
etc.
Notes
The data field is filtered by what is provided in the constructor for the Constant’s type field.
WRITEME
clone()
We clone this object, but we don’t clone the data to lower memory requirement. We suppose
that the data will never change.
value
read-only data access method
class theano.gof.graph.Node
A Node in a theano graph.
Graphs contain two kinds of Nodes – Variable and Apply. Edges in the graph are not explicitly
represented. Instead each Node keeps track of its parents via Variable.owner / Apply.inputs and its
children via Variable.clients / Apply.outputs.
get_parents()
Return a list of the parents of this node. Should return a copy–i.e., modifying the return value
should not modify the graph structure.
class theano.gof.graph.Variable(type, owner=None, index=None, name=None)
A Variable is a node in an expression graph that represents a variable.
The inputs and outputs of every Apply (theano.gof.Apply) are Variable instances. The input and output
arguments to create a function are also Variable instances. A Variable is like a strongly-typed variable
in some other languages; each Variable contains a reference to a Type instance that defines the kind of
value the Variable can take in a computation.
A Variable is a container for four important attributes:
•type a Type instance defining the kind of value this Variable can have,
•owner either None (for graph roots) or the Apply instance of which self is an output,
•index the integer such that owner.outputs[index] is this_variable (ignored if
owner is None),
•name a string to use in pretty-printing and debugging.
There are a few kinds of Variables to be aware of: A Variable which is the output of a symbolic
computation has a reference to the Apply instance to which it belongs (property: owner) and the
position of itself in the owner’s output list (property: index).
•Variable (this base type) is typically the output of a symbolic computation.
•Constant (a subclass) which adds a default and un-replaceable value, and requires that owner
is None.
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•TensorVariable subclass of Variable that represents a numpy.ndarray object.
•TensorSharedVariable Shared version of TensorVariable.
•SparseVariable subclass of Variable that represents a scipy.sparse.{csc,csr}_matrix object.
•CudaNdarrayVariable subclass of Variable that represents our object on the GPU that is a subset
of numpy.ndarray.
•RandomVariable.
A Variable which is the output of a symbolic computation will have an owner not equal to None.
Using the Variables’ owner field and the Apply nodes’ inputs fields, one can navigate a graph from
an output all the way to the inputs. The opposite direction is not possible until a FunctionGraph has
annotated the Variables with the clients field, ie, before the compilation process has begun a Variable
does not know which Apply nodes take it as input.
Parameters
• type (a Type instance) – The type governs the kind of data that can be
associated with this variable.
• owner (None or Apply instance) – The Apply instance which computes
the value for this variable.
• index (None or int) – The position of this Variable in owner.outputs.
• name (None or str) – A string for pretty-printing and debugging.
Examples
import theano
from theano import tensor
a = tensor.constant(1.5)
b = tensor.fscalar()
˓→scalar
# declare a symbolic constant
# declare a symbolic floating-point
c = a + b
# create a simple expression
f = theano.function([b], [c])
˓→associated with it already
# this works because a has a value
assert 4.0 == f(2.5)
˓→evaluate an internal c
# bind 2.5 to an internal copy of b and
theano.function([a], [c])
˓→by c) is undefined
# compilation error because b (required
theano.function([a,b], [c])
# compilation error because a is
˓→constant, it can't be an input
d = tensor.value(1.5)
˓→'a'
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e = d + b
theano.function([d,b], [e])
˓→is ignored.
# this works.
d's default value of 1.5
The python variables a,b,c all refer to instances of type Variable. The Variable refered to by a is
also an instance of Constant.
compile.function uses each Apply instance’s inputs attribute together with each Variable’s owner field
to determine which inputs are necessary to compute the function’s outputs.
clone()
Return a new Variable like self.
Returns A new Variable instance (or subclass instance) with no owner or index.
Return type Variable instance
Notes
Tags are copied to the returned instance.
Name is copied to the returned instance.
eval(inputs_to_values=None)
Evaluates this variable.
Parameters inputs_to_values – A dictionary mapping theano Variables to values.
Examples
>>> import numpy
>>> import theano.tensor as T
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
>>> z = x + y
>>> numpy.allclose(z.eval({x : 16.3, y : 12.1}), 28.4)
True
We passed eval() a dictionary mapping symbolic theano variables to the values to substitute
for them, and it returned the numerical value of the expression.
Notes
eval will be slow the first time you call it on a variable – it needs to call function() to
compile the expression behind the scenes. Subsequent calls to eval() on that same variable
will be fast, because the variable caches the compiled function.
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This way of computing has more overhead than a normal Theano function, so don’t use it too
much in real scripts.
theano.gof.graph.ancestors(variable_list, blockers=None)
Return the variables that contribute to those in variable_list (inclusive).
Parameters variable_list (list of Variable instances) – Output Variable instances
from which to search backward through owners.
Returns All input nodes, in the order found by a left-recursive depth-first search started at
the nodes in variable_list.
Return type list of Variable instances
theano.gof.graph.as_string(i,
o,
leaf_formatter=<type
‘str’>,
node_formatter=<function default_node_formatter>)
WRITEME
Parameters
• i (list) – Input Variable s.
• o (list) – Output Variable s.
• leaf_formatter (theano.function) – Takes a Variable and returns a
string to describe it.
• node_formatter (callable) – Takes an Op and the list of strings corresponding to its arguments and returns a string to describe it.
Returns Returns a string representation of the subgraph between i and o. If the same
op is used by several other ops, the first occurrence will be marked as *n ->
description and all subsequent occurrences will be marked as *n, where n is
an id number (ids are attributed in an unspecified order and only exist for viewing
convenience).
Return type str
theano.gof.graph.clone(i, o, copy_inputs=True)
Copies the subgraph contained between i and o.
Parameters
• i (list) – Input L{Variable}s.
• o (list) – Output L{Variable}s.
• copy_inputs (bool) – If True, the inputs will be copied (defaults to True).
Returns The inputs and outputs of that copy.
Return type object
theano.gof.graph.clone_get_equiv(inputs, outputs, copy_inputs_and_orphans=True,
memo=None)
Return a dictionary that maps from Variable and Apply nodes in the original graph to a new node (a
clone) in a new graph.
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This function works by recursively cloning inputs... rebuilding a directed graph from the bottom
(inputs) up to eventually building new outputs.
Parameters
• inputs (a list of Variables) –
• outputs (a list of Variables) –
• copy_inputs_and_orphans (bool) – True means to create the cloned
graph from new input and constant nodes (the bottom of a feed-upward graph).
False means to clone a graph that is rooted at the original input nodes.
• memo (None or dict) – Optionally start with a partly-filled dictionary for the
return value. If a dictionary is passed, this function will work in-place on that
dictionary and return it.
theano.gof.graph.general_toposort(r_out,
deps,
debug_print=False,
compute_deps_cache=None,
deps_cache=None,
clients=None)
WRITEME
Parameters
• deps – A python function that takes a node as input and returns its dependence.
• compute_deps_cache (optional) – If provided deps_cache should also
be provided. This is a function like deps, but that also cache its results in a dict
passed as deps_cache.
• deps_cache (dict) – Must be used with compute_deps_cache.
• clients (dict) – If a dict is passed it will be filled with a mapping of node ->
clients for each node in the subgraph.
Notes
deps(i) should behave like a pure function (no funny business with internal state).
deps(i) will be cached by this function (to be fast).
The order of the return value list is determined by the order of nodes returned by the deps() function.
deps should be provided or can be None and the caller provides compute_deps_cache and deps_cache.
The second option removes a Python function call, and allows for more specialized code, so it can be
faster.
theano.gof.graph.inputs(variable_list, blockers=None)
Return the inputs required to compute the given Variables.
Parameters variable_list (list of Variable instances) – Output Variable instances
from which to search backward through owners.
Returns Input nodes with no owner, in the order found by a left-recursive depth-first
search started at the nodes in variable_list.
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Return type list of Variable instances
theano.gof.graph.io_connection_pattern(inputs, outputs)
Returns the connection pattern of a subgraph defined by given inputs and outputs.
theano.gof.graph.io_toposort(inputs, outputs, orderings=None, clients=None)
WRITEME
Parameters
• inputs (list or tuple of Variable instances) –
• outputs (list or tuple of Apply instances) –
• orderings (dict) – Key: Apply instance. Value: list of Apply instance. It
is important that the value be a container with a deterministic iteration order. No
sets allowed!
• clients (dict) – If a dict is provided it will be filled with mappings of node>clients for each node in the subgraph that is sorted
theano.gof.graph.is_same_graph(var1, var2, givens=None, debug=False)
Return True iff Variables var1 and var2 perform the same computation.
By ‘performing the same computation’, we mean that they must share the same graph, so that for
instance this function will return False when comparing (x * (y * z)) with ((x * y) * z).
The current implementation is not efficient since, when possible, it verifies equality by calling two
different functions that are expected to return the same output. The goal is to verify this assumption,
to eventually get rid of one of them in the future.
Parameters
• var1 – The first Variable to compare.
• var2 – The second Variable to compare.
• givens – Similar to the givens argument of theano.function, it can be used to
perform substitutions in the computational graph of var1 and var2. This argument
is associated to neither var1 nor var2: substitutions may affect both graphs if the
substituted variable is present in both.
• debug (bool) – If True, then an exception is raised when we are in a situation
where the equal_computations implementation cannot be called. This parameter
is intended to be used in tests only, to make sure we properly test both implementations.
Examples
var1
x+1
x+1
x+1
312
var2
x+1
y+1
y+1
givens
{}
{}
{x: y}
output
True
False
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theano.gof.graph.list_of_nodes(inputs, outputs)
Return the apply nodes of the graph between inputs and outputs.
theano.gof.graph.op_as_string(i,
op,
leaf_formatter=<type
‘str’>,
node_formatter=<function default_node_formatter>)
WRITEME
theano.gof.graph.ops(i, o)
WRITEME
Parameters
• i (list) – Input L{Variable}s.
• o (list) – Output L{Variable}s.
Returns The set of ops that are contained within the subgraph that lies between i and o,
including the owners of the L{Variable}s in o and intermediary ops between i and o,
but not the owners of the L{Variable}s in i.
Return type object
theano.gof.graph.orphans(i, o)
WRITEME
Parameters
• i (list) – Input L{Variable}s.
• o (list) – Output L{Variable}s.
Returns The set of Variables which one or more Variables in o depend on but are neither
in i nor in the subgraph that lies between i and o.
Return type object
Examples
orphans([x], [(x+y).out]) => [y]
theano.gof.graph.stack_search(start, expand, mode=’bfs’, build_inv=False)
Search through a graph, either breadth- or depth-first.
Parameters
• start (deque) – Search from these nodes.
• expand (callable) – When we get to a node, add expand(node) to the list of
nodes to visit. This function should return a list, or None.
Returns The list of nodes in order of traversal.
Return type list of Variable or Apply instances (depends on expend)
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Notes
A node will appear at most once in the return value, even if it appears multiple times in the start
parameter.
Postcondition every element of start is transferred to the returned list.
Postcondition start is empty.
theano.gof.graph.variables(i, o)
WRITEME
Parameters
• i (list) – Input L{Variable}s.
• o (list) – Output L{Variable}s.
Returns The set of Variables that are involved in the subgraph that lies between i and o.
This includes i, o, orphans(i, o) and all values of all intermediary steps from i to o.
Return type object
theano.gof.graph.variables_and_orphans(i, o)
WRITEME
theano.gof.graph.view_roots(r)
Utility function that returns the leaves of a search through consecutive view_map()s.
WRITEME
fg – Graph Container [doc TODO]
FunctionGraph
class theano.gof.FunctionGraph(inputs, outputs, features=None, clone=True, update_mapping=None)
WRITEME A FunctionGraph represents a subgraph bound by a set of input variables and a set of
output variables, ie a subgraph that specifies a theano function. The inputs list should contain all the
inputs on which the outputs depend. Variables of type Constant are not counted as inputs.
The FunctionGraph supports the replace operation which allows to replace a variable in the subgraph
by another, e.g. replace (x + x).out by (2 * x).out. This is the basis for optimization in theano.
This class is also reponsible for verifying that a graph is valid (ie, all the dtypes and broadcast patterns
are compatible with the way the the Variables are used) and for annotating the Variables with a .clients
field that specifies which Apply nodes use the variable. The .clients field combined with the .owner
field and the Apply nodes’ .inputs field allows the graph to be traversed in both directions.
It can also be extended with new features using FunctionGraph.attach_feature(<toolbox.Feature instance>). See toolbox.Feature for event types and documentation. Extra features allow the FunctionGraph to verify new properties of a graph as it is optimized. # TODO: are there other things features
can do to the fgraph?
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Historically, the FunctionGraph was called an Env. Keep this in mind while reading out-of-date
documentation, e-mail support threads, etc.
The constructor creates a FunctionGraph which operates on the subgraph bound by the inputs and
outputs sets.
This class keeps a pointer to the inputs and outputs, and also modifies them.
#TODO: document what variables are[not] set in the FunctionGraph when a feature is added via the
constructor. How constructed is the FunctionGraph?
Parameters
• inputs – Inputs nodes of the graph, usually declared by the user.
• outputs – Outputs nodes of the graph.
• clone – If true, we will clone the graph. This is useful to remove the constant
cache problem.
Notes
The intermediate nodes between ‘inputs’ and ‘outputs’ are not explicitely passed.
*TODO*
Note: FunctionGraph(inputs, outputs) clones the inputs by default. To avoid this behavior, add the
parameter clone=False. This is needed as we do not want cached constants in fgraph.
attach_feature(feature)
Adds a gof.toolbox.Feature to this function_graph and triggers its on_attach callback.
change_input(node, i, new_r, reason=None)
Changes node.inputs[i] to new_r.
WRITEME
new_r.type == old_r.type must be True, where old_r is the current value of node.inputs[i] which
we want to replace.
For each feature that has a ‘on_change_input’ method,
ture.on_change_input(function_graph, node, i, old_r, new_r, reason)
calls:
fea-
check_integrity()
WRITEME
Call this for a diagnosis if things go awry.
clients(r)
Set of all the (node, i) pairs such that node.inputs[i] is r. Told differently, a list of (node,i) such
that each node have r as input at index i.
clone(check_integrity=True)
WRITEME
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clone_get_equiv(check_integrity=True, attach_feature=True)
Clone the graph and get a dict that maps old nodes to new ones
Parameters:
check_integrity: bool Whether to check integrity. Default is True.
attach_feature: bool Whether to attach feature of origin graph to cloned graph. Default is
True.
Returns:
e: FunctionGraph Cloned fgraph. Every node in cloned graph is cloned.
equiv: dict A dict that map old node to new node.
collect_callbacks(name, *args)
Collects callbacks
Returns a dictionary d such that d[feature] == getattr(feature, name)(*args) For each feature
which has a method called after name.
disown()
Cleans up all of this FunctionGraph’s nodes and variables so they are not associated with this
FunctionGraph anymore.
The FunctionGraph should not be used anymore after disown is called.
execute_callbacks(name, *args, **kwargs)
Execute callbacks
Calls getattr(feature, name)(*args) for each feature which has a method called after name.
orderings()
Return dict d s.t. d[node] is a list of nodes that must be evaluated before node itself can be
evaluated.
This is used primarily by the destroy_handler feature to ensure that all clients of any destroyed
inputs have already computed their outputs.
Notes
This only calls the orderings() fct on all features. It does not take care of computing dependencies by itself.
remove_feature(feature)
WRITEME
Removes the feature from the graph.
Calls feature.on_detach(function_graph) if an on_detach method is defined.
replace(r, new_r, reason=None, verbose=None)
WRITEME
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This is the main interface to manipulate the subgraph in FunctionGraph. For every node that
uses r as input, makes it use new_r instead.
replace_all(pairs, reason=None)
WRITEME
toposort()
Toposort
Return an ordering of the graph’s Apply nodes such that
•All the nodes of the inputs of a node are before that node.
•Satisfies the orderings provided by each feature that has an ‘orderings’ method.
If a feature has an ‘orderings’ method, it will be called with this FunctionGraph as sole argument.
It should return a dictionary of {node: predecessors} where predecessors is a list of nodes that
should be computed before the key node.
FunctionGraph Features
class theano.gof.toolbox.Feature
Base class for FunctionGraph extensions.
A Feature is an object with several callbacks that are triggered by various operations on FunctionGraphs. It can be used to enforce graph properties at all stages of graph optimization.
See also:
theano.gof.toolbox for common extensions.
on_attach(function_graph)
Called by FunctionGraph.attach_feature, the method that attaches the feature to the FunctionGraph. Since this is called after the FunctionGraph is initially populated, this is where you
should run checks on the initial contents of the FunctionGraph.
The on_attach method may raise the AlreadyThere exception to cancel the attach operation if it
detects that another Feature instance implementing the same functionality is already atttached to
the FunctionGraph.
The feature has great freedom in what it can do with the function_graph: it may, for example,
add methods to it dynamically.
on_change_input(function_graph, node, i, r, new_r, reason=None)
Called whenever node.inputs[i] is changed from r to new_r. At the moment the callback is done,
the change has already taken place.
If you raise an exception in this function, the state of the graph might be broken for all intents
and purposes.
on_detach(function_graph)
Called by remove_feature(feature). Should remove any dynamically-added functionality that it
installed into the function_graph.
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on_import(function_graph, node, reason)
Called whenever a node is imported into function_graph, which is just before the node is actually
connected to the graph. Note: on_import is not called when the graph is created. If you want
to detect the first nodes to be implemented to the graph, you should do this by implementing
on_attach.
on_prune(function_graph, node, reason)
Called whenever a node is pruned (removed) from the function_graph, after it is disconnected
from the graph.
orderings(function_graph)
Called by toposort. It should return a dictionary of {node: predecessors} where predecessors is
a list of nodes that should be computed before the key node.
If you raise an exception in this function, the state of the graph might be broken for all intents
and purposes.
FunctionGraph Feature List
• ReplaceValidate
• DestroyHandler
toolbox – [doc TODO]
Guide
class theano.gof.toolbox.Bookkeeper(object)
class theano.gof.toolbox.History(object)
revert(fgraph, checkpoint)
Reverts the graph to whatever it was at the provided
checkpoint (undoes all replacements). A checkpoint at any
given time can be obtained using self.checkpoint().
class theano.gof.toolbox.Validator(object)
class theano.gof.toolbox.ReplaceValidate(History, Validator)
replace_validate(fgraph, var, new_var, reason=None)
class theano.gof.toolbox.NodeFinder(Bookkeeper)
class theano.gof.toolbox.PrintListener(object)
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type – Interface for types of variables
Reference
WRITEME
Defines the Type class.
class theano.gof.type.CDataType(ctype, freefunc=None)
Represents opaque C data to be passed around. The intent is to ease passing arbitrary data between
ops C code.
The constructor builds a type made to represent a C pointer in theano.
Parameters
• ctype – The type of the pointer (complete with the *).
• freefunc – A function to call to free the pointer. This function must have a
void return and take a single pointer argument.
class theano.gof.type.CLinkerType
Interface specification for Types that can be arguments to a CLinkerOp.
A CLinkerType instance is mainly reponsible for providing the C code that interfaces python objects
with a C CLinkerOp implementation.
See WRITEME for a general overview of code generation by CLinker.
c_cleanup(name, sub)
Return C code to clean up after c_extract.
This returns C code that should deallocate whatever c_extract allocated or decrease the reference
counts. Do not decrease py_%(name)s’s reference count.
WRITEME
Parameters
• name (WRITEME) – WRITEME
• sub (WRITEME) – WRITEME
Raises MethodNotDefined – Subclass does not implement this method.
c_code_cache_version()
Return a tuple of integers indicating the version of this Type.
An empty tuple indicates an ‘unversioned’ Type that will not be cached between processes.
The cache mechanism may erase cached modules that have been superceded by newer versions.
See ModuleCache for details.
c_declare(name, sub, check_input=True)
Required: Return c code to declare variables that will be instantiated by c_extract.
Parameters
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• name (str) – The name of the PyObject * pointer that will the value for
this Type
• sub (dict string -> string) – a dictionary of special codes. Most
importantly sub[’fail’]. See CLinker for more info on sub and fail.
Notes
It is important to include the name inside of variables which are declared here, so that name
collisions do not occur in the source file that is generated.
The variable called name is not necessarily defined yet where this code is inserted. This code
might be inserted to create class variables for example, whereas the variable name might only
exist inside certain functions in that class.
TODO: Why should variable declaration fail? Is it even allowed to?
Raises MethodNotDefined – Subclass does not implement this method.
Examples
c_extract(name, sub, check_input=True)
Required: Return c code to extract a PyObject * instance.
The code returned from this function must be templated using %(name)s, representing the
name that the caller wants to call this Variable. The Python object self.data is in a variable
called “py_%(name)s” and this code must set the variables declared by c_declare to something
representative of py_%(name)s. If the data is improper, set an appropriate exception and insert
“%(fail)s”.
TODO: Point out that template filling (via sub) is now performed by this function. –jpt
Parameters
• name (str) – The name of the PyObject * pointer that will store the value
for this Type.
• sub (dict string -> string) – A dictionary of special codes. Most
importantly sub[’fail’]. See CLinker for more info on sub and fail.
Raises MethodNotDefined – Subclass does not implement this method.
Examples
c_extract_out(name, sub, check_input=True)
Optional: C code to extract a PyObject * instance.
Unlike c_extract, c_extract_out has to accept Py_None, meaning that the variable should be left
uninitialized.
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c_init(name, sub)
Required: Return c code to initialize the variables that were declared by self.c_declare().
Notes
The variable called name is not necessarily defined yet where this code is inserted. This code
might be inserted in a class constructor for example, whereas the variable name might only exist
inside certain functions in that class.
TODO: Why should variable initialization fail? Is it even allowed to?
Examples
c_is_simple()
Optional: Return True for small or builtin C types.
A hint to tell the compiler that this type is a builtin C type or a small struct and that its memory
footprint is negligible. Simple objects may be passed on the stack.
c_literal(data)
Optional: WRITEME
Parameters data (WRITEME) – WRITEME
Raises MethodNotDefined – Subclass does not implement this method.
c_sync(name, sub)
Required: Return C code to pack C types back into a PyObject.
The code returned from this function must be templated using “%(name)s”, representing the
name that the caller wants to call this Variable. The returned code may set “py_%(name)s” to a
PyObject* and that PyObject* will be accessible from Python via variable.data. Do not forget
to adjust reference counts if “py_%(name)s” is changed from its original value.
Parameters
• name (WRITEME) – WRITEME
• sub (WRITEME) – WRITEME
Raises MethodNotDefined – Subclass does not implement this method.
class theano.gof.type.Generic
Represents a generic Python object.
This class implements the PureType and CLinkerType interfaces for generic PyObject instances.
EXAMPLE of what this means, or when you would use this type.
WRITEME
class theano.gof.type.PureType
Interface specification for variable type instances.
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A Type instance is mainly reponsible for two things:
•creating Variable instances (conventionally, __call__ does this), and
•filtering a value assigned to a Variable so that the value conforms to restrictions imposed by the
type (also known as casting, this is done by filter).
class Constant(type, data, name=None)
A Constant is a Variable with a value field that cannot be changed at runtime.
Constant nodes make eligible numerous optimizations: constant inlining in C code, constant
folding, etc.
Notes
The data field is filtered by what is provided in the constructor for the Constant’s type field.
WRITEME
clone()
We clone this object, but we don’t clone the data to lower memory requirement. We suppose
that the data will never change.
value
read-only data access method
class PureType.Variable(type, owner=None, index=None, name=None)
A Variable is a node in an expression graph that represents a variable.
The inputs and outputs of every Apply (theano.gof.Apply) are Variable instances. The input and
output arguments to create a function are also Variable instances. A Variable is like a stronglytyped variable in some other languages; each Variable contains a reference to a Type instance
that defines the kind of value the Variable can take in a computation.
A Variable is a container for four important attributes:
•type a Type instance defining the kind of value this Variable can have,
•owner either None (for graph roots) or the Apply instance of which self is an output,
•index the integer such that owner.outputs[index] is this_variable (ignored if owner is None),
•name a string to use in pretty-printing and debugging.
There are a few kinds of Variables to be aware of: A Variable which is the output of a symbolic
computation has a reference to the Apply instance to which it belongs (property: owner) and the
position of itself in the owner’s output list (property: index).
•Variable (this base type) is typically the output of a symbolic computation.
•Constant (a subclass) which adds a default and un-replaceable value, and requires that
owner is None.
•TensorVariable subclass of Variable that represents a numpy.ndarray object.
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•TensorSharedVariable Shared version of TensorVariable.
•SparseVariable subclass of Variable that represents a scipy.sparse.{csc,csr}_matrix object.
•CudaNdarrayVariable subclass of Variable that represents our object on the GPU that is a
subset of numpy.ndarray.
•RandomVariable.
A Variable which is the output of a symbolic computation will have an owner not equal to None.
Using the Variables’ owner field and the Apply nodes’ inputs fields, one can navigate a graph
from an output all the way to the inputs. The opposite direction is not possible until a FunctionGraph has annotated the Variables with the clients field, ie, before the compilation process has
begun a Variable does not know which Apply nodes take it as input.
Parameters
• type (a Type instance) – The type governs the kind of data that can be
associated with this variable.
• owner (None or Apply instance) – The Apply instance which computes the value for this variable.
• index (None or int) – The position of this Variable in owner.outputs.
• name (None or str) – A string for pretty-printing and debugging.
Examples
import theano
from theano import tensor
a = tensor.constant(1.5)
b = tensor.fscalar()
˓→scalar
# declare a symbolic constant
# declare a symbolic floating-point
c = a + b
# create a simple expression
f = theano.function([b], [c])
˓→associated with it already
# this works because a has a value
assert 4.0 == f(2.5)
˓→and evaluate an internal c
# bind 2.5 to an internal copy of b
theano.function([a], [c])
˓→(required by c) is undefined
# compilation error because b
theano.function([a,b], [c])
# compilation error because a is
˓→constant, it can't be an input
d = tensor.value(1.5)
˓→constant 'a'
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# create a value similar to the
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e = d + b
theano.function([d,b], [e])
˓→1.5 is ignored.
# this works.
d's default value of
The python variables a,b,c all refer to instances of type Variable. The Variable refered to by
a is also an instance of Constant.
compile.function uses each Apply instance’s inputs attribute together with each Variable’s owner
field to determine which inputs are necessary to compute the function’s outputs.
clone()
Return a new Variable like self.
Returns A new Variable instance (or subclass instance) with no owner or index.
Return type Variable instance
Notes
Tags are copied to the returned instance.
Name is copied to the returned instance.
eval(inputs_to_values=None)
Evaluates this variable.
Parameters inputs_to_values – A dictionary mapping theano Variables to
values.
Examples
>>> import numpy
>>> import theano.tensor as T
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
>>> z = x + y
>>> numpy.allclose(z.eval({x : 16.3, y : 12.1}), 28.4)
True
We passed eval() a dictionary mapping symbolic theano variables to the values to substitute for them, and it returned the numerical value of the expression.
Notes
eval will be slow the first time you call it on a variable – it needs to call function()
to compile the expression behind the scenes. Subsequent calls to eval() on that same
variable will be fast, because the variable caches the compiled function.
This way of computing has more overhead than a normal Theano function, so don’t use it
too much in real scripts.
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PureType.convert_variable(var)
Patch variable so that its type will match self, if possible.
If the variable can’t be converted, this should return None.
The conversion can only happen if the following implication is true for all possible val.
self.is_valid_value(val) => var.type.is_valid_value(val)
For the majority of types this means that you can only have non-broadcastable dimensions become broadcastable and not the inverse.
The default is to not convert anything which is always safe.
PureType.filter(data, strict=False, allow_downcast=None)
Required: Return data or an appropriately wrapped/converted data.
Subclass implementation should raise a TypeError exception if the data is not of an acceptable
type.
If strict is True, the data returned must be the same as the data passed as an argument. If it is
False, and allow_downcast is True, filter may cast it to an appropriate type. If allow_downcast
is False, filter may only upcast it, not lose precision. If allow_downcast is None (default), the
behaviour can be Type-dependent, but for now it means only Python floats can be downcasted,
and only to floatX scalars.
Raises MethodNotDefined – Subclass doesn’t implement this function.
PureType.filter_variable(other, allow_convert=True)
Convert a symbolic variable into this Type, if compatible.
For the moment, the only Types compatible with one another are TensorType and CudaNdarrayType, provided they have the same number of dimensions, same broadcasting pattern, and same
dtype.
If Types are not compatible, a TypeError should be raised.
PureType.is_valid_value(a)
Required: Return True for any python object a that would be a legal value for a Variable of this
Type.
PureType.make_variable(name=None)
Return a new Variable instance of Type self.
Parameters name (None or str) – A pretty string for printing and debugging.
PureType.value_validity_msg(a)
Optional: Return a message explaining the output of is_valid_value.
PureType.values_eq(a, b)
Return True if a and b can be considered exactly equal.
a and b are assumed to be valid values of this Type.
PureType.values_eq_approx(a, b)
Return True if a and b can be considered approximately equal.
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This function is used by theano debugging tools to decide whether two values are equivalent,
admitting a certain amount of numerical instability. For example, for floating-point numbers
this function should be an approximate comparison.
By default, this does an exact comparison.
Parameters
• a – A potential value for a Variable of this Type.
• b – A potential value for a Variable of this Type.
Returns
Return type bool
class theano.gof.type.SingletonType
Convenient Base class for a Type subclass with no attributes.
It saves having to implement __eq__ and __hash__.
class theano.gof.type.Type
Convenience wrapper combining PureType and CLinkerType.
Theano comes with several subclasses of such as:
•Generic: for any python type
•TensorType: for numpy.ndarray
•SparseType: for scipy.sparse
But you are encouraged to write your own, as described in WRITEME.
The following code illustrates the use of a Type instance, here tensor.fvector:
# Declare a symbolic floating-point vector using __call__
b = tensor.fvector()
# Create a second Variable with the same Type instance
c = tensor.fvector()
Whenever you create a symbolic variable in theano (technically, Variable) it will contain a reference
to a Type instance. That reference is typically constant during the lifetime of the Variable. Many
variables can refer to a single Type instance, as do b and c above. The Type instance defines the kind
of value which might end up in that variable when executing a Function. In this sense, theano is like a
strongly-typed language because the types are included in the graph before the values. In our example
above, b is a Variable which is guaranteed to correspond to a numpy.ndarray of rank 1 when we try to
do some computations with it.
Many Op instances will raise an exception if they are applied to inputs with incorrect types. Type
references are also useful to do type-checking in pattern-based optimizations.
utils – Utilities functions operating on the graph
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Reference
exception theano.gof.utils.MethodNotDefined
To be raised by functions defined as part of an interface.
When the user sees such an error, it is because an important interface function has been left out of an
implementation class.
theano.gof.utils.add_tag_trace(thing, user_line=None)
Add tag.trace to an node or variable.
The argument is returned after being affected (inplace).
Parameters
• thing – The object where we add .tag.trace.
• user_line – The max number of user line to keep.
Notes
We alse use config.traceback.limit for the maximum number of stack level we look.
theano.gof.utils.deprecated(filename, msg=’‘)
Decorator which will print a warning message on the first call.
Use it like this:
@deprecated('myfile', 'do something different...')
def fn_name(...)
...
And it will print:
WARNING myfile.fn_name deprecated. do something different...
theano.gof.utils.difference(seq1, seq2)
Returns all elements in seq1 which are not in seq2: i.e seq1\seq2.
theano.gof.utils.flatten(a)
Recursively flatten tuple, list and set in a list.
theano.gof.utils.give_variables_names(variables)
Gives unique names to an iterable of variables. Modifies input.
This function is idempotent.
theano.gof.utils.hash_from_dict(d)
Work around the fact that dict are not hashable in python.
This request that all object have a sorted order that depend only on the key of the object. We support
only integer/float/string keys.
Also, we transform values that are list into tuple as list are not hashable.
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Notes
Special case for OrderedDict, it use the order of the dict, so the key don’t need to be sortable.
theano.gof.utils.hash_from_file(file_path)
Return the MD5 hash of a file.
theano.gof.utils.memoize(f )
Cache the return value for each tuple of arguments (which must be hashable).
theano.gof.utils.remove(predicate, coll)
Return those items of collection for which predicate(item) is true.
Examples
>>> def even(x):
...
return x % 2 == 0
>>> remove(even, [1, 2, 3, 4])
[1, 3]
theano.gof.utils.simple_extract_stack(f=None, limit=None, skips=[])
This is traceback.extract_stack from python 2.7 with this change:
•Comment the update of the cache.
•Skip internal stack trace level.
The update of the cache call os.stat to verify is the cache is up to date. This take too much time on
cluster.
limit - The number of stack level we want to return. If None, mean all what we can.
skips - partial path of stack level we don’t want to keep and count. When we find one level that
isn’t skipped, we stop skipping.
theano.gof.utils.toposort(prereqs_d)
Sorts prereqs_d.keys() topologically.
prereqs_d[x] contains all the elements that must come before x in the ordering.
theano.gof.utils.uniq(seq)
Do not use set, this must always return the same value at the same index. If we just exchange other
values, but keep the same pattern of duplication, we must keep the same order.
gradient – Symbolic Differentiation
Symbolic gradient is usually computed from gradient.grad(), which offers a more convenient syntax for the common case of wanting the gradient in some expressions with respect to a scalar cost. The
grad_sources_inputs() function does the underlying work, and is more flexible, but is also more
awkward to use when gradient.grad() can do the job.
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Gradient related functions
Driver for gradient calculations.
exception theano.gradient.DisconnectedInputError
Raised when grad is asked to compute the gradient with respect to a disconnected input and disconnected_inputs=’raise’.
class theano.gradient.DisconnectedType
A type indicating that a variable is a result of taking the gradient of c with respect to x when c is not
a function of x. A symbolic placeholder for 0, but to convey the extra information that this gradient is
0 because it is disconnected.
exception theano.gradient.GradientError(arg, err_pos, abs_err, rel_err, abs_tol,
rel_tol)
This error is raised when a gradient is calculated, but incorrect.
theano.gradient.Lop(f,
wrt,
eval_points,
consider_constant=None,
disconnected_inputs=’raise’)
Computes the L operation on f wrt to wrt evaluated at points given in eval_points. Mathematically
this stands for the jacobian of f wrt to wrt left muliplied by the eval points.
Return type Variable or list/tuple of Variables depending on type of f
Returns symbolic expression such that L_op[i] = sum_i ( d f[i] / d wrt[j]) eval_point[i]
where the indices in that expression are magic multidimensional indices that specify
both the position within a list and all coordinates of the tensor element in the last If f
is a list/tuple, then return a list/tuple with the results.
exception theano.gradient.NullTypeGradError
Raised when grad encounters a NullType.
theano.gradient.Rop(f, wrt, eval_points)
Computes the R operation on f wrt to wrt evaluated at points given in eval_points. Mathematically
this stands for the jacobian of f wrt to wrt right muliplied by the eval points.
Return type Variable or list/tuple of Variables depending on type of f
Returns symbolic expression such that R_op[i] = sum_j ( d f[i] / d wrt[j]) eval_point[j]
where the indices in that expression are magic multidimensional indices that specify
both the position within a list and all coordinates of the tensor element in the last. If
wrt is a list/tuple, then return a list/tuple with the results.
theano.gradient.consider_constant(x)
DEPRECATED: use zero_grad() or disconnected_grad() instead.
Consider an expression constant when computing gradients.
The expression itself is unaffected, but when its gradient is computed, or the gradient of another
expression that this expression is a subexpression of, it will not be backpropagated through. In other
words, the gradient of the expression is truncated to 0.
Parameters x – A Theano expression whose gradient should be truncated.
Returns The expression is returned unmodified, but its gradient is now truncated to 0.
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New in version 0.7.
theano.gradient.disconnected_grad(x)
Consider an expression constant when computing gradients, while effectively not backpropagating
through it.
The expression itself is unaffected, but when its gradient is computed, or the gradient of another expression that this expression is a subexpression of, it will not be backpropagated through. This is effectively equivalent to truncating the gradient expression to 0, but is executed faster than zero_grad(),
which stilll has to go through the underlying computational graph related to the expression.
Parameters x – A Theano expression whose gradient should not be backpropagated
through.
Returns The expression is returned unmodified, but its gradient is now effectively truncated to 0.
theano.gradient.format_as(use_list, use_tuple, outputs)
Formats the outputs according to the flags use_list and use_tuple. If use_list is True, outputs is returned as a list (if outputs is not a list or a tuple then it is converted in a one element list). If use_tuple
is True, outputs is returned as a tuple (if outputs is not a list or a tuple then it is converted into a one
element tuple). Otherwise (if both flags are false), outputs is returned.
theano.gradient.grad(cost, wrt, consider_constant=None, disconnected_inputs=’raise’,
add_names=True, known_grads=None, return_disconnected=’zero’,
null_gradients=’raise’)
Return symbolic gradients for one or more variables with respect to some cost.
For more information about how automatic differentiation works in Theano, see gradient. For
information on how to implement the gradient of a certain Op, see grad().
Parameters
• cost (Variable scalar (0-dimensional) tensor variable or None) – Value with
respect to which we are differentiating. May be None if known_grads is provided.
• wrt (Variable or list of Variables) – term[s] for which we want gradients
• consider_constant (list of variables) – expressions not to backpropagate through
• disconnected_inputs ({'ignore', 'warn', 'raise'}) – Defines
the behaviour if some of the variables in wrt are not part of the computational
graph computing cost (or if all links are non-differentiable). The possible values
are:
– ‘ignore’: considers that the gradient on these parameters is zero.
– ‘warn’: consider the gradient zero, and print a warning.
– ‘raise’: raise DisconnectedInputError.
• add_names (bool) – If True, variables generated by grad will be named
(d<cost.name>/d<wrt.name>) provided that both cost and wrt have names
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• known_grads (dict, optional) – A dictionary mapping variables to their
gradients. This is useful in the case where you know the gradient on some variables but do not know the original cost.
• return_disconnected ({'zero', 'None', 'Disconnected'}) –
– ‘zero’ [If wrt[i] is disconnected, return value i will be] wrt[i].zeros_like()
– ‘None’ [If wrt[i] is disconnected, return value i will be] None
– ‘Disconnected’ : returns variables of type DisconnectedType
• null_gradients ({'raise', 'return'}) – Defines the behaviour if
some of the variables in wrt have a null gradient. The possibles values are:
– ‘raise’ : raise a NullTypeGradError exception
– ‘return’ : return the null gradients
Returns symbolic expression of gradient of cost with respect to each of the wrt terms. If
an element of wrt is not differentiable with respect to the output, then a zero variable
is returned.
Return type variable or list/tuple of variables (matches wrt)
theano.gradient.grad_clip(x, lower_bound, upper_bound)
This op do a view in the forward, but clip the gradient.
This is an elemwise operation.
Parameters
• x – the variable we want its gradient inputs clipped
• lower_bound – The lower bound of the gradient value
• upper_bound – The upper bound of the gradient value.
Examples x = theano.tensor.scalar()
z = theano.tensor.grad(grad_clip(x, -1, 1)**2, x) z2 = theano.tensor.grad(x**2, x)
f = theano.function([x], outputs = [z, z2])
print(f(2.0)) # output (1.0, 4.0)
Note We register an opt in tensor/opt.py that remove the GradClip. So it have 0 cost in the
forward and only do work in the grad.
theano.gradient.grad_not_implemented(op, x_pos, x, comment=’‘)
Return an un-computable symbolic variable of type x.type.
If any call to tensor.grad results in an expression containing this un-computable variable, an exception
(NotImplementedError) will be raised indicating that the gradient on the x_pos‘th input of op has not
been implemented. Likewise if any call to theano.function involves this variable.
Optionally adds a comment to the exception explaining why this gradient is not implemented.
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theano.gradient.grad_undefined(op, x_pos, x, comment=’‘)
Return an un-computable symbolic variable of type x.type.
If any call to tensor.grad results in an expression containing this un-computable variable, an exception (GradUndefinedError) will be raised indicating that the gradient on the x_pos‘th input of op is
mathematically undefined. Likewise if any call to theano.function involves this variable.
Optionally adds a comment to the exception explaining why this gradient is not defined.
theano.gradient.hessian(cost,
wrt,
consider_constant=None,
nected_inputs=’raise’)
discon-
Parameters
• consider_constant – a list of expressions not to backpropagate through
• disconnected_inputs (string) – Defines the behaviour if some of the
variables in wrt are not part of the computational graph computing cost (or if
all links are non-differentiable). The possible values are: - ‘ignore’: considers
that the gradient on these parameters is zero. - ‘warn’: consider the gradient zero,
and print a warning. - ‘raise’: raise an exception.
Returns either a instance of Variable or list/tuple of Variables (depending upon wrt) repressenting the Hessian of the cost with respect to (elements of) wrt. If an element
of wrt is not differentiable with respect to the output, then a zero variable is returned.
The return value is of same type as wrt: a list/tuple or TensorVariable in all cases.
theano.gradient.jacobian(expression,
wrt,
consider_constant=None,
nected_inputs=’raise’)
discon-
Parameters
• consider_constant – a list of expressions not to backpropagate through
• disconnected_inputs (string) – Defines the behaviour if some of the
variables in wrt are not part of the computational graph computing cost (or if
all links are non-differentiable). The possible values are: - ‘ignore’: considers
that the gradient on these parameters is zero. - ‘warn’: consider the gradient zero,
and print a warning. - ‘raise’: raise an exception.
Returns either a instance of Variable or list/tuple of Variables (depending upon wrt) repesenting the jacobian of expression with respect to (elements of) wrt. If an element of
wrt is not differentiable with respect to the output, then a zero variable is returned.
The return value is of same type as wrt: a list/tuple or TensorVariable in all cases.
class theano.gradient.numeric_grad(f, pt, eps=None, out_type=None)
Compute the numeric derivative of a scalar-valued function at a particular point.
static abs_rel_err(a, b)
Return absolute and relative error between a and b.
The relative error is a small number when a and b are close, relative to how big they are.
Formulas used: abs_err = abs(a - b) rel_err = abs_err / max(abs(a) + abs(b), 1e-8)
The denominator is clipped at 1e-8 to avoid dividing by 0 when a and b are both close to 0.
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The tuple (abs_err, rel_err) is returned
abs_rel_errors(g_pt)
Return the abs and rel error of gradient estimate g_pt
g_pt must be a list of ndarrays of the same length as self.gf, otherwise a ValueError is raised.
Corresponding ndarrays in g_pt and self.gf must have the same shape or ValueError is raised.
max_err(g_pt, abs_tol, rel_tol)
Find the biggest error between g_pt and self.gf.
What is measured is the violation of relative and absolute errors, wrt the provided tolerances
(abs_tol, rel_tol). A value > 1 means both tolerances are exceeded.
Return the argmax of min(abs_err / abs_tol, rel_err / rel_tol) over g_pt, as well as abs_err and
rel_err at this point.
theano.gradient.subgraph_grad(wrt, end, start=None, cost=None, details=False)
With respect to wrt, computes gradients of cost and/or from existing start gradients, up to the end
variables of a symbolic digraph. In other words, computes gradients for a subgraph of the symbolic
theano function. Ignores all disconnected inputs.
This can be useful when one needs to perform the gradient descent iteratively (e.g. one layer at a time
in an MLP), or when a particular operation is not differentiable in theano (e.g. stochastic sampling
from a multinomial). In the latter case, the gradient of the non-differentiable process could be approximated by user-defined formula, which could be calculated using the gradients of a cost with respect
to samples (0s and 1s). These gradients are obtained by performing a subgraph_grad from the cost
or previously known gradients (start) up to the outputs of the stochastic process (end). A dictionary
mapping gradients obtained from the user-defined differentiation of the process, to variables, could
then be fed into another subgraph_grad as start with any other cost (e.g. weight decay).
In an MLP, we could use subgraph_grad to iteratively backpropagate:
x, t = theano.tensor.fvector('x'), theano.tensor.fvector('t')
w1 = theano.shared(np.random.randn(3,4))
w2 = theano.shared(np.random.randn(4,2))
a1 = theano.tensor.tanh(theano.tensor.dot(x,w1))
a2 = theano.tensor.tanh(theano.tensor.dot(a1,w2))
cost2 = theano.tensor.sqr(a2 - t).sum()
cost2 += theano.tensor.sqr(w2.sum())
cost1 = theano.tensor.sqr(w1.sum())
params = [[w2],[w1]]
costs = [cost2,cost1]
grad_ends = [[a1], [x]]
next_grad = None
param_grads = []
for i in xrange(2):
param_grad, next_grad = theano.subgraph_grad(
wrt=params[i], end=grad_ends[i],
start=next_grad, cost=costs[i]
)
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next_grad = dict(zip(grad_ends[i], next_grad))
param_grads.extend(param_grad)
Parameters
• wrt (list of variables) – Gradients are computed with respect to wrt.
• end (list of variables) – Theano variables at which to end gradient descent (they are considered constant in theano.grad). For convenience, the gradients with respect to these variables are also returned.
• start (dictionary of variables) – If not None, a dictionary mapping
variables to their gradients. This is useful when the gradient on some variables are
known. These are used to compute the gradients backwards up to the variables in
end (they are used as known_grad in theano.grad).
• cost (Variable scalar (0-dimensional) variable) – Additional costs for which
to compute the gradients. For example, these could be weight decay, an l1 constraint, MSE, NLL, etc. May optionally be None if start is provided. Warning :
If the gradients of cost with respect to any of the start variables is already part of
the start dictionary, then it may be counted twice with respect to wrt and end.
Warning: If the gradients of cost with respect to any of the start variables is
already part of the start dictionary, then it may be counted twice with respect
to wrt and end.
• details (bool) – When True, additionally returns the list of gradients from
start and of cost, respectively, with respect to wrt (not end).
Return type Tuple of 2 or 4 Lists of Variables
Returns Returns lists of gradients with respect to wrt and end, respectively.
New in version 0.7.
theano.gradient.verify_grad(fun, pt, n_tests=2, rng=None, eps=None, out_type=None,
abs_tol=None,
rel_tol=None,
mode=None,
cast_to_output_type=False)
Test a gradient by Finite Difference Method. Raise error on failure.
Example:
>>> verify_grad(theano.tensor.tanh,
...
(numpy.asarray([[2,3,4], [-1, 3.3, 9.9]]),),
...
rng=numpy.random)
Raises an Exception if the difference between the analytic gradient and numerical gradient (computed
through the Finite Difference Method) of a random projection of the fun’s output to a scalar exceeds
the given tolerance.
Parameters
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• fun – a Python function that takes Theano variables as inputs, and returns a
Theano variable. For instance, an Op instance with a single output.
• pt – the list of numpy.ndarrays to use as input values. These arrays must be either
float32 or float64 arrays.
• n_tests – number of times to run the test
• rng – random number generator used to sample u, we test gradient of sum(u *
fun) at pt
• eps – stepsize used in the Finite Difference Method (Default None is typedependent) Raising the value of eps can raise or lower the absolute and relative
errors of the verification depending on the Op. Raising eps does not lower the verification quality for linear operations. It is better to raise eps than raising abs_tol
or rel_tol.
• out_type – dtype of output, if complex (i.e. ‘complex32’ or ‘complex64’)
• abs_tol – absolute tolerance used as threshold for gradient comparison
• rel_tol – relative tolerance used as threshold for gradient comparison
• cast_to_output_type – if the output is float32 and cast_to_output_type is
True, cast the random projection to float32. Otherwise it is float64.
Note WARNING to unit-test writers: if op is a function that builds a graph, try to make it
a SMALL graph. Often verify grad is run in debug mode, which can be very slow if it
has to verify a lot of intermediate computations.
Note This function does not support multiple outputs. In tests/test_scan.py there is an
experimental verify_grad that covers that case as well by using random projections.
theano.gradient.zero_grad(x)
Consider an expression constant when computing gradients.
The expression itself is unaffected, but when its gradient is computed, or the gradient of another
expression that this expression is a subexpression of, it will be backpropagated through with a value
of zero. In other words, the gradient of the expression is truncated to 0.
Parameters x – A Theano expression whose gradient should be truncated.
Returns The expression is returned unmodified, but its gradient is now truncated to 0.
List of Implemented R op
See the gradient tutorial for the R op documentation.
list of ops that support R-op:
• with test [Most is tensor/tests/test_rop.py]
– SpecifyShape
– MaxAndArgmax
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– Subtensor
– IncSubtensor set_subtensor too
– Alloc
– Dot
– Elemwise
– Sum
– Softmax
– Shape
– Join
– Rebroadcast
– Reshape
– Flatten
– DimShuffle
– Scan [In scan_module/tests/test_scan.test_rop]
• without test
– Split
– ARange
– ScalarFromTensor
– AdvancedSubtensor1
– AdvancedIncSubtensor1
– AdvancedIncSubtensor
Partial list of ops without support for R-op:
• All sparse ops
• All linear algebra ops.
• PermuteRowElements
• Tile
• AdvancedSubtensor
• TensorDot
• Outer
• Prod
• MulwithoutZeros
• ProdWithoutZeros
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• CAReduce(for max,... done for MaxAndArgmax op)
• MaxAndArgmax(only for matrix on axis 0 or 1)
misc.pkl_utils - Tools for serialization.
theano.misc.pkl_utils.dump(obj, file_handler, protocol=2, persistent_id=<class
‘theano.misc.pkl_utils.PersistentSharedVariableID’>)
Pickles an object to a zip file using external persistence.
Parameters
• obj (object) – The object to pickle.
• file_handler (file) – The file handle to save the object to.
• protocol (int, optional) – The pickling protocol to use. Unlike Python’s
built-in pickle, the default is set to 2 instead of 0 for Python 2. The Python 3
default (level 3) is maintained.
• persistent_id (callable) – The callable that persists certain objects
in the object hierarchy to separate files inside of the zip file. For example,
PersistentNdarrayID saves any numpy.ndarray to a separate NPY file
inside of the zip file.
New in version 0.8.
Note: The final file is simply a zipped file containing at least one file, pkl, which contains the pickled
object. It can contain any other number of external objects. Note that the zip files are compatible with
NumPy’s numpy.load() function.
>>> import theano
>>> foo_1 = theano.shared(0, name='foo')
>>> foo_2 = theano.shared(1, name='foo')
>>> with open('model.zip', 'wb') as f:
...
dump((foo_1, foo_2, numpy.array(2)), f)
>>> numpy.load('model.zip').keys()
['foo', 'foo_2', 'array_0', 'pkl']
>>> numpy.load('model.zip')['foo']
array(0)
>>> with open('model.zip', 'rb') as f:
...
foo_1, foo_2, array = load(f)
>>> array
array(2)
theano.misc.pkl_utils.load(f, persistent_load=<class ‘theano.misc.pkl_utils.PersistentNdarrayLoad’>)
Load a file that was dumped to a zip file.
Parameters
• f (file) – The file handle to the zip file to load the object from.
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• persistent_load (callable, optional) – The persistent loading
function to use for unpickling. This must be compatible with the persisten_id
function used when pickling.
New in version 0.8.
class theano.misc.pkl_utils.StripPickler(file,
protocol=0,
tra_tag_to_remove=None)
Subclass of Pickler that strips unnecessary attributes from Theano objects.
ex-
New in version 0.8.
Example of use:
fn_args = dict(inputs=inputs,
outputs=outputs,
updates=updates)
dest_pkl = 'my_test.pkl'
f = open(dest_pkl, 'wb')
strip_pickler = StripPickler(f, protocol=-1)
strip_pickler.dump(fn_args)
f.close()
class theano.misc.pkl_utils.CompatUnpickler(file)
Allow to reload in python 3 some pickled numpy ndarray.
New in version 0.8.
Examples
with open(fname, 'rb') as fp:
if PY3:
u = CompatUnpickler(fp, encoding="latin1")
else:
u = CompatUnpickler(fp)
mat = u.load()
See also:
Loading and Saving
printing – Graph Printing and Symbolic Print Statement
Guide
Printing during execution
Intermediate values in a computation cannot be printed in the normal python way with the print statement,
because Theano has no statements. Instead there is the Print Op.
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>>> from theano import tensor as T, function, printing
>>> x = T.dvector()
>>> hello_world_op = printing.Print('hello world')
>>> printed_x = hello_world_op(x)
>>> f = function([x], printed_x)
>>> r = f([1, 2, 3])
hello world __str__ = [ 1. 2. 3.]
If you print more than one thing in a function like f, they will not necessarily be printed in the order that you
think. The order might even depend on which graph optimizations are applied. Strictly speaking, the order
of printing is not completely defined by the interface – the only hard rule is that if the input of some print
output a is ultimately used as an input to some other print input b (so that b depends on a), then a will print
before b.
Printing graphs
Theano provides two functions (theano.pp() and theano.printing.debugprint()) to print a
graph to the terminal before or after compilation. These two functions print expression graphs in different
ways: pp() is more compact and math-like, debugprint() is more verbose. Theano also provides
theano.printing.pydotprint() that creates a png image of the function.
1. The first is theano.pp().
>>> from theano import pp, tensor as T
>>> x = T.dscalar('x')
>>> y = x ** 2
>>> gy = T.grad(y, x)
>>> pp(gy) # print out the gradient prior to optimization
'((fill((x ** TensorConstant{2}), TensorConstant{1.0}) * TensorConstant{2}) *
˓→(x ** (TensorConstant{2} - TensorConstant{1})))'
>>> f = function([x], gy)
>>> pp(f.maker.fgraph.outputs[0])
'(TensorConstant{2.0} * x)'
The parameter in T.dscalar(‘x’) in the first line is the name of this variable in the graph. This name is used
when printing the graph to make it more readable. If no name is provided the variable x is printed as its type
as returned by x.type(). In this example - <TensorType(float64, scalar)>.
The name parameter can be any string. There are no naming restrictions: in particular, you can have many
variables with the same name. As a convention, we generally give variables a string name that is similar to
the name of the variable in local scope, but you might want to break this convention to include an object
instance, or an iteration number or other kinds of information in the name.
Note: To make graphs legible, pp() hides some Ops that are actually in the graph. For example, automatic
DimShuffles are not shown.
2. The second function to print a graph is theano.printing.debugprint()
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>>> theano.printing.debugprint(f.maker.fgraph.outputs[0])
Elemwise{mul,no_inplace} [id A] ''
|TensorConstant{2.0} [id B]
|x [id C]
Each line printed represents a Variable in the graph. The line |x [id C] means the variable named x
with debugprint identifier [id C] is an input of the Elemwise. If you accidentally have two variables called
x in your graph, their different debugprint identifier will be your clue.
The line |TensorConstant{2.0} [id B] means that there is a constant 2.0 with this debugprint
identifier.
The line Elemwise{mul,no_inplace} [id A] '' is indented less than the other ones, because it
means there is a variable computed by multiplying the other (more indented) ones together.
The | symbol are just there to help read big graph. The group together inputs to a node.
Sometimes, you’ll see a Variable but not the inputs underneath. That can happen when that Variable has
already been printed. Where else has it been printed? Look for debugprint identifier using the Find feature
of your text editor.
>>> theano.printing.debugprint(gy)
Elemwise{mul} [id A] ''
|Elemwise{mul} [id B] ''
| |Elemwise{second,no_inplace} [id C] ''
| | |Elemwise{pow,no_inplace} [id D] ''
| | | |x [id E]
| | | |TensorConstant{2} [id F]
| | |TensorConstant{1.0} [id G]
| |TensorConstant{2} [id F]
|Elemwise{pow} [id H] ''
|x [id E]
|Elemwise{sub} [id I] ''
|TensorConstant{2} [id F]
|DimShuffle{} [id J] ''
|TensorConstant{1} [id K]
>>> theano.printing.debugprint(gy, depth=2)
Elemwise{mul} [id A] ''
|Elemwise{mul} [id B] ''
|Elemwise{pow} [id C] ''
If the depth parameter is provided, it limits the number of levels that are shown.
3. The function theano.printing.pydotprint() will print a compiled theano function to a png
file.
In the image, Apply nodes (the applications of ops) are shown as ellipses and variables are shown as boxes.
The number at the end of each label indicates graph position. Boxes and ovals have their own set of positions,
so you can have apply #1 and also a variable #1. The numbers in the boxes (Apply nodes) are actually their
position in the run-time execution order of the graph. Green ovals are inputs to the graph and blue ovals are
outputs.
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If your graph uses shared variables, those shared variables will appear as inputs. Future versions of the
pydotprint() may distinguish these inplicit inputs from explicit inputs.
If you give updates arguments when creating your function, these are added as extra inputs and outputs
to the graph. Future versions of pydotprint() may distinguish these implicit inputs and outputs from
explicit inputs and outputs.
Reference
class theano.printing.Print(Op)
This identity-like Op has the side effect of printing a message followed by its inputs when it runs.
Default behaviour is to print the __str__ representation. Optionally, one can pass a list of the input
member functions to execute, or attributes to print.
__init__(message=”“, attrs=(“__str__”)
Parameters
• message (string) – prepend this to the output
• attrs (list of strings) – list of input node attributes or member functions to print. Functions are identified through callable(), executed and their
return value printed.
__call__(x)
Parameters x (a Variable) – any symbolic variable
Returns symbolic identity(x)
When you use the return-value from this function in a theano function, running the function will
print the value that x takes in the graph.
theano.printing.debugprint(obj, depth=-1, print_type=False, file=None, ids=’CHAR’,
stop_on_name=False, done=None, print_storage=False)
Print a computation graph as text to stdout or a file.
Parameters
• obj (Variable, Apply, or Function instance) – symbolic thing to print
• depth (integer) – print graph to this depth (-1 for unlimited)
• print_type (boolean) – whether to print the type of printed objects
• file (None, 'str', or file-like object) – print to this file (‘str’
means to return a string)
• ids (str) – How do we print the identifier of the variable id - print the python id
value int - print integer character CHAR - print capital character “” - don’t print
an identifier
• stop_on_name – When True, if a node in the graph has a name, we don’t print
anything below it.
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• done (None or dict) – A dict where we store the ids of printed node. Useful
to have multiple call to debugprint share the same ids.
• print_storage (bool) – If True, this will print the storage map for Theano
functions. Combined with allow_gc=False, after the execution of a Theano function, we see the intermediate result.
Returns string if file == ‘str’, else file arg
Each line printed represents a Variable in the graph. The indentation of lines corresponds to its depth
in the symbolic graph. The first part of the text identifies whether it is an input (if a name or type is
printed) or the output of some Apply (in which case the Op is printed). The second part of the text is
an identifier of the Variable. If print_type is True, we add a part containing the type of the Variable
If a Variable is encountered multiple times in the depth-first search, it is only printed recursively the
first time. Later, just the Variable identifier is printed.
If an Apply has multiple outputs, then a ‘.N’ suffix will be appended to the Apply’s identifier, to
indicate which output a line corresponds to.
theano.pp(*args)
Just a shortcut to theano.printing.pp()
theano.printing.pp(*args)
theano.printing.pydotprint(fct,
outfile=None,
compact=True,
format=’png’,
with_ids=False,
high_contrast=True,
cond_highlight=None,
colorCodes=None,
max_label_size=70,
scan_graphs=False,
var_with_name_simple=False,
print_output_file=True,
return_image=False)
Print to a file the graph of a compiled theano function’s ops. Supports all pydot output formats,
including png and svg.
Parameters
• fct – a compiled Theano function, a Variable, an Apply or a list of Variable.
• outfile – the output file where to put the graph.
• compact – if True, will remove intermediate var that don’t have name.
• format – the file format of the output.
• with_ids – Print the toposort index of the node in the node name. and an index
number in the variable ellipse.
• high_contrast – if true, the color that describes the respective node is filled
with its corresponding color, instead of coloring the border
• colorCodes – dictionary with names of ops as keys and colors as values
• cond_highlight – Highlights a lazy if by sorrounding each of the 3 possible
categories of ops with a border. The categories are: ops that are on the left branch,
ops that are on the right branch, ops that are on both branches As an alternative
you can provide the node that represents the lazy if
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• scan_graphs – if true it will plot the inner graph of each scan op in files with
the same name as the name given for the main file to which the name of the scan
op is concatenated and the index in the toposort of the scan. This index can be
printed with the option with_ids.
• var_with_name_simple – If true and a variable have a name, we will print
only the variable name. Otherwise, we concatenate the type to the var name.
• return_image – If True, it will create the image and return it. Useful to display
the image in ipython notebook.
import theano
v = theano.tensor.vector()
from IPython.display import SVG
SVG(theano.printing.pydotprint(v*2, return_image=True,
format='svg'))
In the graph, ellipses are Apply Nodes (the execution of an op) and boxes are variables. If variables
have names they are used as text (if multiple vars have the same name, they will be merged in the
graph). Otherwise, if the variable is constant, we print its value and finally we print the type + a
unique number to prevent multiple vars from being merged. We print the op of the apply in the Apply
box with a number that represents the toposort order of application of those Apply. If an Apply has
more than 1 input, we label each edge between an input and the Apply node with the input’s index.
Variable color code::
• Cyan boxes are SharedVariable, inputs and/or outputs) of the graph,
• Green boxes are inputs variables to the graph,
• Blue boxes are outputs variables of the graph,
• Grey boxes are variables that are not outputs and are not used,
Default apply node code::
• Red ellipses are transfers from/to the gpu
• Yellow are scan node
• Brown are shape node
• Magenta are IfElse node
• Dark pink are elemwise node
• Purple are subtensor
• Orange are alloc node
For edges, they are black by default. If a node returns a view of an input, we put the corresponding
input edge in blue. If it returns a destroyed input, we put the corresponding edge in red.
Note: Since October 20th, 2014, this print the inner function of all scan separately after the top level
debugprint output.
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sandbox – Experimental Code
sandbox.cuda – The CUDA GPU backend
sandbox.cuda – List of CUDA GPU Op implemented
Normally you should not call directly those Ops! Theano should automatically transform cpu ops to their
gpu equivalent. So this list is just useful to let people know what is implemented on the gpu.
Basic Op
class theano.sandbox.cuda.basic_ops.CopyOnNegativeStrides(use_c_code=’/usr/bin/g++’)
Checks if the input has contains negative strides.
If it does, returns a c contiguous copy.
class theano.sandbox.cuda.basic_ops.GpuAdvancedIncSubtensor1(inplace=False,
set_instead_of_inc=False)
Implement AdvancedIncSubtensor1 on the gpu.
class theano.sandbox.cuda.basic_ops.GpuAdvancedIncSubtensor1_dev20(inplace=False,
set_instead_of_inc=False)
Implement AdvancedIncSubtensor1 on the gpu, but use function only avail on compute capability 2.0
and more recent.
make_node(x, y, ilist)
It defer from GpuAdvancedIncSubtensor1 in that it make sure the index are of type long.
class theano.sandbox.cuda.basic_ops.GpuAdvancedSubtensor1(sparse_grad=False)
Implement AdvancedSubtensor1 on the gpu.
class theano.sandbox.cuda.basic_ops.GpuAlloc(memset_0=False)
Implement Alloc on the gpu.
The memset_0 param is an optimization. When True, we call cudaMemset that is faster.
class theano.sandbox.cuda.basic_ops.GpuAllocEmpty(use_c_code=’/usr/bin/g++’)
Implement Alloc on the gpu, but without initializing memory.
class theano.sandbox.cuda.basic_ops.GpuCAReduce(reduce_mask,
scalar_op,
pre_scalar_op=None)
GpuCAReduce is a Reduction along some dimensions by a scalar op.
The dimensions along which to reduce is specified by the reduce_mask that you pass to the constructor.
The reduce_mask is a tuple of booleans (actually integers 0 or 1) that specify for each input dimension,
whether to reduce it (1) or not (0).
Parameters pre_scalar_op – If present, must be a scalar op with only 1 input. We
will execute it on the input value before reduction.
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Notes
This Op is a work in progress.
This op was recently upgraded from just GpuSum a general CAReduce. Not many code cases are
supported for scalar_op being anything other than scal. Add instances yet.
Important note: if you implement new cases for this op, be sure to benchmark them and make sure
that they actually result in a speedup. GPUs are not especially well-suited to reduction operations so
it is quite possible that the GPU might be slower for some cases.
Examples
When scalar_op is a theano.scalar.basic.Add instance:
•reduce_mask == (1,) sums a vector to a scalar
•reduce_mask == (1,0) computes the sum of each column in a matrix
•reduce_mask == (0,1) computes the sum of each row in a matrix
•reduce_mask == (1,1,1) computes the sum of all elements in a 3-tensor.
..note:: Any reduce_mask of all zeros is a sort of ‘copy’, and may be removed during graph optimization.
c_code_reduce_01X(sio, node, name, x, z, fail, N)
Parameters N (int) – The number of 1 in the pattern N=1 -> 01, N=2 -> 011 N=3
->0111 Works for N=1,2,3.
c_code_reduce_ccontig(sio, node, name, x, z, fail)
WRITEME
IG: I believe, based on how this is called in c_code, that it is for the case where we are reducing
on all axes and x is C contiguous.
supports_c_code(inputs)
Returns True if the current op and reduce pattern has functioning C code.
class theano.sandbox.cuda.basic_ops.GpuContiguous(use_c_code=’/usr/bin/g++’)
Always return a c contiguous output. Copy the input only if it is not already c contiguous.
class theano.sandbox.cuda.basic_ops.GpuDimShuffle(input_broadcastable,
new_order)
Implement DimShuffle on the gpu.
class theano.sandbox.cuda.basic_ops.GpuElemwise(scalar_op,
place_pattern=None,
sync=None)
Implement a generic elemwise on the gpu.
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class theano.sandbox.cuda.basic_ops.GpuFlatten
Implement Flatten on the gpu.
Note: The interface GpuFlatten is deprecated, you should use gpu_flatten.
class theano.sandbox.cuda.basic_ops.GpuFromHost(use_c_code=’/usr/bin/g++’)
Implement the transfer from cpu to the gpu.
class theano.sandbox.cuda.basic_ops.GpuIncSubtensor(idx_list, inplace=False,
set_instead_of_inc=False,
destroyhandler_tolerate_aliased=None)
Implement IncSubtensor on the gpu.
Notes
The optimization to make this inplace is in tensor/opt. The same optimization handles IncSubtensor
and GpuIncSubtensor. This Op has c_code too; it inherits tensor.IncSubtensor’s c_code. The helper
methods like do_type_checking, copy_of_x, etc. specialize the c_code for this Op.
copy_into(view, source)
Parameters
• view (str) – C code expression for an array.
• source (str) – C code expression for an array
Returns A C code expression to copy source into view, and 0 on success.
Return type str
copy_of_x(x)
Parameters x (str) – A string giving the name of a C variable pointing to an array.
Returns C code expression to make a copy of x.
Return type str
Notes
Base class uses PyArrayObject *, subclasses may override for different types of arrays.
do_type_checking(node)
Should raise NotImplementedError if c_code does not support the types involved in this node.
get_helper_c_code_args()
Return a dictionary of arguments to use with helper_c_code.
make_view_array(x, view_ndim)
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Parameters
• x (str) – A string identifying an array to be viewed.
• view_ndim (str) – A string specifying the number of dimensions to have in
the view. This doesn’t need to actually set up the view with the right indexing;
we’ll do that manually later.
class theano.sandbox.cuda.basic_ops.GpuJoin(use_c_code=’/usr/bin/g++’)
Implement Join on the gpu.
class theano.sandbox.cuda.basic_ops.GpuReshape(ndim, name=None)
Implement Reshape on the gpu.
class theano.sandbox.cuda.basic_ops.GpuShape(use_c_code=’/usr/bin/g++’)
Implement Shape on the gpu.
class theano.sandbox.cuda.basic_ops.GpuSubtensor(idx_list)
Implement subtensor on the gpu.
class theano.sandbox.cuda.basic_ops.HostFromGpu(use_c_code=’/usr/bin/g++’)
Implement the transfer from gpu to the cpu.
theano.sandbox.cuda.basic_ops.col(name=None, dtype=None)
Return a symbolic column variable (ndim=2, broadcastable=[False,True]).
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name (str) – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.gpu_flatten(x, outdim=1)
Implement flatten on the gpu. Reshapes the variable x by keeping the first outdim-1 dimension size(s)
of x the same, and making the last dimension size of x equal to the multiplication of its remaining
dimension size(s).
Parameters
• x (theano.tensor.var.TensorVariable) – the variable that should be
reshaped.
• outdim (int) – the number of dimensions of the returned variable
Returns the flattend variable with dimensionality of outdim
Return type theano.tensor.var.TensorVariable
theano.sandbox.cuda.basic_ops.matrix(name=None, dtype=None)
Return a symbolic matrix variable.
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.row(name=None, dtype=None)
Return a symbolic row variable (ndim=2, broadcastable=[True,False]).
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Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name (str) – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.scalar(name=None, dtype=None)
Return a symbolic scalar variable.
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name (str) – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.tensor3(name=None, dtype=None)
Return a symbolic 3-D variable.
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name (str) – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.tensor4(name=None, dtype=None)
Return a symbolic 4-D variable.
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name (str) – A name to attach to this variable.
theano.sandbox.cuda.basic_ops.vector(name=None, dtype=None)
Return a symbolic vector variable.
Parameters
• dtype – Numeric type (None means to use theano.config.floatX).
• name – A name to attach to this variable.
Blas Op
class theano.sandbox.cuda.blas.BaseGpuCorr3dMM(border_mode=’valid’, subsample=(1, 1, 1), pad=(0, 0, 0))
Base class for GpuCorr3dMM, GpuCorr3dMM_gradWeights and GpuCorr3dMM_gradInputs. Cannot be used directly.
c_code_helper(bottom, weights, top, direction, sub, height=None, width=None,
depth=None)
This generates the C code for GpuCorrMM (direction=”forward”), GpuCorrMM_gradWeights
(direction=”backprop weights”), and GpuCorrMM_gradInputs (direction=”backprop inputs”).
Depending on the direction, one of bottom, weights, top will receive the output, while the other
two serve as inputs.
Parameters
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• bottom – Variable name of the input images in the forward pass, or the gradient
of the input images in backprop wrt. inputs.
• weights – Variable name of the filters in the forward pass, or the gradient of
the filters in backprop wrt. weights.
• top – Variable name of the output images / feature maps in the forward pass,
or the gradient of the outputs in the backprop passes.
• direction ({'forward', 'backprop weights', 'backprop
inputs'}) – “forward” to correlate bottom with weights and store results in
top, “backprop weights” to do a valid convolution of bottom with top (swapping
the first two dimensions) and store results in weights, and “backprop inputs” to
do a full convolution of top with weights (swapping the first two dimensions)
and store results in bottom.
• sub – Dictionary of substitutions useable to help generating the C code.
• height – If self.subsample[0] != 1, a variable giving the height of the filters
for direction=”backprop weights” or the height of the input images for direction=”backprop inputs”. If self.pad == ‘half’, a variable giving the height of the
filters for direction=”backprop weights”. Ignored otherwise.
• width – If self.subsample[1] != 1, a variable giving the width of the filters
for direction=”backprop weights” or the width of the input images for direction=”backprop inputs”. If self.pad == ‘half’, a variable giving the width of the
filters for direction=”backprop weights”. Ignored otherwise.
• depth – If self.subsample[2] != 1, a variable giving the depth of the filters
for direction=”backprop weights” or the depth of the input images for direction=”backprop inputs”. If self.pad == ‘half’, a variable giving the depth of the
filters for direction=”backprop weights”. Ignored otherwise.
flops(inp, outp)
Useful with the hack in profilemode to print the MFlops
class theano.sandbox.cuda.blas.BaseGpuCorrMM(border_mode=’valid’,
subsample=(1, 1), pad=(0, 0))
Base class for GpuCorrMM, GpuCorrMM_gradWeights and GpuCorrMM_gradInputs. Cannot be
used directly.
Parameters
• border_mode ({'valid', 'full', 'half'}) – Additionally, the
padding size could be directly specified by an integer or a pair of integers
• subsample – Perform subsampling of the output (default: (1, 1)).
• pad – deprecated, now you should always use border_mode.
c_code_helper(bottom, weights, top, direction, sub, height=None, width=None)
This generates the C code for GpuCorrMM (direction=”forward”), GpuCorrMM_gradWeights
(direction=”backprop weights”), and GpuCorrMM_gradInputs (direction=”backprop inputs”).
Depending on the direction, one of bottom, weights, top will receive the output, while the other
two serve as inputs.
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Parameters
• bottom – Variable name of the input images in the forward pass, or the gradient
of the input images in backprop wrt. inputs
• weights – Variable name of the filters in the forward pass, or the gradient of
the filters in backprop wrt. weights
• top – Variable name of the output images / feature maps in the forward pass,
or the gradient of the outputs in the backprop passes
• direction ({'forward', 'backprop weights', 'backprop
inputs'}) – “forward” to correlate bottom with weights and store results in
top, “backprop weights” to do a valid convolution of bottom with top (swapping
the first two dimensions) and store results in weights, and “backprop inputs” to
do a full convolution of top with weights (swapping the first two dimensions)
and store results in bottom.
• sub – Dictionary of substitutions useable to help generating the C code.
• height – If self.subsample[0] != 1, a variable giving the height of the filters
for direction=”backprop weights” or the height of the input images for direction=”backprop inputs”. If self.border_mode == ‘half’, a variable giving the
height of the filters for direction=”backprop weights”. Ignored otherwise.
• width – If self.subsample[1] != 1, a variable giving the width of the filters
for direction=”backprop weights” or the width of the input images for direction=”backprop inputs”. If self.border_mode == ‘half’, a variable giving the
width of the filters for direction=”backprop weights”. Ignored otherwise.
flops(inp, outp)
Useful with the hack in profilemode to print the MFlops.
class theano.sandbox.cuda.blas.GpuConv(border_mode, subsample=(1, 1), logical_img_hw=None, logical_kern_hw=None,
logical_kern_align_top=True, version=-1, direction_hint=None, verbose=0, kshp=None,
imshp=None,
max_threads_dim0=None,
nkern=None, bsize=None, fft_opt=True)
Implement the batched and stacked 2d convolution on the gpu.
Parameters
• version – Each version of c_code implements many kernel for the convolution.
By default we try to guess the best one. You can force one version with this
parameter. This parameter is used by the tests.
• direction_hint
({'forward', 'bprop weights', 'bprop
inputs'}) – Serves as a hint for graph optimizers replacing GpuConv by other
implementations. If the GpuConv is inserted automatically, we take its value
from ConvOp.
• verbose – For value of 1,2 and 3. Print more information during the execution
of the convolution. Mostly used for optimization or debugging.
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• kshp – The size of the kernel. If provided, can generate faster code. If the
GpuConv op is automatically inserted, We take its value automatically from the
Conv op.
• imshp – The size of the image. Not used for code generation but allows to select
an experimental new version in another repo.
• max_threads_dim0 – The maximum number of threads for the block size
dimensions 0 (blockDim.x) used by the GPU function.
• nkern – The number of kernels. Not used for this op, but can be used by graph
optimizers to select a more optimal convolution implementation. If the GpuConv
op is inserted automatically, we take its value from the Conv op.
• bsize – The batch size. Not used for this op, but can be used by graph optimizers to select a more optimal convolution implementation. If the GpuConv op is
inserted automatically, we take its value from the Conv op.
• fft_opt – Deactivate fft_opt optimization at the op level when set to False.
Note that by default fft optimization aren’t enabled. See convolution documentation to enable them.
flops(inputs, outputs)
Useful with the hack in profilemode to print the MFlops
class theano.sandbox.cuda.blas.GpuCorr3dMM(border_mode=’valid’,
1, 1), pad=(0, 0, 0))
GPU correlation implementation using Matrix Multiplication.
subsample=(1,
Parameters
• border_mode – Currently supports “valid” only; “full” can be simulated
by setting pad=”full” (at the cost of performance), or by using GpuCorrMM_gradInputs.
• subsample – The subsample operation applied to each output image. Should be
a tuple with 3 elements. (sv, sh, sl) is equivalent to GpuCorrMM(...)(...)[:,:,::sv,
::sh, ::sl], but faster. Set to (1, 1, 1) to disable subsampling.
• pad – The width of a border of implicit zeros to pad the input image with. Should
be a tuple with 3 elements giving the numbers of rows and columns to pad on
each side, or “half” to set the padding to (kernel_rows // 2, kernel_columns // 2,
kernel_depth // 2), or “full” to set the padding to (kernel_rows - 1, kernel_columns
- 1, kernel_depth - 1) at runtime. Set to (0, 0, 0) to disable padding.
Notes
Currently, the Op requires the inputs, filters and outputs to be C-contiguous.
gpu_contiguous on these arguments if needed.
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Warning: For 700 series Nvidia GPUs of compute capability 3.5 and CUDA 5.0 to 6.0, there is a
bug in CUBLAS’ matrix multiplication function that can make GpuCorrMM or its gradients crash
for some input and filter shapes. So if you have a Tesla K20, Tesla K40, Quadro K6000, GeForce
GT 640 (DDR5), GeForce GTX 780 (or Ti), GeForce GTX TITAN (or Black or Z) and experience
a crash, switching to CUDA 6.5 or CUDA 4.2 should fix it. If this is not possible, changing the
input or filter shapes (e.g., the batchsize or number of filters) may also work around the CUBLAS
bug.
class theano.sandbox.cuda.blas.GpuCorr3dMM_gradInputs(border_mode=’valid’,
subsample=(1, 1, 1),
pad=(0, 0, 0))
Gradient wrt. inputs for GpuCorr3dMM.
Notes
You will not want to use this directly, but rely on Theano’s automatic differentiation or graph optimization to use it as needed.
class theano.sandbox.cuda.blas.GpuCorr3dMM_gradWeights(border_mode=’valid’,
subsample=(1, 1, 1),
pad=(0, 0, 0))
Gradient wrt. filters for GpuCorr3dMM.
Notes
You will not want to use this directly, but rely on Theano’s automatic differentiation or graph optimization to use it as needed.
class theano.sandbox.cuda.blas.GpuCorrMM(border_mode=’valid’, subsample=(1, 1),
pad=(0, 0))
GPU correlation implementation using Matrix Multiplication.
Parameters
• border_mode – The width of a border of implicit zeros to pad the input with.
Must be a tuple with 2 elements giving the numbers of rows and columns to pad
on each side, or a single integer to pad the same on all sides, or a string shortcut
setting the padding at runtime: 'valid' for (0, 0) (valid convolution, no
padding), 'full' for (kernel_rows - 1, kernel_columns - 1)
(full convolution), 'half' for (kernel_rows // 2, kernel_columns
// 2) (same convolution for odd-sized kernels). Note that the two widths are
each applied twice, once per side (left and right, top and bottom).
• subsample – The subsample operation applied to each output image. Should
be a tuple with 2 elements. (sv, sh) is equivalent to GpuCorrMM(...)(...)[:,:,::sv,
::sh], but faster. Set to (1, 1) to disable subsampling.
• pad – Deprecated alias for border_mode.
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Notes
Currently, the Op requires the inputs, filters and outputs to be C-contiguous. Use gpu_contiguous
on these arguments if needed.
You can either enable the Theano flag optimizer_including=conv_gemm to automatically replace all
convolution operations with GpuCorrMM or one of its gradients, or you can use it as a replacement for
conv2d, called as GpuCorrMM(subsample=...)(image, filters). The latter is currently faster, but note
that it computes a correlation – if you need to compute a convolution, flip the filters as filters[:,:,::1,::-1].
..warning:: For 700 series Nvidia GPUs of compute capability 3.5 and CUDA 5.0 to 6.0, there is
a bug in CUBLAS’ matrix multiplication function that can make GpuCorrMM or its gradients
crash for some input and filter shapes. So if you have a Tesla K20, Tesla K40, Quadro K6000,
GeForce GT 640 (DDR5), GeForce GTX 780 (or Ti), GeForce GTX TITAN (or Black or Z) and
experience a crash, switching to CUDA 6.5 or CUDA 4.2 should fix it. If this is not possible,
changing the input or filter shapes (e.g., the batchsize or number of filters) may also work around
the CUBLAS bug.
class theano.sandbox.cuda.blas.GpuCorrMM_gradInputs(border_mode=’valid’,
subsample=(1,
1),
pad=(0, 0))
Gradient wrt. inputs for GpuCorrMM.
Notes
You will not want to use this directly, but rely on Theano’s automatic differentiation or graph optimization to use it as needed.
class theano.sandbox.cuda.blas.GpuCorrMM_gradWeights(border_mode=’valid’,
subsample=(1,
1),
pad=(0, 0))
Gradient wrt. filters for GpuCorrMM.
Notes
You will not want to use this directly, but rely on Theano’s automatic differentiation or graph optimization to use it as needed.
class theano.sandbox.cuda.blas.GpuDot22(use_c_code=’/usr/bin/g++’)
Implement dot(2d, 2d) on the gpu.
class theano.sandbox.cuda.blas.GpuDot22Scalar(use_c_code=’/usr/bin/g++’)
Implement dot(2d, 2d) * scalar on the gpu.
Notes
Not used anymore. Keep to allow unpickle of old graph.
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class theano.sandbox.cuda.blas.GpuDownsampleFactorMax(ds,
ignore_border=False)
Implement downsample with max on the gpu.
class theano.sandbox.cuda.blas.GpuDownsampleFactorMaxGrad(ds,
ignore_border)
Implement the grad of downsample with max on the gpu.
class theano.sandbox.cuda.blas.GpuDownsampleFactorMaxGradGrad(ds,
ignore_border)
Implement the grad of downsample with max on the gpu.
class theano.sandbox.cuda.blas.GpuGemm(inplace)
implement the gemm on the gpu.
class theano.sandbox.cuda.blas.GpuGemv(inplace)
implement gemv on the gpu.
class theano.sandbox.cuda.blas.GpuGer(inplace)
implement ger on the gpu.
class theano.sandbox.cuda.blas.GpuBatchedDot(stream_threshold=650)
Nnet Op
class theano.sandbox.cuda.nnet.GpuCrossentropySoftmax1HotWithBiasDx(**kwargs)
Implement CrossentropySoftmax1HotWithBiasDx on the gpu.
class theano.sandbox.cuda.nnet.GpuCrossentropySoftmaxArgmax1HotWithBias(use_c_code=’/usr/b
Implement CrossentropySoftmaxArgmax1HotWithBias on the gpu.
class theano.sandbox.cuda.nnet.GpuSoftmax(use_c_code=’/usr/bin/g++’)
Implement Softmax on the gpu.
class theano.sandbox.cuda.nnet.GpuSoftmaxWithBias(use_c_code=’/usr/bin/g++’)
Implement SoftmaxWithBias on the gpu.
Curand Op
Random generator based on the CURAND libraries. It is not inserted automatically.
RAND_RandomStreams - backed by CURAND.
class theano.sandbox.cuda.rng_curand.CURAND_Base(output_type,
tive)
Base class for a random number generator implemented in CURAND.
seed,
Define CUdestruc-
The random number generator itself is an opaque reference managed by CURAND. This Op uses a
generic-typed shared variable to point to a CObject that encapsulates this opaque reference.
Each random variable is created with a generator of False. The actual random number generator is
allocated from the seed, on the first call to allocate random numbers (see c_code).
Parameters
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• output_type – A theano type (e.g. tensor.fvector).
• seed (int) –
• destructive – True or False (on the generator)
Notes
One caveat is that the random number state is simply not serializable. Consequently, attempts to
serialize functions compiled with these random numbers will fail.
as_destructive()
Return an destructive version of self.
classmethod new_auto_update(generator, ndim, dtype, size, seed)
Return a symbolic sample from generator.
cls dictates the random variable (e.g. uniform, normal).
class theano.sandbox.cuda.rng_curand.CURAND_Normal(output_type, seed, destructive)
Op to draw normal numbers using CURAND.
class theano.sandbox.cuda.rng_curand.CURAND_RandomStreams(seed)
RandomStreams instance that creates CURAND-based random variables.
One caveat is that generators are not serializable.
Parameters seed (int) –
next_seed()
Return a unique seed for initializing a random variable.
normal(size=None, avg=0.0, std=1.0, ndim=None, dtype=’float64’)
Return symbolic tensor of normally-distributed numbers.
Parameters size – Can be a list of integer or Theano variable (ex: the shape of other
Theano Variable)
uniform(size, low=0.0, high=1.0, ndim=None, dtype=’float64’)
Return symbolic tensor of uniform numbers.
updates()
List of all (old, new) generator update pairs created by this instance.
class theano.sandbox.cuda.rng_curand.CURAND_Uniform(output_type,
structive)
Op to draw uniform numbers using CURAND.
seed,
de-
sandbox.cuda.var – The Variables for Cuda-allocated arrays
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API
class theano.sandbox.cuda.var.CudaNdarraySharedVariable(name,
type,
value, strict, allow_downcast=None,
container=None)
Shared Variable interface to CUDA-allocated arrays.
get_value(borrow=False, return_internal_type=False)
Return the value of this SharedVariable’s internal array.
Parameters
• borrow – Permit the return of internal storage, when used in conjunction with
return_internal_type=True.
• return_internal_type – True to return the internal cuda_ndarray
instance rather than a numpy.ndarray (Default False).
• default get_value() copies from the GPU to a numpy.
ndarray (By) –
• returns that host-allocated array. (and) –
• will return a GPU-allocated copy of the
(get_value(False,True)) –
• GPU array. (original) –
• will return the original GPU-allocated array
(get_value(True,True)) –
• any copying. (without) –
set_value(value, borrow=False)
Assign value to the GPU-allocated array.
Parameters borrow (bool) – True permits reusing value itself, False requires
that this function copies value into internal storage.
Notes
Prior to Theano 0.3.1, set_value did not work in-place on the GPU. This meant that sometimes,
GPU memory for the new value would be allocated before the old memory was released. If
you’re running near the limits of GPU memory, this could cause you to run out of GPU memory.
Beginning with Theano 0.3.1, set_value will work in-place on the GPU, if the following conditions are met:
•The destination on the GPU must be c_contiguous.
•The source is on the CPU.
•The old value must have the same dtype as the new value (which is a given for now, since
only float32 is supported).
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•The old and new value must have the same shape.
•The old value is being completely replaced by the new value (not partially modified, e.g. by
replacing some subtensor of it).
•You change the value of the shared variable via set_value, not via the .value accessors.
You should not use the .value accessors anyway, since they will soon be deprecated and
removed.
It is also worth mentioning that, for efficient transfer to the GPU, Theano will make the new data
c_contiguous. This can require an extra copy of the data on the host.
The inplace on gpu memory work when borrow is either True or False.
sandbox.cuda.type – The Type object for Cuda-allocated arrays
API
sandbox.cuda.dnn – cuDNN
cuDNN is an NVIDIA library with functionality used by deep neural network. It provides optimized versions
of some operations like the convolution. cuDNN is not currently installed with CUDA 6.5. You must
download and install it yourself.
To install it, decompress the downloaded file and make the *.h and *.so* files available to the compilation
environment. There are at least three possible ways of doing so:
• The easiest is to include them in your CUDA installation. Copy the *.h files to CUDA_ROOT/
include and the *.so* files to CUDA_ROOT/lib64 (by default, CUDA_ROOT is /usr/
local/cuda on Linux).
• Alternatively, on Linux, you can set the environment variables LD_LIBRARY_PATH,
LIBRARY_PATH and CPATH to the directory extracted from the download. If needed, separate
multiple directories with : as in the PATH environment variable.
example:
export LD_LIBRARY_PATH=/home/user/path_to_CUDNN_folder/lib64:$LD_LIBRARY_
˓→PATH
export CPATH=/home/user/path_to_CUDNN_folder/include:$CPATH
export LIBRARY_PATH=/home/user/path_to_CUDNN_folder/lib64:$LD_LIBRARY_
˓→PATH
• And as a third way, also on Linux, you can copy the *.h files to /usr/include and the *.so*
files to /lib64.
By default, Theano will detect if it can use cuDNN. If so, it will use it. If not, Theano optimizations will not
introduce cuDNN ops. So Theano will still work if the user did not introduce them manually.
The recently added Theano flag dnn.enabled allows to change the default behavior to force it or disable
it. Older Theano version do not support this flag. To get an error when cuDNN can not be used with them,
use this flag: optimizer_including=cudnn.
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Note: cuDNN v5rc is supported in Theano master version. So it dropped cuDNN v3 support. Theano 0.8.0
and 0.8.1 support only cuDNN v3 and v4. Theano 0.8.2 will support only v4 and v5.
Note: Starting in cuDNN v3, multiple convolution implementations are offered and it is possible to use
heuristics to automatically choose a convolution implementation well suited to the parameters of the convolution.
The Theano flag dnn.conv.algo_fwd allows to specify the cuDNN convolution implementation that
Theano should use for forward convolutions. Possible values include :
• small (default) : use a convolution implementation with small memory usage
• none : use a slower implementation with minimal memory usage
• large : use a sometimes faster implementation with large memory usage
• fft : use the Fast Fourrier Transform implementation of convolution (very high memory usage)
• fft_tiling : use the Fast Fourrier Transform implementation of convolution with tiling (high
memory usage, but less then fft)
• guess_once : the first time a convolution is executed, the implementation to use is chosen according
to cuDNN’s heuristics and reused for every subsequent execution of the convolution.
• guess_on_shape_change : like guess_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
• time_once : the first time a convolution is executed, every convolution implementation offered by
cuDNN is executed and timed. The fastest is reused for every subsequent execution of the convolution.
• time_on_shape_change : like time_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
The Theano flag dnn.conv.algo_bwd_filter and dnn.conv.algo_bwd_data allows to specify
the cuDNN convolution implementation that Theano should use for gradient convolutions. Possible values
include :
• none (default) : use the default non-deterministic convolution implementation
• deterministic : use a slower but deterministic implementation
• fft : use the Fast Fourrier Transform implementation of convolution (very high memory usage)
• guess_once : the first time a convolution is executed, the implementation to use is chosen according
to cuDNN’s heuristics and reused for every subsequent execution of the convolution.
• guess_on_shape_change : like guess_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
• time_once : the first time a convolution is executed, every convolution implementation offered by
cuDNN is executed and timed. The fastest is reused for every subsequent execution of the convolution.
• time_on_shape_change : like time_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
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• (algo_bwd_data only) fft_tiling : use the Fast Fourrier Transform implementation of convolution with tiling (high memory usage, but less then fft)
• (algo_bwd_data only) small : use a convolution implementation with small memory usage
guess_* and time_* flag values take into account the amount of available memory when selecting an implementation. This means that slower implementations might be selected if not enough memory is available
for the faster implementations.
Note: Normally you should not call GPU Ops directly, but the CPU interface currently does not allow all
options supported by cuDNN ops. So it is possible that you will need to call them manually.
Note: The documentation of CUDNN tells that, for the 2 following operations, the reproducibility is
not guaranteed with the default implementation: cudnnConvolutionBackwardFilter and cudnnConvolutionBackwardData. Those correspond to the gradient wrt the weights and the gradient wrt the input of the
convolution. They are also used sometimes in the forward pass, when they give a speed up.
The Theano flag dnn.conv.algo_bwd can be use to force the use of a slower but deterministic convolution implementation.
Note: There is a problem we do not understand yet when cudnn paths are used with symbolic links. So
avoid using that.
Note: cudnn.so* must be readable and executable by everybody. cudnn.h must be readable by everybody.
Functions
theano.sandbox.cuda.dnn.dnn_conv(img, kerns, border_mode=’valid’, subsample=(1,
1), conv_mode=’conv’, direction_hint=None,
workmem=None, algo=None, precision=None)
GPU convolution using cuDNN from NVIDIA.
The memory layout to use is ‘bc01’, that is ‘batch’, ‘channel’, ‘first dim’, ‘second dim’ in that order.
Parameters
• img – Images to do the convolution over.
• kerns – Convolution filters.
• border_mode – One of ‘valid’, ‘full’, ‘half’; additionally, the padding size can
be directly specified by an integer or a pair of integers (as a tuple), specifying the
amount of zero padding added to _both_ the top and bottom (first entry) and left
and right (second entry) sides of the image.
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• subsample – Perform subsampling of the output (default: (1, 1)).
• conv_mode – Perform convolution (kernels flipped) or cross-correlation. One
of ‘conv’, ‘cross’ (default: ‘conv’).
• direction_hint – Used by graph optimizers to change algorithm choice.
By default, GpuDnnConv will be used to carry out the convolution. If border_mode is ‘valid’, subsample is (1,1) and direction_hint is ‘bprop weights’,
it will use GpuDnnConvGradW. If border_mode is ‘full’, subsample is (1,1) and
direction_hint is ‘bprop inputs’, it will use GpuDnnConvGradI. This parameter is
used internally by graph optimizers and may be removed at any time without a
deprecation period. You have been warned.
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'small', 'large', 'fft',
'guess_once', 'guess_on_shape_change', 'time_once',
'time_on_shape_change'}) – Convolution implementation to use. Some
of its values may require certain versions of cuDNN to be installed. Default is
the value of config.dnn.conv.algo_fwd.
• precision
({'as_input', 'float16', 'float32',
'float64'}) – Description of the dtype in which the computation of the
convolution should be done. Possible values are ‘as_input’, ‘float16’, ‘float32’
and ‘float64’. Default is the value of config.dnn.conv.precision.
theano.sandbox.cuda.dnn.dnn_pool(img, ws, stride=(1, 1), mode=’max’, pad=(0, 0))
GPU pooling using cuDNN from NVIDIA.
The memory layout to use is ‘bc01’, that is ‘batch’, ‘channel’, ‘first dim’, ‘second dim’ in that order.
Parameters
• img – Images to do the pooling over.
• ws – Subsampling window size.
• stride – Subsampling stride (default: (1, 1)).
• mode ({'max', 'average_inc_pad', 'average_exc_pad}) –
• pad – (pad_h, pad_w) padding information. pad_h is the number of zero-valued
pixels added to each of the top and bottom borders. pad_w is the number of
zero-valued pixels added to each of the left and right borders.
Warning: The cuDNN library only works with GPU that have a compute capability of 3.0 or
higer. This means that older GPU will not work with this Op.
Notes
This Op implements the ignore_border=True of max_pool_2d.
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Convolution Ops
class theano.sandbox.cuda.dnn.GpuDnnConvDesc(border_mode,
subsample=(1,
1),
conv_mode=’conv’,
precision=’float32’)
This Op builds a convolution descriptor for use in the other convolution operations.
See the doc of dnn_conv() for a description of the parameters.
class theano.sandbox.cuda.dnn.GpuDnnConv(workmem=None,
algo=None)
The forward convolution.
inplace=False,
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
• workmem – deprecated, use parameter algo instead.
• algo ({'none', 'small', 'large', 'fft', 'fft_tiling',
'guess_once', 'winograd',) – ‘guess_on_shape_change’, ‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_fwd.
static get_out_shape(ishape, kshape, border_mode, subsample)
This function computes the output shape for a convolution with the specified parameters. ishape
and kshape can be symbolic or scalar.
class theano.sandbox.cuda.dnn.GpuDnnConv3d(workmem=None,
algo=None)
The forward convolution.
inplace=False,
Parameters
• image –
• kernel –
• descr – The convolution descriptor
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'small', 'fft_tiling', 'winograd',
'guess_once',)
–
‘guess_on_shape_change’,
‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_fwd.
static get_out_shape(ishape, kshape, border_mode, subsample)
This function computes the output shape for a convolution with the specified parameters. ishape
and kshape can be symbolic or scalar.
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class theano.sandbox.cuda.dnn.GpuDnnConvGradW(inplace=False,
algo=None)
The convolution gradient with respect to the weights.
workmem=None,
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'deterministic', 'fft', 'small',
'guess_once',)
–
‘guess_on_shape_change’,
‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_bwd_filter.
class theano.sandbox.cuda.dnn.GpuDnnConv3dGradW(inplace=False,
workmem=None, algo=None)
The convolution gradient with respect to the weights.
Parameters
• image –
• kernel –
• descr – The convolution descriptor
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'small', 'guess_once',
'guess_on_shape_change',) – ‘time_once’, ‘time_on_shape_change’}
Default is the value of config.dnn.conv.algo_bwd_filter.
class theano.sandbox.cuda.dnn.GpuDnnConvGradI(inplace=False,
algo=None)
The convolution gradient with respect to the inputs.
workmem=None,
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'deterministic', 'fft', 'fft_tiling',
'winograd', 'guess_once',) – ‘guess_on_shape_change’, ‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_bwd_data.
class theano.sandbox.cuda.dnn.GpuDnnConv3dGradI(inplace=False,
workmem=None, algo=None)
The convolution gradient with respect to the inputs.
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Parameters
• image –
• kernel –
• descr – The convolution descriptor
• workmem – deprecated, use parameter algo instead.
• algo
({'none', 'deterministic, 'fft_tiling',
'winograd', 'guess_once',) – ‘guess_on_shape_change’, ‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_bwd_data.
Pooling Ops
class theano.sandbox.cuda.dnn.GpuDnnPoolDesc(ws=(1,
1),
stride=(1,
mode=’max’, pad=(0, 0))
This Op builds a pooling descriptor for use in the other pooling operations.
1),
Parameters
• ws – Windows size.
• stride – (dx, dy).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ correspond to ‘average_inc_pad’.
• pad – (pad_h, pad_w) padding information. pad_h is the number of zero-valued
pixels added to each of the top and bottom borders. pad_w is the number of
zero-valued pixels added to each of the left and right borders.
class theano.sandbox.cuda.dnn.GpuDnnPool(mode=’max’)
Pooling.
Parameters
• img – The image 4d or 5d tensor.
• ws – Windows size.
• stride – (dx, dy).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ correspond to ‘average_inc_pad’.
• pad – (padX, padY) padding information. padX is the size of the left and right
borders, padY is the size of the top and bottom borders.
class theano.sandbox.cuda.dnn.GpuDnnPoolGrad(mode=’max’)
The pooling gradient.
Parameters
• inp – The input of the pooling.
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• out – The output of the pooling in the forward.
• inp_grad – Same size as out, but is the corresponding gradient information.
• ws – Windows size.
• stride – (dx, dy).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ correspond to ‘average_inc_pad’.
• pad – (padX, padY) padding information. padX is the size of the left and right
borders, padY is the size of the top and bottom borders.
Softmax Ops
class theano.sandbox.cuda.dnn.GpuDnnSoftmax(tensor_format, algo, mode)
Op for the cuDNN Softmax.
Parameters
• tensor_format – Always set to ‘bc01’.
• algo ({'fast', 'accurate'}) – Indicating whether computations should
be optimized for speed or accuracy respectively.
• mode ({'instance', 'channel'}) – Indicating whether the softmax
should be computed per image across ‘c01’ or per spatial location ‘01’ per image across ‘c’.
class theano.sandbox.cuda.dnn.GpuDnnSoftmaxGrad(tensor_format, algo, mode)
Op for the cuDNN SoftmaxGrad.
Parameters
• tensor_format – Always set to ‘bc01’.
• algo ({'fast', 'accurate'}) – Indicating whether computations should
be optimized for speed or accuracy respectively.
• mode ({'instance', 'channel'}) – Indicating whether the softmax
should be computed per image across ‘c01’ or per spatial location ‘01’ per image across ‘c’.
theano.sandbox.gpuarray – The (new) GPU backend
List of gpuarray Ops implemented
Normally you should not call directly those Ops! Theano should automatically transform cpu ops to their
gpu equivalent. So this list is just useful to let people know what is implemented on the gpu.
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Basic Op
class theano.sandbox.gpuarray.basic_ops.GpuAlloc(context_name,
set_0=False)
Allocate initialized memory on the GPU.
mem-
Parameters
• context_name (str) – The name of the context in which to allocate memory
• memset_0 (bool) – It’s only an optimized version. True, it means the value is
always 0, so the c code call memset as it is faster.
class theano.sandbox.gpuarray.basic_ops.GpuAllocEmpty(dtype, context_name)
Allocate uninitialized memory on the GPU.
class theano.sandbox.gpuarray.basic_ops.GpuContiguous(use_c_code=’/usr/bin/g++’)
Return a C contiguous version of the input.
This may either pass the object as-is (if already C contiguous) or make a copy.
class theano.sandbox.gpuarray.basic_ops.GpuEye(dtype=None,
text_name=None)
Eye for GPU.
con-
class theano.sandbox.gpuarray.basic_ops.GpuFromHost(context_name)
Transfer data to GPU.
class theano.sandbox.gpuarray.basic_ops.GpuJoin(use_c_code=’/usr/bin/g++’)
Join for GPU.
class theano.sandbox.gpuarray.basic_ops.GpuKernelBase
Base class for operations that need to compile kernels.
It is not mandatory to use this class, but it helps with a lot of the small things that you have to pay
attention to.
gpu_kernels(node, name)
This is the method to override. This should return an iterable of Kernel objects that describe the
kernels this op will need.
kernel_version(node)
If you override c_code_cache_version_apply(), call this method to have the version
of the kernel support code and device.
Parameters node (apply node) – The node that we need the cache version for.
class theano.sandbox.gpuarray.basic_ops.GpuReshape(ndim, name=None)
Reshape for GPU variables.
class theano.sandbox.gpuarray.basic_ops.GpuSplit(len_splits)
Split for GPU.
class theano.sandbox.gpuarray.basic_ops.GpuToGpu(context_name)
Transfer data between GPUs.
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class theano.sandbox.gpuarray.basic_ops.HostFromGpu(use_c_code=’/usr/bin/g++’)
Transfer data to CPU.
class theano.sandbox.gpuarray.basic_ops.Kernel(code, params, name, flags, codevar=None, binvar=None, objvar=None)
This class groups together all the attributes of a gpu kernel.
theano.sandbox.gpuarray.basic_ops.as_gpuarray_variable(x, context_name)
This will attempt to convert x into a variable on the GPU.
It can take either a value of another variable. If x is already suitable, it will be returned as-is.
Parameters
• x – Object to convert
• context_name (str or None) – target context name for the result
theano.sandbox.gpuarray.basic_ops.infer_context_name(*vars)
Infer the context name to use from the inputs given
Blas Op
class theano.sandbox.gpuarray.blas.GpuDot22(use_c_code=’/usr/bin/g++’)
Dot22 on the GPU.
class theano.sandbox.gpuarray.blas.GpuGemm(inplace=False)
Gemm on the GPU.
class theano.sandbox.gpuarray.blas.GpuGemv(inplace=False)
Gemv on the GPU.
class theano.sandbox.gpuarray.blas.GpuGer(inplace=False)
Ger on the GPU.
class theano.sandbox.gpuarray.nerv.Gemm16(relu=False, inplace=False)
Gemm for float16 using the nervena kernels.
Elemwise Op
theano.sandbox.gpuarray.elemwise.GpuCAReduce
alias of GpuCAReduceCPY
class theano.sandbox.gpuarray.elemwise.GpuCAReduceCPY(scalar_op, axis=None,
dtype=None,
acc_dtype=None)
CAReduce that reuse the python code from gpuarray.
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class theano.sandbox.gpuarray.elemwise.GpuCAReduceCuda(scalar_op,
axis=None,
reduce_mask=None,
dtype=None,
acc_dtype=None,
pre_scalar_op=None)
GpuCAReduceCuda is a Reduction along some dimensions by a scalar op.
Parameters
• reduce_mask – The dimensions along which to reduce. The reduce_mask is a
tuple of booleans (actually integers 0 or 1) that specify for each input dimension,
whether to reduce it (1) or not (0).
• pre_scalar_op – If present, must be a scalar op with only 1 input. We will
execute it on the input value before reduction.
Examples
When scalar_op is a theano.scalar.basic.Add instance:
•reduce_mask == (1,) sums a vector to a scalar
•reduce_mask == (1,0) computes the sum of each column in a matrix
•reduce_mask == (0,1) computes the sum of each row in a matrix
•reduce_mask == (1,1,1) computes the sum of all elements in a 3-tensor.
Notes
Any reduce_mask of all zeros is a sort of ‘copy’, and may be removed during graph optimization.
This Op is a work in progress.
This op was recently upgraded from just GpuSum a general CAReduce. Not many code cases are
supported for scalar_op being anything other than scal.Add instances yet.
Important note: if you implement new cases for this op, be sure to benchmark them and make sure
that they actually result in a speedup. GPUs are not especially well-suited to reduction operations so
it is quite possible that the GPU might be slower for some cases.
c_code_reduce_01X(sio, node, name, x, z, fail, N)
Parameters N – The number of 1 in the pattern N=1 -> 01, N=2 -> 011 N=3 ->0111
Work for N=1,2,3.
supports_c_code(inputs)
Returns True if the current op and reduce pattern has functioning C code.
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class theano.sandbox.gpuarray.elemwise.GpuDimShuffle(input_broadcastable,
new_order,
inplace=False)
DimShuffle on the GPU.
class theano.sandbox.gpuarray.elemwise.GpuElemwise(scalar_op,
place_pattern=None,
name=None,
nfunc_spec=None,
openmp=None)
Elemwise on the GPU.
in-
exception theano.sandbox.gpuarray.elemwise.SupportCodeError
We do not support certain things (such as the C++ complex struct).
Subtensor Op
class theano.sandbox.gpuarray.subtensor.GpuAdvancedIncSubtensor1(inplace=False,
set_instead_of_inc=False)
Implement AdvancedIncSubtensor1 on the gpu.
class theano.sandbox.gpuarray.subtensor.GpuAdvancedIncSubtensor1_dev20(inplace=False,
set_instead_of_inc=F
Implement AdvancedIncSubtensor1 on the gpu, but use function only avail on compute capability 2.0
and more recent.
make_node(x, y, ilist)
It differs from GpuAdvancedIncSubtensor1 in that it makes sure the indexes are of type long.
class theano.sandbox.gpuarray.subtensor.GpuAdvancedSubtensor1(sparse_grad=False)
AdvancedSubrensor1 on the GPU.
class theano.sandbox.gpuarray.subtensor.GpuIncSubtensor(idx_list,
inplace=False,
set_instead_of_inc=False,
destroyhandler_tolerate_aliased=None)
Implement IncSubtensor on the gpu.
Notes
The optimization to make this inplace is in tensor/opt. The same optimization handles IncSubtensor
and GpuIncSubtensor. This Op has c_code too; it inherits tensor.IncSubtensor’s c_code. The helper
methods like do_type_checking(), copy_of_x(), etc. specialize the c_code for this Op.
copy_into(view, source)
Parameters
• view (string) – C code expression for an array.
• source (string) – C code expression for an array.
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Returns C code expression to copy source into view, and 0 on success.
Return type str
copy_of_x(x)
Parameters x – A string giving the name of a C variable pointing to an array.
Returns C code expression to make a copy of x.
Return type str
Notes
Base class uses PyArrayObject *, subclasses may override for different types of arrays.
do_type_checking(node)
Should raise NotImplementedError if c_code does not support the types involved in this node.
get_helper_c_code_args()
Return a dictionary of arguments to use with helper_c_code.
make_view_array(x, view_ndim)
//TODO
Parameters
• x – A string identifying an array to be viewed.
• view_ndim – A string specifying the number of dimensions to have in the
view. This doesn’t need to actually set up the view with the right indexing; we’ll
do that manually later.
class theano.sandbox.gpuarray.subtensor.GpuSubtensor(idx_list)
Subtensor on the GPU.
Nnet Op
class theano.sandbox.gpuarray.nnet.GpuCrossentropySoftmax1HotWithBiasDx(use_c_code=’/usr/b
Implement CrossentropySoftmax1HotWithBiasDx on the gpu.
Gradient wrt x of the CrossentropySoftmax1Hot Op.
class theano.sandbox.gpuarray.nnet.GpuCrossentropySoftmaxArgmax1HotWithBias(use_c_code=
Implement CrossentropySoftmaxArgmax1HotWithBias on the gpu.
class theano.sandbox.gpuarray.nnet.GpuSoftmax(use_c_code=’/usr/bin/g++’)
Implement Softmax on the gpu.
class theano.sandbox.gpuarray.nnet.GpuSoftmaxWithBias(use_c_code=’/usr/bin/g++’)
Implement SoftmaxWithBias on the gpu.
class theano.sandbox.gpuarray.neighbours.GpuImages2Neibs(mode=’valid’)
Images2Neibs for the GPU.
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theano.sandbox.gpuarray.dnn – cuDNN
cuDNN is an NVIDIA library with functionality used by deep neural networks. It provides optimized
versions of some operations like the convolution. cuDNN is not currently installed with CUDA. You must
download and install it yourself.
To install it, decompress the downloaded file and make the *.h and *.so* files available to the compilation
environment. There are at least three possible ways of doing so:
• The easiest is to include them in your CUDA installation. Copy the *.h files to CUDA_ROOT/
include and the *.so* files to CUDA_ROOT/lib64 (by default, CUDA_ROOT is /usr/
local/cuda on Linux).
• Alternatively, on Linux, you can set the environment variables LD_LIBRARY_PATH,
LIBRARY_PATH and CPATH to the directory extracted from the download. If needed, separate
multiple directories with : as in the PATH environment variable.
example:
export LD_LIBRARY_PATH=/home/user/path_to_CUDNN_folder/lib64:$LD_LIBRARY_
˓→PATH
export CPATH=/home/user/path_to_CUDNN_folder/include:$CPATH
export LIBRARY_PATH=/home/user/path_to_CUDNN_folder/lib64:$LD_LIBRARY_
˓→PATH
• And as a third way, also on Linux, you can copy the *.h files to /usr/include and the *.so*
files to /lib64.
By default, Theano will detect if it can use cuDNN. If so, it will use it. If not, Theano optimizations will not
introduce cuDNN ops. So Theano will still work if the user did not introduce them manually.
To get an error if Theano can not use cuDNN, use this Theano flag: optimizer_including=cudnn.
Note: cuDNN v5rc is supported in Theano master version. So it dropped cuDNN v3 support. Theano 0.8.0
and 0.8.1 support only cuDNN v3 and v4. Theano 0.8.2 will support only v4 and v5.
Note: Starting in cuDNN v3, multiple convolution implementations are offered and it is possible to use
heuristics to automatically choose a convolution implementation well suited to the parameters of the convolution.
The Theano flag dnn.conv.algo_fwd allows to specify the cuDNN convolution implementation that
Theano should use for forward convolutions. Possible values include :
• small (default) : use a convolution implementation with small memory usage
• none : use a slower implementation with minimal memory usage
• large : use a sometimes faster implementation with large memory usage
• fft : use the Fast Fourrier Transform implementation of convolution (very high memory usage)
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• guess_once : the first time a convolution is executed, the implementation to use is chosen according
to cuDNN’s heuristics and reused for every subsequent execution of the convolution.
• guess_on_shape_change : like guess_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
• time_once : the first time a convolution is executed, every convolution implementation offered by
cuDNN is executed and timed. The fastest is reused for every subsequent execution of the convolution.
• time_on_shape_change : like time_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
The Theano flag dnn.conv.algo_bwd allows to specify the cuDNN convolution implementation that
Theano should use for gradient convolutions. Possible values include :
• none (default) : use the default non-deterministic convolution implementation
• deterministic : use a slower but deterministic implementation
• fft : use the Fast Fourrier Transform implementation of convolution (very high memory usage)
• guess_once : the first time a convolution is executed, the implementation to use is chosen according
to cuDNN’s heuristics and reused for every subsequent execution of the convolution.
• guess_on_shape_change : like guess_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
• time_once : the first time a convolution is executed, every convolution implementation offered by
cuDNN is executed and timed. The fastest is reused for every subsequent execution of the convolution.
• time_on_shape_change : like time_once but a new convolution implementation selected
every time the shapes of the inputs and kernels don’t match the shapes from the last execution.
guess_* and time_* flag values take into account the amount of available memory when selecting an implementation. This means that slower implementations might be selected if not enough memory is available
for the faster implementations.
Note: Normally you should not call GPU Ops directly, but the CPU interface currently does not allow all
options supported by cuDNN ops. So it is possible that you will need to call them manually.
Note: The documentation of CUDNN tells that, for the 2 following operations, the reproducibility is
not guaranteed with the default implementation: cudnnConvolutionBackwardFilter and cudnnConvolutionBackwardData. Those correspond to the gradient wrt the weights and the gradient wrt the input of the
convolution. They are also used sometimes in the forward pass, when they give a speed up.
The Theano flag dnn.conv.algo_bwd can be use to force the use of a slower but deterministic convolution implementation.
Note: There is a problem we do not understand yet when cudnn paths are used with symbolic links. So
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avoid using that.
Note: cudnn.so* must be readable and executable by everybody. cudnn.h must be readable by everybody.
Functions
theano.sandbox.gpuarray.dnn.dnn_conv(img, kerns, border_mode=’valid’, subsample=(1, 1), conv_mode=’conv’, direction_hint=None,
workmem=None,
algo=None, precision=None)
GPU convolution using cuDNN from NVIDIA.
The memory layout to use is ‘bc01’, that is ‘batch’, ‘channel’, ‘first dim’, ‘second dim’ in that order.
Parameters
• img – Images to do the convolution over.
• kerns – Convolution filters.
• border_mode – One of ‘valid’, ‘full’, ‘half’; additionally, the padding size
could be directly specified by an integer or a pair of integers.
• subsample – Perform subsampling of the output (default: (1, 1)).
• conv_mode – Perform convolution (kernels flipped) or cross-correlation. One
of ‘conv’, ‘cross’ (default: ‘conv’).
• direction_hint – Used by graph optimizers to change algorithm choice. By
default, GpuDnnConv will be used to carry out the convolution. If border_mode
is ‘valid’, subsample is (1, 1) and direction_hint is ‘bprop weights’, it will use
GpuDnnConvGradW. If border_mode is ‘full’, subsample is (1, 1) and direction_hint is not ‘forward!’, it will use GpuDnnConvGradI. This parameter is used
internally by graph optimizers and may be removed at any time without a deprecation period. You have been warned.
• algo
({'none', 'small', 'large', 'fft',
'guess_once', 'guess_on_shape_change', 'time_once',
'time_on_shape_change'}) – Convolution implementation to use. Some
of its values may require certain versions of cuDNN to be installed. Default is
the value of config.dnn.conv.algo_fwd.
• precision
({'as_input', 'float16', 'float32',
'float64'}) – Description of the dtype in which the computation of the
convolution should be done. Possible values are ‘as_input’, ‘float16’, ‘float32’
and ‘float64’. Default is the value of config.dnn.conv.precision.
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Warning: The cuDNN library only works with GPUs that have a compute capability of 3.0 or
higer. This means that older GPUs will not work with this Op.
theano.sandbox.gpuarray.dnn.dnn_pool(img, ws, stride=(1, 1), mode=’max’, pad=(0,
0))
GPU pooling using cuDNN from NVIDIA.
The memory layout to use is ‘bc01’, that is ‘batch’, ‘channel’, ‘first dim’, ‘second dim’ in that order.
ws, stride and pad must have the same length.
Parameters
• img – Images to do the pooling over.
• ws (tuple) – Subsampling window size.
• stride (tuple) – Subsampling stride (default: (1, 1)).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
• pad (tuple) – (padX, padY) or (padX, padY, padZ) default: (0, 0)
Warning: The cuDNN library only works with GPU that have a compute capability of 3.0 or
higer. This means that older GPU will not work with this Op.
Notes
This Op implements the ignore_border=True of max_pool_2d.
Convolution Ops
class theano.sandbox.gpuarray.dnn.GpuDnnConvDesc(border_mode, subsample=(1,
1), conv_mode=’conv’, precision=’float32’)
This Op builds a convolution descriptor for use in the other convolution operations.
See the doc of dnn_conv() for a description of the parameters
class theano.sandbox.gpuarray.dnn.GpuDnnConv(algo=None, inplace=False)
The forward convolution.
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
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• algo ({'small', 'none', 'large', 'fft', 'fft_tiling',
'winograd', 'guess_once',) – ‘guess_on_shape_change’, ‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_fwd.
static get_out_shape(ishape, kshape, border_mode, subsample)
This function computes the output shape for a convolution with the specified parameters. ishape
and kshape can be symbolic or scalar.
class theano.sandbox.gpuarray.dnn.GpuDnnConvGradW(inplace=False, algo=None)
The convolution gradient with respect to the weights.
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
• algo
({'none', 'deterministic', 'fft', 'small',
'guess_once',)
–
‘guess_on_shape_change’,
‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_bwd_filter.
class theano.sandbox.gpuarray.dnn.GpuDnnConvGradI(inplace=False, algo=None)
The convolution gradient with respect to the inputs.
Parameters
• image –
• kernel –
• descr – The convolution descriptor.
• algo
({'none', 'deterministic', 'fft', 'fft_tiling',
'winograd', 'guess_once',) – ‘guess_on_shape_change’, ‘time_once’,
‘time_on_shape_change’} Default is the value of config.dnn.conv.
algo_bwd_data.
Pooling Ops
class theano.sandbox.gpuarray.dnn.GpuDnnPoolDesc(ws=(1, 1), stride=(1, 1),
mode=’max’, pad=(0, 0))
This Op builds a pooling descriptor for use in the other pooling operations.
ws, stride and pad must have the same length.
Parameters
• ws (tuple) – Window size.
• stride (tuple) – (dx, dy) or (dx, dy, dz).
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• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ corresponds to ‘average_inc_pad’.
• pad (tuple) – (padX, padY) or (padX, padY, padZ)
class theano.sandbox.gpuarray.dnn.GpuDnnPool(mode=’max’)
Parameters
• img (tensor) – The image 4d or 5d tensor.
• ws (tensor) – Window size.
• stride (tensor) – (dx, dy) or (dx, dy, dz).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ corresponds to ‘average_inc_pad’.
• pad (tensor) – (padX, padY) or (padX, padY, padZ)
class theano.sandbox.gpuarray.dnn.GpuDnnPoolGrad(mode=’max’)
The pooling gradient.
Parameters
• inp – The input of the pooling.
• out – The output of the pooling in the forward.
• out_grad – Same size as out, but is the corresponding gradient information.
• ws (tensor variable) – Window size.
• stride (tensor variable) – (dx, dy) or (dx, dy, dz).
• mode ({'max', 'average_inc_pad', 'average_exc_pad'}) –
The old deprecated name ‘average’ corresponds to ‘average_inc_pad’.
• pad (tensor) – (padX, padY) or (padX, padY, padZ)
Softmax Ops
class theano.sandbox.gpuarray.dnn.GpuDnnSoftmax(algo, mode)
Op for the cuDNN Softmax.
algo [{‘fast’, ‘accurate’, ‘log’}] Indicating whether, respectively, computations should be optimized
for speed, for accuracy, or if cuDNN should rather compute the log-softmax instead.
mode [{‘instance’, ‘channel’}] Indicating whether the softmax should be computed per image across
‘c01’ or per spatial location ‘01’ per image across ‘c’.
class theano.sandbox.gpuarray.dnn.GpuDnnSoftmaxGrad(algo, mode)
Op for the cuDNN SoftmaxGrad.
Parameters
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• algo – ‘fast’, ‘accurate’ or ‘log’ indicating whether, respectively, computations
should be optimized for speed, for accuracy, or if cuDNN should rather compute
the gradient of the log-softmax instead.
• mode – ‘instance’ or ‘channel’ indicating whether the softmax should be computed per image across ‘c01’ or per spatial location ‘01’ per image across ‘c’.
theano.sandbox.gpuarray.type – Type classes
class theano.sandbox.gpuarray.type.GpuArrayConstant(type, data, name=None)
A constant representing a value on a certain GPU.
This supports all the operations that TensorType supports.
See also:
Constant
class theano.sandbox.gpuarray.type.GpuArraySharedVariable(name,
type,
value, strict, allow_downcast=None,
container=None)
A variable representing a shared value on a certain GPU.
This supports all the operations that TensorType supports.
See also:
SharedVariable
class theano.sandbox.gpuarray.type.GpuArrayType(dtype, broadcastable, context_name=None, name=None)
The type that represents an array on a gpu.
The dtype indicates what scalar data type the elements of variables of this type will be.
broadcastable indicates whether each dimension is broadcastable or not (to be broadcastable a dimension must always be of length 1).
The context_name is the name of the context on will values of variables of this type will be stored.
Parameters
• dtype (str) – The name of a numpy dtype
• broadcastable (tuple of bools) – A tuple that indicates both the number of dimensions (by its length) and whether those dimensions are broadcastable
or not (by the boolean values).
• context_name (str) – The name of the context the that this type is attached
to (default: None, which is the context specified by config.device).
• name (string, optional) – A name for the type that will be used in printouts.
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dtype
str – Data type used for scalar elements of variables.
broadcastable
tuple of bools – Indicates whether the dimensions are broadcastable or not.
ndim
int – The number of dimensions
context_name
str – The name of a gpu context on which variables will have their values.
name
str – A string used to print the type if given.
typecode
int – The gpuarray typecode for dtype
See also:
theano.gof.type.PureType
Constant
alias of GpuArrayConstant
SharedVariable
alias of GpuArraySharedVariable
Variable
alias of GpuArrayVariable
context
The context object mapped to the type’s context_name. This is a property.
dtype_specs()
Return a tuple (python type, c type, numpy typenum) that corresponds to self.dtype.
This function is used internally as part of C code generation.
class theano.sandbox.gpuarray.type.GpuArrayVariable(type, owner=None, index=None, name=None)
A variable representing a computation on a certain GPU.
This supports all the operations that TensorType supports.
See also:
Variable
class theano.sandbox.gpuarray.type.GpuContextType
Minimal type used for passing contexts to nodes.
This Type is not a complete type and should never be used for regular graph operations.
theano.sandbox.gpuarray.type.get_context(name)
Retrive the context associated with a name.
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Return the context object mapped to ref that was previously register through reg_context().
Trying to get the context for an unregistered ref will raise a exception.
Parameters name (hashable object) – Name associated with the context we want
(usually a string)
theano.sandbox.gpuarray.type.gpuarray_shared_constructor(value,
name=None,
strict=False,
allow_downcast=None,
borrow=False,
broadcastable=None,
target=None)
SharedVariable constructor for GpuArrayType.
See theano.shared().
theano.sandbox.gpuarray.type.list_contexts()
Return an iterable of all the registered context names.
theano.sandbox.gpuarray.type.reg_context(name, ctx)
Register a context by mapping it to a name.
The context must be of type GpuContext and the name can be anything hashable (but is usually a
string). Only one context can be registered per name and the second registration for a given name will
raise an error.
Parameters
• name (hashable object) – Name to associate the context with (usually a
string)
• ctx (GpuContext) – Context instance
Utility functions
Optimisation
theano.sandbox.gpuarray.opt_util.alpha_merge(cls, alpha_in, beta_in)
Decorator to merge multiplication by a scalar on the output.
This will find a pattern of scal * <yourop>(some, params, alpha, beta) and update it so that the scalar
multiplication happens as part of your op.
The op needs to accept an alpha and a beta scalar which act this way:
out = Op() * alpha + out_like * beta
Where out_like is a buffer that has the same size as the output and gets added to the “real” output of
the operation. An example of an operation that respects this pattern is GEMM from blas.
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The decorated function must have this signature:
maker(node, *inputs)
The node argument you recieve is the original apply node that contains your op. You should use it
to grab relevant properties for your op so that the new version performs the same computation. The
*inputs parameters contains the new inputs for your op. You MUST use those inputs instead of the
ones on node. Note that this function can be as simple as:
def maker(node, *inputs):
return node.op(*inputs)
Parameters
• cls (op class) – The class of the op you want to merge
• alpha_in (int) – The input index for the alpha scalar for your op (in
node.inputs).
• beta_in (int) – The input index for the beta scalar for your op (in node.inputs).
Returns an unregistered local optimizer that has the same name as the decorated function.
Return type local optimizer
Notes
This was factored out since the code to deal with intervening transfers and correctness in the presence
of different values of alpha and beta scaling factors is not trivial.
theano.sandbox.gpuarray.opt_util.find_node(v, cls, ignore_clients=False)
Find the node that has an op of of type cls in v.
This digs through possibly redundant transfers to for the node that has the type cls. If ignore_clients
is False (the default) it will only dig through nodes that have a single client to avoid duplicating
computations.
Parameters
• v – The variable to dig through
• cls (Op class) – The type of the node we are looking for
• ignore_clients (bool, optional) – Whether to ignore multiple clients
or not.
theano.sandbox.gpuarray.opt_util.grab_cpu_scalar(v, nd)
Get a scalar variable value from the tree at v.
This function will dig through transfers and dimshuffles to get the constant value. If no such constant
is found, it returns None.
Parameters
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• v – Theano variable to extract the constant value from.
• nd (int) – Expected number of dimensions for the variable (for broadcasted
constants).
theano.sandbox.gpuarray.opt_util.inplace_allocempty(op, idx)
Wrapper to make an inplace optimization that deals with AllocEmpty
This will duplicate the alloc input if it has more than one client to allow the op to work on it inplace.
The decorated function must have this signature:
maker(node, inputs)
The node argument you recieve is the original apply node that contains your op. You should use it
to grab relevant properties for your op so that the new version performs the same computation. You
should also switch the op to work inplace. The *inputs parameters contains the new inputs for your
op. You MUST use those inputs instead of the ones on node. Note that this function can be as simple
as:
def maker(node, inputs):
return [node.op.__class__(inplace=True)(*inputs)]
Parameters
• op (op class) – The op class to look for to make inplace
• idx (int) – The index of the (possibly) AllocEmpty input (in node.inputs).
Returns an unregistered inplace local optimizer that has the same name as the decorated
function.
Return type local optimizer
theano.sandbox.gpuarray.opt_util.is_equal(var, val)
Returns True if var is always equal to val.
This will only return True if the variable will always be equal to the value. If it might not be true in
some cases then it returns False.
Parameters
• var – Variable to compare
• val – Python value
theano.sandbox.gpuarray.opt_util.output_merge(cls, alpha_in, beta_in, out_in)
Decorator to merge addition by a value on the output.
This will find a pattern of val * <yourop>(some, params, alpha, beta, out_like) and update it so that
the addtition happens as part of your op.
The op needs to accept an alpha and a beta scalar which act this way:
out = Op() * alpha + out_like * beta
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Where out_like is a buffer that has the same size as the output and gets added to the “real” output of
the operation. An example of an operation that respects this pattern is GEMM from blas.
The decorated function must have this signature:
maker(node, *inputs)
The node argument you recieve is the original apply node that contains your op. You should use it
to grab relevant properties for your op so that the new version performs the same computation. The
*inputs parameters contains the new inputs for your op. You MUST use those inputs instead of the
ones on node. Note that this function can be as simple as:
def maker(node, *inputs):
return node.op(*inputs)
Parameters
• cls (op class) – The class of the op you want to merge
• alpha_in (int) – The input index for the alpha scalar for your op (in
node.inputs).
• beta_in (int) – The input index for the beta scalar for your op (in node.inputs).
• out_in (int) – The input index for the out_like input for your op (in
node.inputs).
Returns an unregistered local optimizer that has the same name as the decorated function.
Return type local optimizer
Notes
This was factored out since the code to deal with intervening transfers and correctness in the presence
of different values of alpha and beta scaling factors is not trivial.
This also correctly handles the case where the added value is broadcasted (by not performing the
replacement).
Kernel generation
Helper routines for generating gpu kernels for nvcc.
theano.sandbox.gpuarray.kernel_codegen.code_version(version)
Decorator to support version-based cache mechanism.
theano.sandbox.gpuarray.kernel_codegen.inline_reduce(N, buf, pos, count,
manner_fn)
Return C++ code for a function that reduces a contiguous buffer.
Parameters
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• N – Length of the buffer.
• buf – buffer pointer.
• pos – Index of executing thread.
• count – Number of executing threads.
• manner_fn – A function that accepts strings of arguments a and b, and returns
c code for their reduction.
return “%(a)s + %(b)s”
for a sum reduction.
Notes
buf should be in gpu shared memory, we access it many times.
This function leaves the answer in position 0 of the buffer. The rest of the buffer is trashed by this
function.
theano.sandbox.gpuarray.kernel_codegen.inline_reduce_fixed_shared(N,
buf,
x,
stride_x,
load_x,
pos,
count,
manner_fn,
manner_init,
b=’‘,
stride_b=’‘,
load_b=’‘,
dtype=’float32’)
Return C++ code for a function that reduces a contiguous buffer.
This function leaves the answer in position 0 of the buffer. The rest of the buffer is trashed by this
function.
Parameters
• N – Length of the buffer.
• buf – Buffer pointer of size warpSize * sizeof(dtype).
• x – Input data.
• stride_x – Input data stride.
• load_x – Wrapper to read from x.
• pos – Index of executing thread.
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• count – Number of executing threads.
• b – Optional, pointer to the bias.
• stride_b – Optional, the stride of b if b is provided.
• load_b – Optional, wrapper to read from b if b is provided.
• dtype – Optional, the dtype of the output.
• manner_fn – A function that accepts strings of arguments a and b, and returns
c code for their reduction.
return “%(a)s + %(b)s”
for a sum reduction.
• manner_init – A function that accepts strings of arguments a and return c
code for its initialization.
Notes
buf should be in gpu shared memory, we access it many times.
theano.sandbox.gpuarray.kernel_codegen.inline_softmax(N, buf, buf2, threadPos, threadCount,
dtype=’float32’)
Generate code for a softmax.
On entry, buf and buf2 must contain two identical copies of the input to softmax.
After the code returns buf contains the softmax, buf2 contains un-normalized softmax.
Parameters
• N – Length of the buffer.
• threadPos – Index of executing thread.
• threadCount – Number of executing threads.
• dtype – Dtype of the softmax’s output.
Notes
buf and buf2 should be in gpu shared memory, we access it many times.
We use __i as an int variable in a loop.
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theano.sandbox.gpuarray.kernel_codegen.inline_softmax_fixed_shared(N,
buf,
x,
stride_x,
load_x,
sm,
sm_stride,
write_sm,
threadPos,
threadCount,
b=’‘,
stride_b=’‘,
load_b=’‘,
dtype=’float32’)
Generate code to perform softmax with a fixed amount of shared memory.
On entry, buf is assumed to be empty.
On exit, buf[0] contains the softmax, buf2 contains un-normalized softmax.
Parameters
• N – Length of the buffer, atleast waprSize(32).
• buf – A shared memory buffer of size warpSize * sizeof(dtype).
• x – A ptr to the gpu memory where the row is stored.
• stride_x – The stride between each element in x.
• load_x – Wrapper to read from x.
• sm – A ptr to the gpu memory to store the result.
• sm_stride – The stride between each sm element.
• write_sm – Wrapper before writing to sm.
• threadPos – Index of executing thread.
• threadCount – Number of executing threads.
• b – Optional, pointer to the bias.
• stride_b – Optional, the stride of b if b is provided.
• load_b – Optional, wrapper to read from b if b is provided.
• dtype – Optional, the dtype of the softmax’s output if not float32.
Notes
buf should be in gpu shared memory, we access it many times.
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We use tx as an int variable in a loop.
theano.sandbox.gpuarray.kernel_codegen.nvcc_kernel(name, params, body)
Return the c code of a kernel function.
Parameters
• params – The parameters to the function as one or more strings.
• body – The [nested] list of statements for the body of the function. These will be
separated by ‘;’ characters.
sandbox.linalg – Linear Algebra Ops
API
class theano.sandbox.linalg.ops.Hint(**kwargs)
Provide arbitrary information to the optimizer.
These ops are removed from the graph during canonicalization in order to not interfere with other
optimizations. The idea is that prior to canonicalization, one or more Features of the fgraph should
register the information contained in any Hint node, and transfer that information out of the graph.
class theano.sandbox.linalg.ops.HintsFeature
FunctionGraph Feature to track matrix properties.
This is a similar feature to variable ‘tags’. In fact, tags are one way to provide hints.
This class exists because tags were not documented well, and the semantics of how tag information
should be moved around during optimizations was never clearly spelled out.
Hints are assumptions about mathematical properties of variables. If one variable is substituted for
another by an optimization, then it means that the assumptions should be transferred to the new variable.
Hints are attached to ‘positions in a graph’ rather than to variables in particular, although Hints are
originally attached to a particular positition in a graph via a variable in that original graph.
Examples of hints are: - shape information - matrix properties (e.g. symmetry, psd, banded, diagonal)
Hint information is propagated through the graph similarly to graph optimizations, except that adding
a hint does not change the graph. Adding a hint is not something that debugmode will check.
#TODO: should a Hint be an object that can actually evaluate its # truthfulness? # Should the PSD
property be an object that can check the # PSD-ness of a variable?
class theano.sandbox.linalg.ops.HintsOptimizer
Optimizer that serves to add HintsFeature as an fgraph feature.
theano.sandbox.linalg.ops.psd(v)
Apply a hint that the variable v is positive semi-definite, i.e. it is a symmetric matrix and 𝑥𝑇 𝐴𝑥 ≥ 0
for any vector x.
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theano.sandbox.linalg.ops.spectral_radius_bound(X, log2_exponent)
Returns upper bound on the largest eigenvalue of square symmetrix matrix X.
log2_exponent must be a positive-valued integer. The larger it is, the slower and tighter the bound.
Values up to 5 should usually suffice. The algorithm works by multiplying X by itself this many times.
From V.Pan, 1990. “Estimating the Extremal Eigenvalues of a Symmetric Matrix”, Computers Math
Applic. Vol 20 n. 2 pp 17-22. Rq: an efficient algorithm, not used here, is defined in this paper.
sandbox.neighbours – Neighbours Ops
Moved
sandbox.rng_mrg – MRG random number generator
API
Implementation of MRG31k3p random number generator for Theano.
Generator code in SSJ package (L’Ecuyer & Simard). http://www.iro.umontreal.ca/~simardr/ssj/indexe.html
class theano.sandbox.rng_mrg.DotModulo(use_c_code=’/usr/bin/g++’)
Efficient and numerically stable implementation of a dot product followed by a modulo operation.
This performs the same function as matVecModM.
We do this 2 times on 2 triple inputs and concatenating the output.
class theano.sandbox.rng_mrg.MRG_RandomStreams(seed=12345, use_cuda=None)
Module component with similar interface to numpy.random (numpy.random.RandomState).
Parameters seed (int or list of 6 int) – A default seed to initialize the random state. If a single int is given, it will be replicated 6 times. The first 3 values of the
seed must all be less than M1 = 2147483647, and not all 0; and the last 3 values must
all be less than M2 = 2147462579, and not all 0.
get_substream_rstates(n_streams, dtype, inc_rstate=True)
Initialize a matrix in which each row is a MRG stream state, and they are spaced by 2**72
samples.
inc_rstate()
Update self.rstate to be skipped 2^134 steps forward to the next stream start.
multinomial(size=None, n=1, pvals=None, ndim=None, dtype=’int64’, nstreams=None)
Sample n (n needs to be >= 1, default 1) times from a multinomial distribution defined by
probabilities pvals.
Example : pvals = [[.98, .01, .01], [.01, .49, .50]] and n=1 will probably result in [[1,0,0],[0,0,1]].
When setting n=2, this will probably result in [[2,0,0],[0,1,1]].
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Notes
-size and ndim are only there keep the same signature as other uniform, binomial, normal, etc.
TODO : adapt multinomial to take that into account
-Does not do any value checking on pvals, i.e. there is no check that the elements are nonnegative, less than 1, or sum to 1. passing pvals = [[-2., 2.]] will result in sampling [[0, 0]]
multinomial_wo_replacement(size=None,
n=1,
pvals=None,
ndim=None,
dtype=’int64’, nstreams=None)
Sample n times WITHOUT replacement from a multinomial distribution defined by probabilities
pvals, and returns the indices of the sampled elements. n needs to be in [1, m], where m is the
number of elements to select from, i.e. m == pvals.shape[1]. By default n = 1.
Example : pvals = [[.98, .01, .01], [.01, .49, .50]] and n=1 will probably result in [[0],[2]]. When
setting n=2, this will probably result in [[0,1],[2,1]].
Notes
-size and ndim are only there keep the same signature as other uniform, binomial, normal, etc.
TODO : adapt multinomial to take that into account
-Does not do any value checking on pvals, i.e. there is no check that the elements are nonnegative, less than 1, or sum to 1. passing pvals = [[-2., 2.]] will result in sampling [[0, 0]]
normal(size, avg=0.0, std=1.0, ndim=None, dtype=None, nstreams=None)
Parameters
• size – Can be a list of integers or Theano variables (ex: the shape of another
Theano Variable).
• dtype – The output data type. If dtype is not specified, it will be inferred from
the dtype of low and high, but will be at least as precise as floatX.
• nstreams – Number of streams.
seed(seed=None)
Re-initialize each random stream.
Parameters seed (None or integer in range 0 to 2**30) – Each random stream will be assigned a unique state that depends deterministically on this
value.
Returns
Return type None
uniform(size, low=0.0, high=1.0, ndim=None, dtype=None, nstreams=None)
Sample a tensor of given size whose element from a uniform distribution between low and high.
If the size argument is ambiguous on the number of dimensions, ndim may be a plain integer to
supplement the missing information.
Parameters
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• low – Lower bound of the interval on which values are sampled. If the dtype
arg is provided, low will be cast into dtype. This bound is excluded.
• high – Higher bound of the interval on which values are sampled. If the dtype
arg is provided, high will be cast into dtype. This bound is excluded.
• size – Can be a list of integer or Theano variable (ex: the shape of other
Theano Variable).
• dtype – The output data type. If dtype is not specified, it will be inferred from
the dtype of low and high, but will be at least as precise as floatX.
theano.sandbox.rng_mrg.guess_n_streams(size, warn=False)
Return a guess at a good number of streams.
Parameters warn (bool, optional) – If True, warn when a guess cannot be made
(in which case we return 60 * 256).
theano.sandbox.rng_mrg.multMatVect(v, A, m1, B, m2)
Multiply the first half of v by A with a modulo of m1 and the second half by B with a modulo of m2.
Notes
The parameters of dot_modulo are passed implicitly because passing them explicitly takes more time
than running the function’s C-code.
scalar – Symbolic Scalar Types, Ops [doc TODO]
scan – Looping in Theano
Guide
The scan functions provides the basic functionality needed to do loops in Theano. Scan comes with many
whistles and bells, which we will introduce by way of examples.
Simple loop with accumulation: Computing 𝐴𝑘
Assume that, given k you want to get A**k using a loop. More precisely, if A is a tensor you want to
compute A**k elemwise. The python/numpy code might look like:
result = 1
for i in range(k):
result = result * A
There are three things here that we need to handle: the initial value assigned to result, the accumulation of results in result, and the unchanging variable A. Unchanging variables are passed to scan as
non_sequences. Initialization occurs in outputs_info, and the accumulation happens automatically.
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The equivalent Theano code would be:
import theano
import theano.tensor as T
k = T.iscalar("k")
A = T.vector("A")
# Symbolic description of the result
result, updates = theano.scan(fn=lambda prior_result, A: prior_result * A,
outputs_info=T.ones_like(A),
non_sequences=A,
n_steps=k)
# We only care about A**k, but scan has provided us with A**1 through A**k.
# Discard the values that we don't care about. Scan is smart enough to
# notice this and not waste memory saving them.
final_result = result[-1]
# compiled function that returns A**k
power = theano.function(inputs=[A,k], outputs=final_result, updates=updates)
print(power(range(10),2))
print(power(range(10),4))
[
[
0.
1.
4.
9. 16. 25. 36.
0.00000000e+00
1.00000000e+00
2.56000000e+02
6.25000000e+02
4.09600000e+03
6.56100000e+03]
49. 64. 81.]
1.60000000e+01
1.29600000e+03
8.10000000e+01
2.40100000e+03
Let us go through the example line by line. What we did is first to construct a function (using a lambda
expression) that given prior_result and A returns prior_result * A. The order of parameters is
fixed by scan: the output of the prior call to fn (or the initial value, initially) is the first parameter, followed
by all non-sequences.
Next we initialize the output as a tensor with same shape and dtype as A, filled with ones. We give A to scan
as a non sequence parameter and specify the number of steps k to iterate over our lambda expression.
Scan returns a tuple containing our result (result) and a dictionary of updates (empty in this case). Note
that the result is not a matrix, but a 3D tensor containing the value of A**k for each step. We want the last
value (after k steps) so we compile a function to return just that. Note that there is an optimization, that at
compile time will detect that you are using just the last value of the result and ensure that scan does not store
all the intermediate values that are used. So do not worry if A and k are large.
Iterating over the first dimension of a tensor: Calculating a polynomial
In addition to looping a fixed number of times, scan can iterate over the leading dimension of tensors (similar
to Python’s for x in a_list).
The tensor(s) to be looped over should be provided to scan using the sequence keyword argument.
Here’s an example that builds a symbolic calculation of a polynomial from a list of its coefficients:
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import numpy
coefficients = theano.tensor.vector("coefficients")
x = T.scalar("x")
max_coefficients_supported = 10000
# Generate the components of the polynomial
components, updates = theano.scan(fn=lambda coefficient, power, free_
˓→variable: coefficient * (free_variable ** power),
outputs_info=None,
sequences=[coefficients, theano.tensor.
˓→arange(max_coefficients_supported)],
non_sequences=x)
# Sum them up
polynomial = components.sum()
# Compile a function
calculate_polynomial = theano.function(inputs=[coefficients, x],
˓→outputs=polynomial)
# Test
test_coefficients = numpy.asarray([1, 0, 2], dtype=numpy.float32)
test_value = 3
print(calculate_polynomial(test_coefficients, test_value))
print(1.0 * (3 ** 0) + 0.0 * (3 ** 1) + 2.0 * (3 ** 2))
19.0
19.0
There are a few things to note here.
First, we calculate the polynomial by first generating each of the coefficients, and then summing them at the
end. (We could also have accumulated them along the way, and then taken the last one, which would have
been more memory-efficient, but this is an example.)
Second, there is no accumulation of results, we can set outputs_info to None. This indicates to scan
that it doesn’t need to pass the prior result to fn.
The general order of function parameters to fn is:
sequences (if any), prior result(s) (if needed), non-sequences (if any)
Third, there’s a handy trick used to simulate python’s enumerate: simply include theano.tensor.
arange to the sequences.
Fourth, given multiple sequences of uneven lengths, scan will truncate to the shortest of them. This makes
it safe to pass a very long arange, which we need to do for generality, since arange must have its length
specified at creation time.
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Simple accumulation into a scalar, ditching lambda
Although this example would seem almost self-explanatory, it stresses a pitfall to be careful of: the initial
output state that is supplied, that is outputs_info, must be of a shape similar to that of the output
variable generated at each iteration and moreover, it must not involve an implicit downcast of the latter.
import numpy as np
import theano
import theano.tensor as T
up_to = T.iscalar("up_to")
# define a named function, rather than using lambda
def accumulate_by_adding(arange_val, sum_to_date):
return sum_to_date + arange_val
seq = T.arange(up_to)
#
#
#
#
An unauthorized implicit downcast from the dtype of 'seq', to that of
'T.as_tensor_variable(0)' which is of dtype 'int8' by default would occur
if this instruction were to be used instead of the next one:
outputs_info = T.as_tensor_variable(0)
outputs_info = T.as_tensor_variable(np.asarray(0, seq.dtype))
scan_result, scan_updates = theano.scan(fn=accumulate_by_adding,
outputs_info=outputs_info,
sequences=seq)
triangular_sequence = theano.function(inputs=[up_to], outputs=scan_result)
# test
some_num = 15
print(triangular_sequence(some_num))
print([n * (n + 1) // 2 for n in range(some_num)])
[ 0
1
3
6 10 15 21 28 36 45 55 66 78 91 105]
[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105]
Another simple example
Unlike some of the prior examples, this one is hard to reproduce except by using scan.
This takes a sequence of array indices, and values to place there, and a “model” output array (whose shape
and dtype will be mimicked), and produces a sequence of arrays with the shape and dtype of the model, with
all values set to zero except at the provided array indices.
location = T.imatrix("location")
values = T.vector("values")
output_model = T.matrix("output_model")
def set_value_at_position(a_location, a_value, output_model):
zeros = T.zeros_like(output_model)
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zeros_subtensor = zeros[a_location[0], a_location[1]]
return T.set_subtensor(zeros_subtensor, a_value)
result, updates = theano.scan(fn=set_value_at_position,
outputs_info=None,
sequences=[location, values],
non_sequences=output_model)
assign_values_at_positions = theano.function(inputs=[location, values, output_
˓→model], outputs=result)
# test
test_locations = numpy.asarray([[1, 1], [2, 3]], dtype=numpy.int32)
test_values = numpy.asarray([42, 50], dtype=numpy.float32)
test_output_model = numpy.zeros((5, 5), dtype=numpy.float32)
print(assign_values_at_positions(test_locations, test_values, test_output_
˓→model))
[[[
[
[
[
[
0.
0.
0.
0.
0.
0.
42.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
[[
[
[
[
[
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
50.
0.
0.
0.]
0.]
0.]
0.]
0.]]
0.]
0.]
0.]
0.]
0.]]]
This demonstrates that you can introduce new Theano variables into a scan function.
Using shared variables - Gibbs sampling
Another useful feature of scan, is that it can handle shared variables. For example, if we want to implement
a Gibbs chain of length 10 we would do the following:
import theano
from theano import tensor as T
W = theano.shared(W_values) # we assume that ``W_values`` contains the
# initial values of your weight matrix
bvis = theano.shared(bvis_values)
bhid = theano.shared(bhid_values)
trng = T.shared_randomstreams.RandomStreams(1234)
def OneStep(vsample) :
hmean = T.nnet.sigmoid(theano.dot(vsample, W) + bhid)
hsample = trng.binomial(size=hmean.shape, n=1, p=hmean)
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vmean = T.nnet.sigmoid(theano.dot(hsample, W.T) + bvis)
return trng.binomial(size=vsample.shape, n=1, p=vmean,
dtype=theano.config.floatX)
sample = theano.tensor.vector()
values, updates = theano.scan(OneStep, outputs_info=sample, n_steps=10)
gibbs10 = theano.function([sample], values[-1], updates=updates)
The first, and probably most crucial observation is that the updates dictionary becomes important in this
case. It links a shared variable with its updated value after k steps. In this case it tells how the random
streams get updated after 10 iterations. If you do not pass this update dictionary to your function, you will
always get the same 10 sets of random numbers. You can even use the updates dictionary afterwards.
Look at this example :
a = theano.shared(1)
values, updates = theano.scan(lambda: {a: a+1}, n_steps=10)
In this case the lambda expression does not require any input parameters and returns an update dictionary
which tells how a should be updated after each step of scan. If we write :
b = a + 1
c = updates[a] + 1
f = theano.function([], [b, c], updates=updates)
print(b)
print(c)
print(a.get_value())
We will see that because b does not use the updated version of a, it will be 2, c will be 12, while a.value
is 11. If we call the function again, b will become 12, c will be 22 and a.value 21. If we do not pass the
updates dictionary to the function, then a.value will always remain 1, b will always be 2 and c will
always be 12.
The second observation is that if we use shared variables ( W, bvis, bhid) but we do not iterate over them
(ie scan doesn’t really need to know anything in particular about them, just that they are used inside the
function applied at each step) you do not need to pass them as arguments. Scan will find them on its own
and add them to the graph. However, passing them to the scan function is a good practice, as it avoids Scan
Op calling any earlier (external) Op over and over. This results in a simpler computational graph, which
speeds up the optimization and the execution. To pass the shared variables to Scan you need to put them in
a list and give it to the non_sequences argument. Here is the Gibbs sampling code updated:
W = theano.shared(W_values) # we assume that ``W_values`` contains the
# initial values of your weight matrix
bvis = theano.shared(bvis_values)
bhid = theano.shared(bhid_values)
trng = T.shared_randomstreams.RandomStreams(1234)
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# OneStep, with explicit use of the shared variables (W, bvis, bhid)
def OneStep(vsample, W, bvis, bhid):
hmean = T.nnet.sigmoid(theano.dot(vsample, W) + bhid)
hsample = trng.binomial(size=hmean.shape, n=1, p=hmean)
vmean = T.nnet.sigmoid(theano.dot(hsample, W.T) + bvis)
return trng.binomial(size=vsample.shape, n=1, p=vmean,
dtype=theano.config.floatX)
sample = theano.tensor.vector()
# The new scan, with the shared variables passed as non_sequences
values, updates = theano.scan(fn=OneStep,
outputs_info=sample,
non_sequences=[W, bvis, bhid],
n_steps=10)
gibbs10 = theano.function([sample], values[-1], updates=updates)
Using shared variables - the strict flag
As we just saw, passing the shared variables to scan may result in a simpler computational graph, which
speeds up the optimization and the execution. A good way to remember to pass every shared variable used
during scan is to use the strict flag. When set to true, scan assumes that all the necessary shared variables
in fn are passed as a part of non_sequences. This has to be ensured by the user. Otherwise, it will result
in an error.
Using the previous Gibbs sampling example:
# The new scan, using strict=True
values, updates = theano.scan(fn=OneStep,
outputs_info=sample,
non_sequences=[W, bvis, bhid],
n_steps=10,
strict=True)
If you omit to pass W, bvis or bhid as a non_sequence, it will result in an error.
Multiple outputs, several taps values - Recurrent Neural Network with Scan
The examples above showed simple uses of scan. However, scan also supports referring not only to the prior
result and the current sequence value, but also looking back more than one step.
This is needed, for example, to implement a RNN using scan. Assume that our RNN is defined as follows :
𝑥(𝑛) = tanh(𝑊 𝑥(𝑛 − 1) + 𝑊1𝑖𝑛 𝑢(𝑛) + 𝑊2𝑖𝑛 𝑢(𝑛 − 4) + 𝑊 𝑓 𝑒𝑒𝑑𝑏𝑎𝑐𝑘 𝑦(𝑛 − 1))
𝑦(𝑛) = 𝑊 𝑜𝑢𝑡 𝑥(𝑛 − 3)
Note that this network is far from a classical recurrent neural network and might be useless. The reason we
defined as such is to better illustrate the features of scan.
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In this case we have a sequence over which we need to iterate u, and two outputs x and y. To implement
this with scan we first construct a function that computes one iteration step :
def oneStep(u_tm4, u_t, x_tm3, x_tm1, y_tm1, W, W_in_1, W_in_2,
˓→W_out):
x_t = T.tanh(theano.dot(x_tm1,
theano.dot(u_t,
theano.dot(u_tm4,
theano.dot(y_tm1,
y_t = theano.dot(x_tm3, W_out)
W_feedback,
W) + \
W_in_1) + \
W_in_2) + \
W_feedback))
return [x_t, y_t]
As naming convention for the variables we used a_tmb to mean a at t-b and a_tpb to be a at t+b. Note
the order in which the parameters are given, and in which the result is returned. Try to respect chronological
order among the taps ( time slices of sequences or outputs) used. For scan is crucial only for the variables
representing the different time taps to be in the same order as the one in which these taps are given. Also,
not only taps should respect an order, but also variables, since this is how scan figures out what should be
represented by what. Given that we have all the Theano variables needed we construct our RNN as follows
:
W = T.matrix()
W_in_1 = T.matrix()
W_in_2 = T.matrix()
W_feedback = T.matrix()
W_out = T.matrix()
u = T.matrix() # it is a sequence of vectors
x0 = T.matrix() # initial state of x has to be a matrix, since
# it has to cover x[-3]
y0 = T.vector() # y0 is just a vector since scan has only to provide
# y[-1]
([x_vals, y_vals], updates) = theano.scan(fn=oneStep,
sequences=dict(input=u, taps=[-4,˓→0]),
outputs_info=[dict(initial=x0,
˓→taps=[-3,-1]), y0],
non_sequences=[W, W_in_1, W_in_2, W_
˓→feedback, W_out],
strict=True)
# for second input y, scan adds -1 in output_taps by default
Now x_vals and y_vals are symbolic variables pointing to the sequence of x and y values generated
by iterating over u. The sequence_taps, outputs_taps give to scan information about what slices
are exactly needed. Note that if we want to use x[t-k] we do not need to also have x[t-(k-1)],
x[t-(k-2)],.., but when applying the compiled function, the numpy array given to represent this sequence should be large enough to cover this values. Assume that we compile the above function, and
we give as u the array uvals = [0,1,2,3,4,5,6,7,8]. By abusing notations, scan will consider
uvals[0] as u[-4], and will start scaning from uvals[4] towards the end.
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Conditional ending of Scan
Scan can also be used as a repeat-until block. In such a case scan will stop when either the maximal
number of iteration is reached, or the provided condition evaluates to True.
For an example, we will compute all powers of two smaller then some provided value max_value.
def power_of_2(previous_power, max_value):
return previous_power*2, theano.scan_module.until(previous_power*2 > max_
˓→value)
max_value = T.scalar()
values, _ = theano.scan(power_of_2,
outputs_info = T.constant(1.),
non_sequences = max_value,
n_steps = 1024)
f = theano.function([max_value], values)
print(f(45))
[
2.
4.
8.
16.
32.
64.]
As you can see, in order to terminate on condition, the only thing required is that the inner function power_of_2 to return also the condition wrapped in the class theano.scan_module.until.
The condition has to be expressed in terms of the arguments of the inner function (in this case
previous_power and max_value).
As a rule, scan always expects the condition to be the last thing returned by the inner function, otherwise an
error will be raised.
Optimizing Scan’s performance
This section covers some ways to improve performance of a Theano function using Scan.
Minimizing Scan usage
Scan makes it possible to define simple and compact graphs that can do the same work as much larger and
more complicated graphs. However, it comes with a significant overhead. As such, when performance is the
objective, a good rule of thumb is to perform as much of the computation as possible outside of Scan. This
may have the effect of increasing memory usage but can also reduce the overhead introduces by using Scan.
Explicitly passing inputs of the inner function to scan
It is possible, inside of Scan, to use variables previously defined outside of the Scan without explicitly
passing them as inputs to the Scan. However, it is often more efficient to explicitly pass them as nonsequence inputs instead. Section Using shared variables - Gibbs sampling provides an explanation for this
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and section Using shared variables - the strict flag describes the strict flag, a tool that Scan provides to help
ensure that the inputs to the function inside Scan have all been provided as explicit inputs to the scan()
function.
Deactivating garbage collecting in Scan
Deactivating the garbage collection for Scan can allow it to reuse memory between executions instead of
always having to allocate new memory. This can improve performance at the cost of increased memory
usage. By default, Scan reuses memory between iterations of the same execution but frees the memory after
the last iteration.
There are two ways to achieve this, using the Theano flag config.scan.allow_gc and setting it to
False, or using the argument allow_gc of the function theano.scan() and set it to False (when a value is
not provided for this argument, the value of the flag config.scan.allow_gc is used).
Graph optimizations
This one is simple but still worth pointing out. Theano is able to automatically recognize and optimize
many computation patterns. However, there are patterns that Theano doesn’t optimize because doing so
would change the user interface (such as merging shared variables together into a single one, for instance).
Additionaly, Theano doesn’t catch every case that it could optimize and so it remains useful for performance
that the user defines an efficient graph in the first place. This is also the case, and sometimes even more so,
for the graph inside of Scan. This is because it will be executed many times for every execution of the
Theano function that contains it.
The LSTM tutorial on DeepLearning.net provides an example of an optimization that Theano cannot perform. Instead of performing many matrix multiplications between matrix 𝑥𝑡 and each of the shared matrices
𝑊𝑖 , 𝑊𝑐 , 𝑊𝑓 and 𝑊𝑜 , the matrices 𝑊* , are merged into a single shared matrix 𝑊 and the graph performs
a single larger matrix multiplication between 𝑊 and 𝑥𝑡 . The resulting matrix is then sliced to obtain the
results of that the small individual matrix multiplications would have produced. This optimization replaces
several small and inefficient matrix multiplications by a single larger one and thus improves performance at
the cost of a potentially higher memory usage.
reference
This module provides the Scan Op.
Scanning is a general form of recurrence, which can be used for looping. The idea is that you scan a function
along some input sequence, producing an output at each time-step that can be seen (but not modified) by the
function at the next time-step. (Technically, the function can see the previous K time-steps of your outputs
and L time steps (from the past and future) of your inputs.
So for example, sum() could be computed by scanning the z+x_i function over a list, given an initial
state of z=0.
Special cases:
• A reduce operation can be performed by returning only the last output of a scan.
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• A map operation can be performed by applying a function that ignores previous steps of the outputs.
Often a for-loop can be expressed as a scan() operation, and scan is the closest that theano comes to
looping. The advantage of using scan over for loops is that it allows the number of iterations to be a part
of the symbolic graph.
The Scan Op should typically be used by calling any of the following functions: scan(), map(),
reduce(), foldl(), foldr().
theano.map(fn, sequences, non_sequences=None, truncate_gradient=-1, go_backwards=False,
mode=None, name=None)
Similar behaviour as python’s map.
Parameters
• fn – The function that map applies at each iteration step (see scan for more
info).
• sequences – List of sequences over which map iterates (see scan for more
info).
• non_sequences – List of arguments passed to fn. map will not iterate over
these arguments (see scan for more info).
• truncate_gradient – See scan.
• go_backwards (bool) – Decides the direction of iteration. True means that
sequences are parsed from the end towards the begining, while False is the other
way around.
• mode – See scan.
• name – See scan.
theano.reduce(fn, sequences, outputs_info, non_sequences=None, go_backwards=False,
mode=None, name=None)
Similar behaviour as python’s reduce.
Parameters
• fn – The function that reduce applies at each iteration step (see scan for more
info).
• sequences – List of sequences over which reduce iterates (see scan for
more info).
• outputs_info – List of dictionaries describing the outputs of reduce (see
scan for more info).
• non_sequences –
List of arguments passed to fn. reduce will not iterate over these arguments
(see scan for more info).
• go_backwards (bool) – Decides the direction of iteration. True means that
sequences are parsed from the end towards the begining, while False is the other
way around.
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• mode – See scan.
• name – See scan.
theano.foldl(fn, sequences, outputs_info, non_sequences=None, mode=None, name=None)
Similar behaviour as haskell’s foldl.
Parameters
• fn – The function that foldl applies at each iteration step (see scan for more
info).
• sequences – List of sequences over which foldl iterates (see scan for more
info).
• outputs_info – List of dictionaries describing the outputs of reduce (see
scan for more info).
• non_sequences – List of arguments passed to fn. foldl will not iterate over
these arguments (see scan for more info).
• mode – See scan.
• name – See scan.
theano.foldr(fn, sequences, outputs_info, non_sequences=None, mode=None, name=None)
Similar behaviour as haskell’ foldr.
Parameters
• fn – The function that foldr applies at each iteration step (see scan for more
info).
• sequences – List of sequences over which foldr iterates (see scan for more
info).
• outputs_info – List of dictionaries describing the outputs of reduce (see
scan for more info).
• non_sequences – List of arguments passed to fn. foldr will not iterate over
these arguments (see scan for more info).
• mode – See scan.
• name – See scan.
theano.scan(fn, sequences=None, outputs_info=None, non_sequences=None, n_steps=None,
truncate_gradient=-1, go_backwards=False, mode=None, name=None, profile=False, allow_gc=None, strict=False)
This function constructs and applies a Scan op to the provided arguments.
Parameters
• fn – fn is a function that describes the operations involved in one step of scan.
fn should construct variables describing the output of one iteration step. It should
expect as input theano variables representing all the slices of the input sequences
and previous values of the outputs, as well as all other arguments given to scan as
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non_sequences. The order in which scan passes these variables to fn is the
following :
– all time slices of the first sequence
– all time slices of the second sequence
– ...
– all time slices of the last sequence
– all past slices of the first output
– all past slices of the second otuput
– ...
– all past slices of the last output
– all other arguments (the list given as non_sequences to scan)
The order of the sequences is the same as the one in the list sequences given to
scan. The order of the outputs is the same as the order of outputs_info. For
any sequence or output the order of the time slices is the same as the one in which
they have been given as taps. For example if one writes the following :
scan(fn, sequences = [ dict(input= Sequence1, taps = [-3,2,
˓→-1])
, Sequence2
, dict(input = Sequence3, taps = 3) ]
, outputs_info = [ dict(initial = Output1, taps =
˓→[-3,-5])
, dict(initial = Output2, taps =
˓→None)
, Output3 ]
, non_sequences = [ Argument1, Argument2])
fn should expect the following arguments in this given order:
1. Sequence1[t-3]
2. Sequence1[t+2]
3. Sequence1[t-1]
4. Sequence2[t]
5. Sequence3[t+3]
6. Output1[t-3]
7. Output1[t-5]
8. Output3[t-1]
9. Argument1
10. Argument2
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The list of non_sequences can also contain shared variables used in the function, though scan is able to figure those out on its own so they can be skipped.
For the clarity of the code we recommend though to provide them to scan. To
some extend scan can also figure out other non sequences (not shared) even
if not passed to scan (but used by fn). A simple example of this would be :
import theano.tensor as TT
W
= TT.matrix()
W_2 = W**2
def f(x):
return TT.dot(x,W_2)
The function is expected to return two things. One is a list of outputs ordered
in the same order as outputs_info, with the difference that there should be
only one output variable per output initial state (even if no tap value is used).
Secondly fn should return an update dictionary (that tells how to update any shared
variable after each iteration step). The dictionary can optionally be given as a list
of tuples. There is no constraint on the order of these two list, fn can return either
(outputs_list, update_dictionary) or (update_dictionary,
outputs_list) or just one of the two (in case the other is empty).
To use scan as a while loop, the user needs to change the function fn such
that also a stopping condition is returned. To do so, he/she needs to wrap the
condition in an until class. The condition should be returned as a third element,
for example:
...
return [y1_t, y2_t], {x:x+1}, theano.scan_module.until(x <
˓→50)
Note that a number of steps (considered in here as the maximum number of steps
) is still required even though a condition is passed (and it is used to allocate
memory if needed). = {}):
• sequences – sequences is the list of Theano variables or dictionaries describing the sequences scan has to iterate over. If a sequence is given as wrapped
in a dictionary, then a set of optional information can be provided about the sequence. The dictionary should have the following keys:
– input (mandatory) – Theano variable representing the sequence.
– taps – Temporal taps of the sequence required by fn. They are provided as a
list of integers, where a value k impiles that at iteration step t scan will pass to
fn the slice t+k. Default value is [0]
Any Theano variable in the list sequences is automatically wrapped into a
dictionary where taps is set to [0]
• outputs_info – outputs_info is the list of Theano variables or dictionaries describing the initial state of the outputs computed recurrently. When this
initial states are given as dictionary optional information can be provided about
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the output corresponding to these initial states. The dictionary should have the
following keys:
– initial – Theano variable that represents the initial state of a given output.
In case the output is not computed recursively (think of a map) and does not
require an initial state this field can be skipped. Given that (only) the previous time step of the output is used by fn, the initial state should have the
same shape as the output and should not involve a downcast of the data
type of the output. If multiple time taps are used, the initial state should
have one extra dimension that should cover all the possible taps. For example if we use -5, -2 and -1 as past taps, at step 0, fn will require (by an
abuse of notation) output[-5], output[-2] and output[-1]. This
will be given by the initial state, which in this case should have the shape
(5,)+output.shape. If this variable containing the initial state is called init_y
then init_y[0] corresponds to output[-5]. init_y[1] correponds
to output[-4], init_y[2] corresponds to output[-3], init_y[3]
coresponds to output[-2], init_y[4] corresponds to output[-1].
While this order might seem strange, it comes natural from splitting an array at a given point. Assume that we have a array x, and we choose k to be
time step 0. Then our initial state would be x[:k], while the output will be
x[k:]. Looking at this split, elements in x[:k] are ordered exactly like those
in init_y.
– taps – Temporal taps of the output that will be pass to fn. They are provided
as a list of negative integers, where a value k implies that at iteration step t
scan will pass to fn the slice t+k.
scan will follow this logic if partial information is given:
– If an output is not wrapped in a dictionary, scan will wrap it in one assuming
that you use only the last step of the output (i.e. it makes your tap value list
equal to [-1]).
– If you wrap an output in a dictionary and you do not provide any taps but you
provide an initial state it will assume that you are using only a tap value of -1.
– If you wrap an output in a dictionary but you do not provide any initial state, it
assumes that you are not using any form of taps.
– If you provide a None instead of a variable or a empty dictionary scan assumes that you will not use any taps for this output (like for example in case of
a map)
If outputs_info is an empty list or None, scan assumes that no tap is used
for any of the outputs. If information is provided just for a subset of the outputs
an exception is raised (because there is no convention on how scan should map
the provided information to the outputs of fn)
• non_sequences – non_sequences is the list of arguments that are passed
to fn at each steps. One can opt to exclude variable used in fn from this list as
long as they are part of the computational graph, though for clarity we encourage
not to do so.
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• n_steps – n_steps is the number of steps to iterate given as an int or Theano
scalar. If any of the input sequences do not have enough elements, scan will raise
an error. If the value is 0 the outputs will have 0 rows. If the value is negative,
scan will run backwards in time. If the go_backwards flag is already set
and also n_steps is negative, scan will run forward in time. If n_steps is not
provided, scan will figure out the amount of steps it should run given its input
sequences.
• truncate_gradient – truncate_gradient is the number of steps to
use in truncated BPTT. If you compute gradients through a scan op, they are
computed using backpropagation through time. By providing a different value
then -1, you choose to use truncated BPTT instead of classical BPTT, where you
go for only truncate_gradient number of steps back in time.
• go_backwards – go_backwards is a flag indicating if scan should go
backwards through the sequences. If you think of each sequence as indexed by
time, making this flag True would mean that scan goes back in time, namely that
for any sequence it starts from the end and goes towards 0.
• name – When profiling scan, it is crucial to provide a name for any instance
of scan. The profiler will produce an overall profile of your code as well as
profiles for the computation of one step of each instance of scan. The name
of the instance appears in those profiles and can greatly help to disambiguate
information.
• mode – It is recommended to leave this argument to None, especially when profiling scan (otherwise the results are not going to be accurate). If you prefer the
computations of one step of scan to be done differently then the entire function,
you can use this parameter to describe how the computations in this loop are done
(see theano.function for details about possible values and their meaning).
• profile – Flag or string. If true, or different from the empty string, a profile
object will be created and attached to the inner graph of scan. In case profile
is True, the profile object will have the name of the scan instance, otherwise it
will have the passed string. Profile object collect (and print) information only
when running the inner graph with the new cvm linker ( with default modes, other
linkers this argument is useless)
• allow_gc – Set the value of allow gc for the internal graph of scan. If set to
None, this will use the value of config.scan.allow_gc.
• strict – If true, all the shared variables used in fn must be provided as a part
of non_sequences or sequences.
Returns Tuple of the form (outputs, updates); outputs is either a Theano variable or
a list of Theano variables representing the outputs of scan (in the same order as in
outputs_info). updates is a subclass of dictionary specifying the update rules
for all shared variables used in scan. This dictionary should be passed to theano.
function when you compile your function. The change compared to a normal
dictionary is that we validate that keys are SharedVariable and addition of those dictionary are validated to be consistent.
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Return type tuple
sparse – Symbolic Sparse Matrices
In the tutorial section, you can find a sparse tutorial.
The sparse submodule is not loaded when we import Theano. You must import theano.sparse to enable
it.
The sparse module provides the same functionality as the tensor module. The difference lies under the covers
because sparse matrices do not store data in a contiguous array. Note that there are no GPU implementations
for sparse matrices in Theano. The sparse module has been used in:
• NLP: Dense linear transformations of sparse vectors.
• Audio: Filterbank in the Fourier domain.
Compressed Sparse Format
This section tries to explain how information is stored for the two sparse formats of SciPy supported by
Theano. There are more formats that can be used with SciPy and some documentation about them may be
found here.
Theano supports two compressed sparse formats: csc and csr, respectively based on columns and rows.
They have both the same attributes: data, indices, indptr and shape.
• The data attribute is a one-dimensional ndarray which contains all the non-zero elements of the
sparse matrix.
• The indices and indptr attributes are used to store the position of the data in the sparse matrix.
• The shape attribute is exactly the same as the shape attribute of a dense (i.e. generic) matrix. It
can be explicitly specified at the creation of a sparse matrix if it cannot be infered from the first three
attributes.
CSC Matrix
In the Compressed Sparse Column format, indices stands for indexes inside the column vectors of the
matrix and indptr tells where the column starts in the data and in the indices attributes. indptr
can be thought of as giving the slice which must be applied to the other attribute in order to get each column
of the matrix. In other words, slice(indptr[i], indptr[i+1]) corresponds to the slice needed
to find the i-th column of the matrix in the data and indices fields.
The following example builds a matrix and returns its columns. It prints the i-th column, i.e. a list of indices
in the column and their corresponding value in the second list.
>>>
>>>
>>>
>>>
404
import numpy as np
import scipy.sparse as sp
data = np.asarray([7, 8, 9])
indices = np.asarray([0, 1, 2])
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>>> indptr = np.asarray([0, 2, 3, 3])
>>> m = sp.csc_matrix((data, indices, indptr), shape=(3, 3))
>>> m.toarray()
array([[7, 0, 0],
[8, 0, 0],
[0, 9, 0]])
>>> i = 0
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([0, 1], dtype=int32), array([7, 8]))
>>> i = 1
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([2], dtype=int32), array([9]))
>>> i = 2
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([], dtype=int32), array([], dtype=int64))
CSR Matrix
In the Compressed Sparse Row format, indices stands for indexes inside the row vectors of the matrix
and indptr tells where the row starts in the data and in the indices attributes. indptr can be thought
of as giving the slice which must be applied to the other attribute in order to get each row of the matrix. In
other words, slice(indptr[i], indptr[i+1]) corresponds to the slice needed to find the i-th row
of the matrix in the data and indices fields.
The following example builds a matrix and returns its rows. It prints the i-th row, i.e. a list of indices in the
row and their corresponding value in the second list.
>>> import numpy as np
>>> import scipy.sparse as sp
>>> data = np.asarray([7, 8, 9])
>>> indices = np.asarray([0, 1, 2])
>>> indptr = np.asarray([0, 2, 3, 3])
>>> m = sp.csr_matrix((data, indices, indptr), shape=(3, 3))
>>> m.toarray()
array([[7, 8, 0],
[0, 0, 9],
[0, 0, 0]])
>>> i = 0
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([0, 1], dtype=int32), array([7, 8]))
>>> i = 1
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([2], dtype=int32), array([9]))
>>> i = 2
>>> m.indices[m.indptr[i]:m.indptr[i+1]], m.data[m.indptr[i]:m.indptr[i+1]]
(array([], dtype=int32), array([], dtype=int64))
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List of Implemented Operations
• Moving from and to sparse
– dense_from_sparse. Both grads are implemented. Structured by default.
– csr_from_dense, csc_from_dense. The grad implemented is structured.
– Theano SparseVariable objects have a method toarray() that is the same as
dense_from_sparse.
• Construction of Sparses and their Properties
– CSM and CSC, CSR to construct a matrix. The grad implemented is regular.
– csm_properties. to get the properties of a sparse matrix. The grad implemented is
regular.
– csm_indices(x), csm_indptr(x), csm_data(x) and csm_shape(x) or x.shape.
– sp_ones_like. The grad implemented is regular.
– sp_zeros_like. The grad implemented is regular.
– square_diagonal. The grad implemented is regular.
– construct_sparse_from_list. The grad implemented is regular.
• Cast
– cast with bcast, wcast, icast, lcast, fcast, dcast, ccast, and zcast. The
grad implemented is regular.
• Transpose
– transpose. The grad implemented is regular.
• Basic Arithmetic
– neg. The grad implemented is regular.
– eq.
– neq.
– gt.
– ge.
– lt.
– le.
– add. The grad implemented is regular.
– sub. The grad implemented is regular.
– mul. The grad implemented is regular.
– col_scale to multiply by a vector along the columns. The grad implemented is structured.
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– row_slace to multiply by a vector along the rows. The grad implemented is structured.
• Monoid (Element-wise operation with only one sparse input). They all have a structured grad.
– structured_sigmoid
– structured_exp
– structured_log
– structured_pow
– structured_minimum
– structured_maximum
– structured_add
– sin
– arcsin
– tan
– arctan
– sinh
– arcsinh
– tanh
– arctanh
– rad2deg
– deg2rad
– rint
– ceil
– floor
– trunc
– sgn
– log1p
– expm1
– sqr
– sqrt
• Dot Product
– dot.
* One of the inputs must be sparse, the other sparse or dense.
* The grad implemented is regular.
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* No C code for perform and no C code for grad.
* Returns a dense for perform and a dense for grad.
– structured_dot.
* The first input is sparse, the second can be sparse or dense.
* The grad implemented is structured.
* C code for perform and grad.
* It returns a sparse output if both inputs are sparse and dense one if one of the inputs is
dense.
* Returns a sparse grad for sparse inputs and dense grad for dense inputs.
– true_dot.
* The first input is sparse, the second can be sparse or dense.
* The grad implemented is regular.
* No C code for perform and no C code for grad.
* Returns a Sparse.
* The gradient returns a Sparse for sparse inputs and by default a dense for dense inputs.
The parameter grad_preserves_dense can be set to False to return a sparse grad
for dense inputs.
– sampling_dot.
* Both inputs must be dense.
* The grad implemented is structured for p.
* Sample of the dot and sample of the gradient.
* C code for perform but not for grad.
* Returns sparse for perform and grad.
– usmm.
* You shouldn’t insert this op yourself!
· There is an optimization that transform a dot to Usmm when possible.
* This op is the equivalent of gemm for sparse dot.
* There is no grad implemented for this op.
* One of the inputs must be sparse, the other sparse or dense.
* Returns a dense from perform.
• Slice Operations
– sparse_variable[N, N], returns a tensor scalar. There is no grad implemented for this operation.
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– sparse_variable[M:N, O:P], returns a sparse matrix There is no grad implemented for this
operation.
– Sparse variables don’t support [M, N:O] and [M:N, O] as we don’t support sparse vectors
and returning a sparse matrix would break the numpy interface. Use [M:M+1, N:O] and
[M:N, O:O+1] instead.
– diag. The grad implemented is regular.
• Concatenation
– hstack. The grad implemented is regular.
– vstack. The grad implemented is regular.
• Probability There is no grad implemented for these operations.
– Poisson and poisson
– Binomial and
csr_dbinomial
csc_fbinomial,
csc_dbinomial
csr_fbinomial,
– Multinomial and multinomial
• Internal Representation They all have a regular grad implemented.
– ensure_sorted_indices.
– remove0.
– clean to resort indices and remove zeros
• To help testing
– theano.sparse.tests.test_basic.sparse_random_inputs()
sparse – Sparse Op
Classes for handling sparse matrices.
To read about different sparse formats, see http://www-users.cs.umn.edu/~saad/software/SPARSKIT/paper.
ps
class theano.sparse.basic.CSM(format, kmap=None)
Indexing to speficied what part of the data parameter should be used to construct the sparse matrix.
theano.sparse.basic.add(x, y)
Add two matrices, at least one of which is sparse.
This method will provide the right op according to the inputs.
Parameters
• x – A matrix variable.
• y – A matrix variable.
Returns x + y
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Return type A sparse matrix
Notes
At least one of x and y must be a sparse matrix.
The grad will be structured only when one of the variable will be a dense matrix.
theano.sparse.basic.as_sparse(x, name=None)
Wrapper around SparseVariable constructor to construct a Variable with a sparse matrix with the same
dtype and format.
Parameters x – A sparse matrix.
Returns SparseVariable version of x.
Return type object
theano.sparse.basic.as_sparse_or_tensor_variable(x, name=None)
Same as as_sparse_variable but if we can’t make a sparse variable, we try to make a tensor variable.
Parameters x – A sparse matrix.
Returns
Return type SparseVariable or TensorVariable version of x
theano.sparse.basic.as_sparse_variable(x, name=None)
Wrapper around SparseVariable constructor to construct a Variable with a sparse matrix with the same
dtype and format.
Parameters x – A sparse matrix.
Returns SparseVariable version of x.
Return type object
theano.sparse.basic.cast(variable, dtype)
Cast sparse variable to the desired dtype.
Parameters
• variable – Sparse matrix.
• dtype – The dtype wanted.
Returns
Return type Same as x but having dtype as dtype.
Notes
The grad implemented is regular, i.e. not structured.
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theano.sparse.basic.clean(x)
Remove explicit zeros from a sparse matrix, and re-sort indices.
CSR column indices are not necessarily sorted. Likewise for CSC row indices. Use clean when sorted
indices are required (e.g. when passing data to other libraries) and to ensure there are no zeros in the
data.
Parameters x – A sparse matrix.
Returns The same as x with indices sorted and zeros removed.
Return type A sparse matrix
Notes
The grad implemented is regular, i.e. not structured.
theano.sparse.basic.col_scale(x, s)
Scale each columns of a sparse matrix by the corresponding element of a dense vector.
Parameters
• x – A sparse matrix.
• s – A dense vector with length equal to the number of columns of x.
Returns
• A sparse matrix in the same format as x which each column had been
• multiply by the corresponding element of s.
Notes
The grad implemented is structured.
theano.sparse.basic.csm_data(csm)
Return the data field of the sparse variable.
theano.sparse.basic.csm_indices(csm)
Return the indices field of the sparse variable.
theano.sparse.basic.csm_indptr(csm)
Return the indptr field of the sparse variable.
theano.sparse.basic.csm_shape(csm)
Return the shape field of the sparse variable.
theano.sparse.basic.dot(x, y)
Operation for efficiently calculating the dot product when one or all operands is sparse. Supported
format are CSC and CSR. The output of the operation is dense.
Parameters
• x – Sparse or dense matrix variable.
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• y – Sparse or dense matrix variable.
Returns
Return type The dot product x.‘y‘ in a dense format.
Notes
The grad implemented is regular, i.e. not structured.
At least one of x or y must be a sparse matrix.
When the operation has the form dot(csr_matrix, dense) the gradient of this operation can be performed inplace by UsmmCscDense. This leads to significant speed-ups.
theano.sparse.basic.hstack(blocks, format=None, dtype=None)
Stack sparse matrices horizontally (column wise).
This wrap the method hstack from scipy.
Parameters
• blocks – List of sparse array of compatible shape.
• format – String representing the output format. Default is csc.
• dtype – Output dtype.
Returns The concatenation of the sparse array column wise.
Return type array
Notes
The number of line of the sparse matrix must agree.
The grad implemented is regular, i.e. not structured.
theano.sparse.basic.mul(x, y)
Multiply elementwise two matrices, at least one of which is sparse.
This method will provide the right op according to the inputs.
Parameters
• x – A matrix variable.
• y – A matrix variable.
Returns x + y
Return type A sparse matrix
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Notes
At least one of x and y must be a sparse matrix. The grad is regular, i.e. not structured.
theano.sparse.basic.row_scale(x, s)
Scale each row of a sparse matrix by the corresponding element of a dense vector.
Parameters
• x – A sparse matrix.
• s – A dense vector with length equal to the number of rows of x.
Returns A sparse matrix in the same format as x whose each row has been multiplied by
the corresponding element of s.
Return type A sparse matrix
Notes
The grad implemented is structured.
theano.sparse.basic.sp_ones_like(x)
Construct a sparse matrix of ones with the same sparsity pattern.
Parameters x – Sparse matrix to take the sparsity pattern.
Returns The same as x with data changed for ones.
Return type A sparse matrix
theano.sparse.basic.sp_sum(x, axis=None, sparse_grad=False)
Calculate the sum of a sparse matrix along the specified axis.
It operates a reduction along the specified axis. When axis is None, it is applied along all axes.
Parameters
• x – Sparse matrix.
• axis – Axis along which the sum is applied. Integer or None.
• sparse_grad (bool) – True to have a structured grad.
Returns The sum of x in a dense format.
Return type object
Notes
The grad implementation is controlled with the sparse_grad parameter. True will provide a structured
grad and False will provide a regular grad. For both choices, the grad returns a sparse matrix having
the same format as x.
This op does not return a sparse matrix, but a dense tensor matrix.
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theano.sparse.basic.sp_zeros_like(x)
Construct a sparse matrix of zeros.
Parameters x – Sparse matrix to take the shape.
Returns The same as x with zero entries for all element.
Return type A sparse matrix
theano.sparse.basic.structured_dot(x, y)
Structured Dot is like dot, except that only the gradient wrt non-zero elements of the sparse matrix a
are calculated and propagated.
The output is presumed to be a dense matrix, and is represented by a TensorType instance.
Parameters
• a – A sparse matrix.
• b – A sparse or dense matrix.
Returns The dot product of a and b.
Return type A sparse matrix
Notes
The grad implemented is structured.
theano.sparse.basic.sub(x, y)
Subtract two matrices, at least one of which is sparse.
This method will provide the right op according to the inputs.
Parameters
• x – A matrix variable.
• y – A matrix variable.
Returns x - y
Return type A sparse matrix
Notes
At least one of x and y must be a sparse matrix.
The grad will be structured only when one of the variable will be a dense matrix.
theano.sparse.basic.true_dot(x, y, grad_preserves_dense=True)
Operation for efficiently calculating the dot product when one or all operands are sparse. Supported
formats are CSC and CSR. The output of the operation is sparse.
Parameters
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• x – Sparse matrix.
• y – Sparse matrix or 2d tensor variable.
• grad_preserves_dense (bool) – If True (default), makes the grad of dense
inputs dense. Otherwise the grad is always sparse.
Returns
• The dot product x.‘y‘ in a sparse format.
• Notex
• —–
• The grad implemented is regular, i.e. not structured.
theano.sparse.basic.verify_grad_sparse(op,
pt,
structured=False,
*args,
**kwargs)
Wrapper for theano.test.unittest_tools.py:verify_grad wich converts sparse variables back and forth.
Parameters
• op – Op to check.
• pt – List of inputs to realize the tests.
• structured – True to tests with a structured grad, False otherwise.
• args – Other verify_grad parameters if any.
• kwargs – Other verify_grad keywords if any.
Returns
Return type None
theano.sparse.basic.vstack(blocks, format=None, dtype=None)
Stack sparse matrices vertically (row wise).
This wrap the method vstack from scipy.
Parameters
• blocks – List of sparse array of compatible shape.
• format – String representing the output format. Default is csc.
• dtype – Output dtype.
Returns The concatenation of the sparse array row wise.
Return type array
Notes
The number of column of the sparse matrix must agree.
The grad implemented is regular, i.e. not structured.
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theano.sparse.tests.test_basic.sparse_random_inputs(format, shape, n=1,
out_dtype=None,
p=0.5, gap=None, explicit_zero=False, unsorted_indices=False)
Return a tuple containing everything needed to perform a test.
If out_dtype is None, theano.config.floatX is used.
Parameters
• format – Sparse format.
• shape – Shape of data.
• n – Number of variable.
• out_dtype – dtype of output.
• p – Sparsity proportion.
• gap – Tuple for the range of the random sample. When length is 1, it is assumed
to be the exclusive max, when gap = (a, b) it provide a sample from [a, b[. If
None is used, it provide [0, 1] for float dtypes and [0, 50[ for integer dtypes.
• explicit_zero – When True, we add explicit zero in the returned sparse matrix
• unsorted_indices – when True, we make sure there is unsorted indices in
the returned sparse matrix.
Returns (variable, data) where both variable and data are list.
Note explicit_zero and unsorted_indices was added in Theano 0.6rc4
sparse.sandbox – Sparse Op Sandbox
API
Convolution-like operations with sparse matrix multiplication.
To read about different sparse formats, see U{http://www-users.cs.umn.edu/~saad/software/SPARSKIT/
paper.ps}.
@todo: Automatic methods for determining best sparse format?
class theano.sparse.sandbox.sp.ConvolutionIndices(use_c_code=’/usr/bin/g++’)
Build indices for a sparse CSC matrix that could implement A (convolve) B.
This generates a sparse matrix M, which generates a stack of image patches when computing the dot product of M with image patch. Convolution is then simply the dot product of
(img x M) and the kernels.
static evaluate(inshp, kshp, strides=(1, 1), nkern=1, mode=’valid’, ws=True)
Build a sparse matrix which can be used for performing... * convolution: in this case, the dot
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product of this matrix with the input images will generate a stack of images patches. Convolution
is then a tensordot operation of the filters and the patch stack. * sparse local connections: in this
case, the sparse matrix allows us to operate the weight matrix as if it were fully-connected. The
structured-dot with the input image gives the output for the following layer.
Parameters
• ker_shape – shape of kernel to apply (smaller than image)
• img_shape – shape of input images
• mode – ‘valid’ generates output only when kernel and image overlap overlap
fully. Convolution obtained by zero-padding the input
• ws – must be always True
• (dx,dy) – offset parameter. In the case of no weight sharing, gives the pixel
offset between two receptive fields. With weight sharing gives the offset between the top-left pixels of the generated patches
Return type tuple(indices, indptr, logical_shape, sp_type, out_img_shp)
Returns the structure of a sparse matrix, and the logical dimensions of the image
which will be the result of filtering.
theano.sparse.sandbox.sp.convolve(kerns, kshp, nkern, images, imgshp, step=(1, 1),
bias=None, mode=’valid’, flatten=True)
Convolution implementation by sparse matrix multiplication.
Note For best speed, put the matrix which you expect to be smaller as the ‘kernel’ argument
“images” is assumed to be a matrix of shape batch_size x img_size, where the second dimension
represents each image in raster order
If flatten is “False”, the output feature map will have shape:
batch_size x number of kernels x output_size
If flatten is “True”, the output feature map will have shape:
batch_size x number of kernels * output_size
Note: IMPORTANT: note that this means that each feature map (image generate by each kernel) is
contiguous in memory. The memory layout will therefore be: [ <feature_map_0> <feature_map_1>
... <feature_map_n>], where <feature_map> represents a “feature map” in raster order
kerns is a 2D tensor of shape nkern x N.prod(kshp)
Parameters
• kerns – 2D tensor containing kernels which are applied at every pixel
• kshp – tuple containing actual dimensions of kernel (not symbolic)
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• nkern – number of kernels/filters to apply. nkern=1 will apply one common
filter to all input pixels
• images – tensor containing images on which to apply convolution
• imgshp – tuple containing image dimensions
• step – determines number of pixels between adjacent receptive fields (tuple containing dx,dy values)
• mode – ‘full’, ‘valid’ see CSM.evaluate function for details
• sumdims – dimensions over which to sum for the tensordot operation. By default
((2,),(1,)) assumes kerns is a nkern x kernsize matrix and images is a batchsize x
imgsize matrix containing flattened images in raster order
• flatten – flatten the last 2 dimensions of the output. By default, instead of
generating a batchsize x outsize x nkern tensor, will flatten to batchsize x outsize*nkern
Returns out1, symbolic result
Returns out2, logical shape of the output img (nkern,heigt,width)
TODO test for 1D and think of how to do n-d convolutions
theano.sparse.sandbox.sp.max_pool(images, imgshp, maxpoolshp)
Implements a max pooling layer
Takes as input a 2D tensor of shape batch_size x img_size and performs max pooling. Max pooling
downsamples by taking the max value in a given area, here defined by maxpoolshp. Outputs a 2D
tensor of shape batch_size x output_size.
Parameters
• images – 2D tensor containing images on which to apply convolution. Assumed
to be of shape batch_size x img_size
• imgshp – tuple containing image dimensions
• maxpoolshp – tuple containing shape of area to max pool over
Returns out1, symbolic result (2D tensor)
Returns out2, logical shape of the output
class theano.sparse.sandbox.sp2.Binomial(format, dtype)
Return a sparse matrix having random values from a binomial density having number of experiment
n and probability of succes p.
WARNING: This Op is NOT deterministic, as calling it twice with the same inputs will NOT give the
same result. This is a violation of Theano’s contract for Ops
Parameters
• n – Tensor scalar representing the number of experiment.
• p – Tensor scalar representing the probability of success.
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• shape – Tensor vector for the output shape.
Returns A sparse matrix of integers representing the number of success.
class theano.sparse.sandbox.sp2.Multinomial(use_c_code=’/usr/bin/g++’)
Return a sparse matrix having random values from a multinomial density having number of experiment n and probability of succes p.
WARNING: This Op is NOT deterministic, as calling it twice with the same inputs will NOT give the
same result. This is a violation of Theano’s contract for Ops
Parameters
• n – Tensor type vector or scalar representing the number of experiment for each
row. If n is a scalar, it will be used for each row.
• p – Sparse matrix of probability where each row is a probability vector representing the probability of succes. N.B. Each row must sum to one.
Returns A sparse matrix of random integers from a multinomial density for each row.
Note It will works only if p have csr format.
class theano.sparse.sandbox.sp2.Poisson(use_c_code=’/usr/bin/g++’)
Return a sparse having random values from a Poisson density with mean from the input.
WARNING: This Op is NOT deterministic, as calling it twice with the same inputs will NOT give the
same result. This is a violation of Theano’s contract for Ops
Parameters x – Sparse matrix.
Returns A sparse matrix of random integers of a Poisson density with mean of x element
wise.
tensor – Types and Ops for Symbolic numpy
Theano’s strength is in expressing symbolic calculations involving tensors. There are many types of symbolic expressions for tensors. They are grouped into the following sections:
Basic Tensor Functionality
Theano supports any kind of Python object, but its focus is support for symbolic matrix expressions. When
you type,
>>> x = T.fmatrix()
the x is a TensorVariable instance. The T.fmatrix object itself is an instance of TensorType.
Theano knows what type of variable x is because x.type points back to T.fmatrix.
This chapter explains the various ways of creating tensor variables, the attributes and methods of
TensorVariable and TensorType, and various basic symbolic math and arithmetic that Theano supports for tensor variables.
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Creation
Theano provides a list of predefined tensor types that can be used to create a tensor variables. Variables
can be named to facilitate debugging, and all of these constructors accept an optional name argument. For
example, the following each produce a TensorVariable instance that stands for a 0-dimensional ndarray of
integers with the name 'myvar':
>>> x = scalar('myvar', dtype='int32')
>>> x = iscalar('myvar')
>>> x = TensorType(dtype='int32', broadcastable=())('myvar')
Constructors with optional dtype
These are the simplest and often-preferred methods for creating symbolic variables in your code. By default,
they produce floating-point variables (with dtype determined by config.floatX, see floatX) so if you use
these constructors it is easy to switch your code between different levels of floating-point precision.
theano.tensor.scalar(name=None, dtype=config.floatX)
Return a Variable for a 0-dimensional ndarray
theano.tensor.vector(name=None, dtype=config.floatX)
Return a Variable for a 1-dimensional ndarray
theano.tensor.row(name=None, dtype=config.floatX)
Return a Variable for a 2-dimensional ndarray in which the number of rows is guaranteed to be 1.
theano.tensor.col(name=None, dtype=config.floatX)
Return a Variable for a 2-dimensional ndarray in which the number of columns is guaranteed to be 1.
theano.tensor.matrix(name=None, dtype=config.floatX)
Return a Variable for a 2-dimensional ndarray
theano.tensor.tensor3(name=None, dtype=config.floatX)
Return a Variable for a 3-dimensional ndarray
theano.tensor.tensor4(name=None, dtype=config.floatX)
Return a Variable for a 4-dimensional ndarray
All Fully-Typed Constructors
The following TensorType instances are provided in the theano.tensor module. They are all callable, and
accept an optional name argument. So for example:
from theano.tensor import *
x = dmatrix()
# creates one Variable with no name
x = dmatrix('x')
# creates one Variable with name 'x'
xyz = dmatrix('xyz') # creates one Variable with name 'xyz'
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Constructor
bscalar
bvector
brow
bcol
bmatrix
btensor3
btensor4
wscalar
wvector
wrow
wcol
wmatrix
wtensor3
wtensor4
iscalar
ivector
irow
icol
imatrix
itensor3
itensor4
lscalar
lvector
lrow
lcol
lmatrix
ltensor3
ltensor4
dscalar
dvector
drow
dcol
dmatrix
dtensor3
dtensor4
fscalar
fvector
frow
fcol
fmatrix
ftensor3
ftensor4
cscalar
cvector
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dtype
int8
int8
int8
int8
int8
int8
int8
int16
int16
int16
int16
int16
int16
int16
int32
int32
int32
int32
int32
int32
int32
int64
int64
int64
int64
int64
int64
int64
float64
float64
float64
float64
float64
float64
float64
float32
float32
float32
float32
float32
float32
float32
complex64
complex64
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(?,?,?,?)
()
(?,)
(1,?)
(?,1)
(?,?)
(?,?,?)
(?,?,?,?)
()
(?,)
(1,?)
(?,1)
(?,?)
(?,?,?)
(?,?,?,?)
()
(?,)
(1,?)
(?,1)
(?,?)
(?,?,?)
(?,?,?,?)
()
(?,)
broadcastable
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
(True, False)
(False, True)
(False, False)
(False, False, False)
(False, False, False, False)
()
(False,)
Continued on next page
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Table 6.1 – continued from previous page
Constructor dtype
ndim shape
broadcastable
crow
complex64
2
(1,?)
(True, False)
ccol
complex64
2
(?,1)
(False, True)
cmatrix
complex64
2
(?,?)
(False, False)
ctensor3
complex64
3
(?,?,?)
(False, False, False)
ctensor4
complex64
4
(?,?,?,?) (False, False, False, False)
zscalar
complex128 0
()
()
zvector
complex128 1
(?,)
(False,)
zrow
complex128 2
(1,?)
(True, False)
zcol
complex128 2
(?,1)
(False, True)
zmatrix
complex128 2
(?,?)
(False, False)
ztensor3
complex128 3
(?,?,?)
(False, False, False)
ztensor4
complex128 4
(?,?,?,?) (False, False, False, False)
Plural Constructors
There are several constructors that can produce multiple variables at once. These are not frequently used in
practice, but often used in tutorial examples to save space!
iscalars, lscalars, fscalars, dscalars
Return one or more scalar variables.
ivectors, lvectors, fvectors, dvectors
Return one or more vector variables.
irows, lrows, frows, drows
Return one or more row variables.
icols, lcols, fcols, dcols
Return one or more col variables.
imatrices, lmatrices, fmatrices, dmatrices
Return one or more matrix variables.
Each of these plural constructors accepts an integer or several strings. If an integer is provided, the method
will return that many Variables and if strings are provided, it will create one Variable for each string, using
the string as the Variable’s name. For example:
from theano.tensor import *
x, y, z = dmatrices(3) # creates three matrix Variables with no names
x, y, z = dmatrices('x', 'y', 'z') # creates three matrix Variables named 'x',
˓→ 'y' and 'z'
Custom tensor types
If you would like to construct a tensor variable with a non-standard broadcasting pattern, or a larger number
of dimensions you’ll need to create your own TensorType instance. You create such an instance by
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passing the dtype and broadcasting pattern to the constructor. For example, you can create your own 5dimensional tensor type
>>> dtensor5 = TensorType('float64', (False,)*5)
>>> x = dtensor5()
>>> z = dtensor5('z')
You can also redefine some of the provided types and they will interact correctly:
>>> my_dmatrix = TensorType('float64', (False,)*2)
>>> x = my_dmatrix()
# allocate a matrix variable
>>> my_dmatrix == dmatrix
True
See TensorType for more information about creating new types of Tensor.
Converting from Python Objects
Another way of creating a TensorVariable (a TensorSharedVariable to be precise) is by calling shared()
x = shared(numpy.random.randn(3,4))
This will return a shared variable whose .value is a numpy ndarray. The number of dimensions and
dtype of the Variable are inferred from the ndarray argument. The argument to shared will not be copied,
and subsequent changes will be reflected in x.value.
For additional information, see the shared() documentation. Finally, when you use a numpy ndarry
or a Python number together with TensorVariable instances in arithmetic expressions, the result is a
TensorVariable. What happens to the ndarray or the number? Theano requires that the inputs to all
expressions be Variable instances, so Theano automatically wraps them in a TensorConstant.
Note: Theano makes a copy of any ndarray that you use in an expression, so subsequent changes to that
ndarray will not have any effect on the Theano expression.
For numpy ndarrays the dtype is given, but the broadcastable pattern must be inferred. The TensorConstant
is given a type with a matching dtype, and a broadcastable pattern with a True for every shape dimension
that is 1.
For python numbers, the broadcastable pattern is () but the dtype must be inferred. Python integers are
stored in the smallest dtype that can hold them, so small constants like 1 are stored in a bscalar. Likewise,
Python floats are stored in an fscalar if fscalar suffices to hold them perfectly, but a dscalar otherwise.
Note: When config.floatX==float32 (see config), then Python floats are stored instead as single-precision
floats.
For fine control of this rounding policy, see theano.tensor.basic.autocast_float.
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theano.tensor.as_tensor_variable(x, name=None, ndim=None)
Turn an argument x into a TensorVariable or TensorConstant.
Many tensor Ops run their arguments through this function as pre-processing. It passes through TensorVariable instances, and tries to wrap other objects into TensorConstant.
When x is a Python number, the dtype is inferred as described above.
When x is a list or tuple it is passed through numpy.asarray
If the ndim argument is not None, it must be an integer and the output will be broadcasted if necessary
in order to have this many dimensions.
Return type TensorVariable or TensorConstant
TensorType and TensorVariable
class theano.tensor.TensorType(Type)
The Type class used to mark Variables that stand for numpy.ndarray values (numpy.memmap, which is
a subclass of numpy.ndarray, is also allowed). Recalling to the tutorial, the purple box in the tutorial’s
graph-structure figure is an instance of this class.
broadcastable
A tuple of True/False values, one for each dimension. True in position ‘i’ indicates that at
evaluation-time, the ndarray will have size 1 in that ‘i’-th dimension. Such a dimension is called
a broadcastable dimension (see Broadcasting in Theano vs. Numpy).
The broadcastable pattern indicates both the number of dimensions and whether a particular
dimension must have length 1.
Here is a table mapping some broadcastable patterns to what they mean:
pattern
[]
[True]
[True, True]
[False]
[False, False]
[False] * n
[True, False]
[False, True]
[False, True, False]
[True, False, False]
[False, False, False]
interpretation
scalar
1D scalar (vector of length 1)
2D scalar (1x1 matrix)
vector
matrix
nD tensor
row (1xN matrix)
column (Mx1 matrix)
A Mx1xP tensor (a)
A 1xNxP tensor (b)
A MxNxP tensor (pattern of a + b)
For dimensions in which broadcasting is False, the length of this dimension can be 1 or more.
For dimensions in which broadcasting is True, the length of this dimension must be 1.
When two arguments to an element-wise operation (like addition or subtraction) have a different
number of dimensions, the broadcastable pattern is expanded to the left, by padding with True.
For example, a vector’s pattern, [False], could be expanded to [True, False], and would
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behave like a row (1xN matrix). In the same way, a matrix ([False, False]) would behave
like a 1xNxP tensor ([True, False, False]).
If we wanted to create a type representing a matrix that would broadcast over the middle dimension of a 3-dimensional tensor when adding them together, we would define it like this:
>>> middle_broadcaster = TensorType('complex64', [False, True,
˓→False])
ndim
The number of dimensions that a Variable’s value will have at evaluation-time. This must be
known when we are building the expression graph.
dtype
A string indicating the numerical type of the ndarray for which a Variable of this Type is standing. The dtype attribute of a TensorType instance can be any of the following strings.
dtype
'int8'
'int16'
'int32'
'int64'
'uint8'
'uint16'
'uint32'
'uint64'
'float32'
'float64'
'complex64'
'complex128'
domain
signed integer
signed integer
signed integer
signed integer
unsigned integer
unsigned integer
unsigned integer
unsigned integer
floating point
floating point
complex
complex
bits
8
16
32
64
8
16
32
64
32
64
64 (two float32)
128 (two float64)
__init__(self, dtype, broadcastable)
If you wish to use a type of tensor which is not already available (for example, a 5D tensor) you
can build an appropriate type by instantiating TensorType.
TensorVariable
class theano.tensor.TensorVariable(Variable, _tensor_py_operators)
The result of symbolic operations typically have this type.
See _tensor_py_operators for most of the attributes and methods you’ll want to call.
class theano.tensor.TensorConstant(Variable, _tensor_py_operators)
Python and numpy numbers are wrapped in this type.
See _tensor_py_operators for most of the attributes and methods you’ll want to call.
class theano.tensor.TensorSharedVariable(Variable, _tensor_py_operators)
This type is returned by shared() when the value to share is a numpy ndarray.
See _tensor_py_operators for most of the attributes and methods you’ll want to call.
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class theano.tensor._tensor_py_operators
This mix-in class adds convenient attributes, methods, and support to TensorVariable, TensorConstant and TensorSharedVariable for Python operators (see Operator Support).
type
A reference to the TensorType instance describing the sort of values that might be
associated with this variable.
ndim
The number of dimensions of this tensor. Aliased to TensorType.ndim.
dtype
The numeric type of this tensor. Aliased to TensorType.dtype.
reshape(shape, ndim=None)
Returns a view of this tensor that has been reshaped as in numpy.reshape. If the shape
is a Variable argument, then you might need to use the optional ndim parameter to
declare how many elements the shape has, and therefore how many dimensions the
reshaped Variable will have.
See reshape().
dimshuffle(*pattern)
Returns a view of this tensor with permuted dimensions. Typically the pattern will
include the integers 0, 1, ... ndim-1, and any number of ‘x’ characters in dimensions
where this tensor should be broadcasted.
A few examples of patterns and their effect:
•(‘x’) -> make a 0d (scalar) into a 1d vector
•(0, 1) -> identity for 2d vectors
•(1, 0) -> inverts the first and second dimensions
•(‘x’, 0) -> make a row out of a 1d vector (N to 1xN)
•(0, ‘x’) -> make a column out of a 1d vector (N to Nx1)
•(2, 0, 1) -> AxBxC to CxAxB
•(0, ‘x’, 1) -> AxB to Ax1xB
•(1, ‘x’, 0) -> AxB to Bx1xA
•(1,) -> This remove dimensions 0. It must be a broadcastable dimension (1xA to
A)
flatten(ndim=1)
Returns a view of this tensor with ndim dimensions, whose shape for the first ndim-1
dimensions will be the same as self, and shape in the remaining dimension will be
expanded to fit in all the data from self.
See flatten().
ravel()
return self.flatten(). For NumPy compatibility.
T
Transpose of this tensor.
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>>> x = T.zmatrix()
>>> y = 3+.2j * x.T
Note: In numpy and in Theano, the transpose of a vector is exactly the same vector!
Use reshape or dimshuffle to turn your vector into a row or column matrix.
{any,all}(axis=None, keepdims=False)
{sum,prod,mean}(axis=None, dtype=None, keepdims=False, acc_dtype=None)
{var,std,min,max,argmin,argmax}(axis=None, keepdims=False),
diagonal(offset=0, axis1=0, axis2=1)
astype(dtype)
take(indices, axis=None, mode=’raise’)
copy() Return a new symbolic variable that is a copy of the variable. Does
norm(L, axis=None)
nonzero(self, return_matrix=False)
nonzero_values(self )
sort(self, axis=-1, kind=’quicksort’, order=None)
argsort(self, axis=-1, kind=’quicksort’, order=None)
clip(self, a_min, a_max)
conf()
repeat(repeats, axis=None)
round(mode=”half_away_from_zero”)
trace()
get_scalar_constant_value()
zeros_like(model, dtype=None)
All the above methods are equivalent to NumPy for Theano on the current tensor.
__{abs,neg,lt,le,gt,ge,invert,and,or,add,sub,mul,div,truediv,floordiv}__
Those elemwise operation are supported via Python syntax.
argmax(axis=None, keepdims=False)
See theano.tensor.argmax.
argmin(axis=None, keepdims=False)
See theano.tensor.argmin.
argsort(axis=-1, kind=’quicksort’, order=None)
See theano.tensor.argsort.
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broadcastable
The broadcastable signature of this tensor.
See also:
broadcasting
choose(a, choices, out=None, mode=’raise’)
Construct an array from an index array and a set of arrays to choose from.
clip(a_min, a_max)
Clip (limit) the values in an array.
compress(a, axis=None)
Return selected slices only.
conj()
See theano.tensor.conj.
conjugate()
See theano.tensor.conj.
copy(name=None)
Return a symbolic copy and optionally assign a name.
Does not copy the tags.
dimshuffle(*pattern)
Reorder the dimensions of this variable, optionally inserting broadcasted dimensions.
Parameters pattern – List/tuple of int mixed with ‘x’ for broadcastable dimensions.
Examples
For example, to create a 3D view of a [2D] matrix, call dimshuffle([0,'x',1]). This
will create a 3D view such that the middle dimension is an implicit broadcasted dimension. To
do the same thing on the transpose of that matrix, call dimshuffle([1, 'x', 0]).
Notes
This function supports the pattern passed as a tuple, or as a variable-length argument (e.g. a.
dimshuffle(pattern) is equivalent to a.dimshuffle(*pattern) where pattern
is a list/tuple of ints mixed with ‘x’ characters).
See also:
DimShuffle()
dtype
The dtype of this tensor.
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fill(value)
Fill inputted tensor with the assigned value.
imag
Return imaginary component of complex-valued tensor z
Generalizes a scalar op to tensors.
All the inputs must have the same number of dimensions. When the Op is performed, for each
dimension, each input’s size for that dimension must be the same. As a special case, it can also
be 1 but only if the input’s broadcastable flag is True for that dimension. In that case, the tensor
is (virtually) replicated along that dimension to match the size of the others.
The dtypes of the outputs mirror those of the scalar Op that is being generalized to tensors. In
particular, if the calculations for an output are done inplace on an input, the output type must
be the same as the corresponding input type (see the doc of scalar.ScalarOp to get help about
controlling the output type)
Parameters
• scalar_op – An instance of a subclass of scalar.ScalarOp which works
uniquely on scalars.
• inplace_pattern – A dictionary that maps the index of an output to the
index of an input so the output is calculated inplace using the input’s storage.
(Just like destroymap, but without the lists.)
• nfunc_spec – Either None or a tuple of three elements, (nfunc_name, nin,
nout) such that getattr(numpy, nfunc_name) implements this operation, takes
nin inputs and nout outputs. Note that nin cannot always be inferred from the
scalar op’s own nin field because that value is sometimes 0 (meaning a variable
number of inputs), whereas the numpy function may not have varargs.
Note:
Elemwise(add) represents + on tensors (x + y)
Elemwise(add, {0 : 0}) represents the += operation (x += y)
Elemwise(add, {0 : 1}) represents += on the second argument (y += x)
Elemwise(mul)(rand(10, 5), rand(1, 5)) the second input is completed along the first dimension
to match the first input
Elemwise(true_div)(rand(10, 5), rand(10, 1)) same but along the second dimension
Elemwise(int_div)(rand(1, 5), rand(10, 1)) the output has size (10, 5)
Elemwise(log)(rand(3, 4, 5))
max(axis=None, keepdims=False)
See theano.tensor.max.
mean(axis=None, dtype=None, keepdims=False, acc_dtype=None)
See theano.tensor.mean.
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min(axis=None, keepdims=False)
See theano.tensor.min.
ndim
The rank of this tensor.
nonzero(return_matrix=False)
See theano.tensor.nonzero.
nonzero_values()
See theano.tensor.nonzero_values.
prod(axis=None, dtype=None, keepdims=False, acc_dtype=None)
See theano.tensor.prod.
ptp(axis=None)
See ‘theano.tensor.ptp’.
real
Return real component of complex-valued tensor z
Generalizes a scalar op to tensors.
All the inputs must have the same number of dimensions. When the Op is performed, for each
dimension, each input’s size for that dimension must be the same. As a special case, it can also
be 1 but only if the input’s broadcastable flag is True for that dimension. In that case, the tensor
is (virtually) replicated along that dimension to match the size of the others.
The dtypes of the outputs mirror those of the scalar Op that is being generalized to tensors. In
particular, if the calculations for an output are done inplace on an input, the output type must
be the same as the corresponding input type (see the doc of scalar.ScalarOp to get help about
controlling the output type)
Parameters
• scalar_op – An instance of a subclass of scalar.ScalarOp which works
uniquely on scalars.
• inplace_pattern – A dictionary that maps the index of an output to the
index of an input so the output is calculated inplace using the input’s storage.
(Just like destroymap, but without the lists.)
• nfunc_spec – Either None or a tuple of three elements, (nfunc_name, nin,
nout) such that getattr(numpy, nfunc_name) implements this operation, takes
nin inputs and nout outputs. Note that nin cannot always be inferred from the
scalar op’s own nin field because that value is sometimes 0 (meaning a variable
number of inputs), whereas the numpy function may not have varargs.
Note:
Elemwise(add) represents + on tensors (x + y)
Elemwise(add, {0 : 0}) represents the += operation (x += y)
Elemwise(add, {0 : 1}) represents += on the second argument (y += x)
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Elemwise(mul)(rand(10, 5), rand(1, 5)) the second input is completed along the first dimension
to match the first input
Elemwise(true_div)(rand(10, 5), rand(10, 1)) same but along the second dimension
Elemwise(int_div)(rand(1, 5), rand(10, 1)) the output has size (10, 5)
Elemwise(log)(rand(3, 4, 5))
repeat(repeats, axis=None)
See theano.tensor.repeat.
reshape(shape, ndim=None)
Return a reshaped view/copy of this variable.
Parameters
• shape – Something that can be converted to a symbolic vector of integers.
• ndim – The length of the shape. Passing None here means for Theano to try
and guess the length of shape.
Warning: This has a different signature than numpy’s ndarray.reshape! In numpy you do
not need to wrap the shape arguments in a tuple, in theano you do need to.
round(mode=’half_away_from_zero’)
See theano.tensor.round.
sort(axis=-1, kind=’quicksort’, order=None)
See theano.tensor.sort.
squeeze()
Remove broadcastable dimensions from the shape of an array.
It returns the input array, but with the broadcastable dimensions removed. This is always x itself
or a view into x.
std(axis=None, keepdims=False)
See theano.tensor.std.
sum(axis=None, dtype=None, keepdims=False, acc_dtype=None)
See theano.tensor.sum.
swapaxes(axis1, axis2)
Return ‘tensor.swapaxes(self, axis1, axis2).
If a matrix is provided with the right axes, its transpose will be returned.
transfer(target)
If target is ‘cpu’ this will transfer to a TensorType (if not already one). Other types may define
additional targets.
Parameters target (str) – The desired location of the output variable
transpose(*axes)
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Returns
• object – tensor.transpose(self, axes) or tensor.transpose(self, axes[0]).
• If only one axes argument is provided and it is iterable, then it is
• assumed to be the entire axes tuple, and passed intact to
• tensor.transpose.
var(axis=None, keepdims=False)
See theano.tensor.var.
Shaping and Shuffling
To re-order the dimensions of a variable, to insert or remove broadcastable dimensions, see
_tensor_py_operators.dimshuffle().
theano.tensor.shape(x)
Returns an lvector representing the shape of x.
theano.tensor.reshape(x, newshape, ndim=None)
Parameters
• x (any TensorVariable (or compatible)) – variable to be reshaped
• newshape (lvector (or compatible)) – the new shape for x
• ndim – optional - the length that newshape‘s value will have. If this is None,
then reshape() will infer it from newshape.
Return type variable with x’s dtype, but ndim dimensions
Note: This function can infer the length of a symbolic newshape in some cases, but if it cannot and
you do not provide the ndim, then this function will raise an Exception.
theano.tensor.shape_padleft(x, n_ones=1)
Reshape x by left padding the shape with n_ones 1s. Note that all this new dimension will be broadcastable. To make them non-broadcastable see the unbroadcast().
Parameters x (any TensorVariable (or compatible)) – variable to be reshaped
theano.tensor.shape_padright(x, n_ones=1)
Reshape x by right padding the shape with n_ones 1s. Note that all this new dimension will be
broadcastable. To make them non-broadcastable see the unbroadcast().
Parameters x (any TensorVariable (or compatible)) – variable to be reshaped
theano.tensor.shape_padaxis(t, axis)
Reshape t by inserting 1 at the dimension axis. Note that this new dimension will be broadcastable.
To make it non-broadcastable see the unbroadcast().
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Parameters
• x (any TensorVariable (or compatible)) – variable to be reshaped
• axis (int) – axis where to add the new dimension to x
Example:
>>> tensor = theano.tensor.tensor3()
>>> theano.tensor.shape_padaxis(tensor,
DimShuffle{x,0,1,2}.0
>>> theano.tensor.shape_padaxis(tensor,
DimShuffle{0,x,1,2}.0
>>> theano.tensor.shape_padaxis(tensor,
DimShuffle{0,1,2,x}.0
>>> theano.tensor.shape_padaxis(tensor,
DimShuffle{0,1,2,x}.0
axis=0)
axis=1)
axis=3)
axis=-1)
theano.tensor.unbroadcast(x, *axes)
Make the input impossible to broadcast in the specified axes.
For example, addbroadcast(x, 0) will make the first dimension of x broadcastable. When performing
the function, if the length of x along that dimension is not 1, a ValueError will be raised.
We apply the opt here not to pollute the graph especially during the gpu optimization
Parameters
• x (tensor_like) – Input theano tensor.
• axis
(an int or an iterable object such as list or
tuple of int values) – The dimension along which the tensor x should
be unbroadcastable. If the length of x along these dimensions is not 1, a
ValueError will be raised.
Returns A theano tensor, which is unbroadcastable along the specified dimensions.
Return type tensor
theano.tensor.addbroadcast(x, *axes)
Make the input broadcastable in the specified axes.
For example, addbroadcast(x, 0) will make the first dimension of x broadcastable. When performing
the function, if the length of x along that dimension is not 1, a ValueError will be raised.
We apply the opt here not to pollute the graph especially during the gpu optimization
Parameters
• x (tensor_like) – Input theano tensor.
• axis
(an int or an iterable object such as list or
tuple of int values) – The dimension along which the tensor x should
be broadcastable. If the length of x along these dimensions is not 1, a ValueError
will be raised.
Returns A theano tensor, which is broadcastable along the specified dimensions.
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Return type tensor
theano.tensor.patternbroadcast(x, broadcastable)
Make the input adopt a specific broadcasting pattern.
Broadcastable must be iterable. For example, patternbroadcast(x, (True, False)) will make the first
dimension of x broadcastable and the second dimension not broadcastable, so x will now be a row.
We apply the opt here not to pollute the graph especially during the gpu optimization.
Parameters
• x (tensor_like) – Input theano tensor.
• broadcastable (an iterable object such as list or tuple
of bool values) – A set of boolean values indicating whether a dimension
should be broadcastable or not. If the length of x along these dimensions is not 1,
a ValueError will be raised.
Returns A theano tensor, which is unbroadcastable along the specified dimensions.
Return type tensor
theano.tensor.flatten(x, outdim=1)
Similar to reshape(), but the shape is inferred from the shape of x.
Parameters
• x (any TensorVariable (or compatible)) – variable to be flattened
• outdim (int) – the number of dimensions in the returned variable
Return type variable with same dtype as x and outdim dimensions
Returns variable with the same shape as x in the leading outdim-1 dimensions, but with
all remaining dimensions of x collapsed into the last dimension.
For example, if we flatten a tensor of shape (2, 3, 4, 5) with flatten(x, outdim=2), then we’ll have the
same (2-1=1) leading dimensions (2,), and the remaining dimensions are collapsed. So the output in
this example would have shape (2, 60).
theano.tensor.tile(x, reps, ndim=None)
Construct an array by repeating the input x according to reps pattern.
Tiles its input according to reps. The length of reps is the number of dimension of x and contains the
number of times to tile x in each dimension.
See numpy.tile documentation for examples.
See theano.tensor.extra_ops.repeat
Note Currently, reps must be a constant, x.ndim and len(reps) must be equal and, if specified, ndim must be equal to both.
theano.tensor.roll(x, shift, axis=None)
Convenience function to roll TensorTypes along the given axis.
Syntax copies numpy.roll function.
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Parameters
• x (tensor_like) – Input tensor.
• shift (int (symbolic or literal)) – The number of places by which
elements are shifted.
• axis (int (symbolic or literal), optional) – The axis along
which elements are shifted. By default, the array is flattened before shifting, after
which the original shape is restored.
Returns Output tensor, with the same shape as x.
Return type tensor
Creating Tensor
theano.tensor.zeros_like(x)
Parameters x – tensor that has same shape as output
Returns a tensor filled with 0s that has same shape as x.
theano.tensor.ones_like(x)
Parameters x – tensor that has same shape as output
Returns a tensor filled with 1s that has same shape as x.
theano.tensor.zeros(shape, dtype=None)
Parameters
• shape – a tuple/list of scalar with the shape information.
• dtype – the dtype of the new tensor. If None, will use floatX.
Returns a tensor filled with 0s of the provided shape.
theano.tensor.ones(shape, dtype=None)
Parameters
• shape – a tuple/list of scalar with the shape information.
• dtype – the dtype of the new tensor. If None, will use floatX.
Returns a tensor filled with 1s of the provided shape.
theano.tensor.fill(a, b)
Parameters
• a – tensor that has same shape as output
• b – theano scalar or value with which you want to fill the output
Create a matrix by filling the shape of a with b
theano.tensor.alloc(value, *shape)
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Parameters
• value – a value with which to fill the output
• shape – the dimensions of the returned array
Returns an N-dimensional tensor initialized by value and having the specified shape.
theano.tensor.eye(n, m=None, k=0, dtype=theano.config.floatX)
Parameters
• n – number of rows in output (value or theano scalar)
• m – number of columns in output (value or theano scalar)
• k – Index of the diagonal: 0 refers to the main diagonal, a positive value refers
to an upper diagonal, and a negative value to a lower diagonal. It can be a theano
scalar.
Returns An array where all elements are equal to zero, except for the k-th diagonal, whose
values are equal to one.
theano.tensor.identity_like(x)
Parameters x – tensor
Returns A tensor of same shape as x that is filled with 0s everywhere except for the main
diagonal, whose values are equal to one. The output will have same dtype as x.
theano.tensor.stack(tensors, axis=0)
Stack tensors in sequence on given axis (default is 0).
Take a sequence of tensors and stack them on given axis to make a single tensor. The size in dimension
axis of the result will be equal to the number of tensors passed.
Parameters
• tensors – a list or a tuple of one or more tensors of the same rank.
• axis – the axis along which the tensors will be stacked. Default value is 0.
Returns A tensor such that rval[0] == tensors[0], rval[1] == tensors[1], etc.
Examples:
>>>
>>>
>>>
>>>
>>>
1
>>>
>>>
>>>
>>>
>>>
5
>>>
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a = theano.tensor.scalar()
b = theano.tensor.scalar()
c = theano.tensor.scalar()
x = theano.tensor.stack([a, b, c])
x.ndim # x is a vector of length 3.
a = theano.tensor.tensor4()
b = theano.tensor.tensor4()
c = theano.tensor.tensor4()
x = theano.tensor.stack([a, b, c])
x.ndim # x is a 5d tensor.
rval = x.eval(dict((t, np.zeros((2, 2, 2, 2))) for t in [a, b, c]))
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>>> rval.shape # 3 tensors are stacked on axis 0
(3, 2, 2, 2, 2)
We can also specify different axis than default value 0
>>>
>>>
5
>>>
>>>
(2,
>>>
>>>
5
>>>
>>>
(2,
x = theano.tensor.stack([a, b, c], axis=3)
x.ndim
rval = x.eval(dict((t, np.zeros((2, 2, 2, 2))) for t in [a, b, c]))
rval.shape # 3 tensors are stacked on axis 3
2, 2, 3, 2)
x = theano.tensor.stack([a, b, c], axis=-2)
x.ndim
rval = x.eval(dict((t, np.zeros((2, 2, 2, 2))) for t in [a, b, c]))
rval.shape # 3 tensors are stacked on axis -2
2, 2, 3, 2)
theano.tensor.stack(*tensors)
Warning: The interface stack(*tensors) is deprecated! Use stack(tensors, axis=0) instead.
Stack tensors in sequence vertically (row wise).
Take a sequence of tensors and stack them vertically to make a single tensor.
Parameters tensors – one or more tensors of the same rank
Returns A tensor such that rval[0] == tensors[0], rval[1] == tensors[1], etc.
>>>
>>>
>>>
>>>
>>>
1
x0 = T.scalar()
x1 = T.scalar()
x2 = T.scalar()
x = T.stack(x0, x1, x2)
x.ndim # x is a vector of length 3.
theano.tensor.concatenate(tensor_list, axis=0)
Parameters
• tensor_list (a list or tuple of Tensors that all have the same shape in the axes
not specified by the axis argument.) – one or more Tensors to be concatenated
together into one.
• axis (literal or symbolic integer) – Tensors will be joined along
this axis, so they may have different shape[axis]
>>> x0 = T.fmatrix()
>>> x1 = T.ftensor3()
>>> x2 = T.fvector()
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>>> x = T.concatenate([x0, x1[0], T.shape_padright(x2)], axis=1)
>>> x.ndim
2
theano.tensor.stacklists(tensor_list)
Parameters tensor_list (an iterable that contains either tensors or other iterables of
the same type as tensor_list (in other words, this is a tree whose leaves are tensors).)
– tensors to be stacked together.
Recursively stack lists of tensors to maintain similar structure.
This function can create a tensor from a shaped list of scalars:
>>> from theano.tensor import stacklists, scalars, matrices
>>> from theano import function
>>> a, b, c, d = scalars('abcd')
>>> X = stacklists([[a, b], [c, d]])
>>> f = function([a, b, c, d], X)
>>> f(1, 2, 3, 4)
array([[ 1., 2.],
[ 3., 4.]])
We can also stack arbitrarily shaped tensors. Here we stack matrices into a 2 by 2 grid:
>>>
>>>
>>>
>>>
>>>
>>>
(2,
from numpy import ones
a, b, c, d = matrices('abcd')
X = stacklists([[a, b], [c, d]])
f = function([a, b, c, d], X)
x = ones((4, 4), 'float32')
f(x, x, x, x).shape
2, 4, 4)
theano.tensor.basic.choose(a, choices, out=None, mode=’raise’)
Construct an array from an index array and a set of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples - in its full generality, this
function is less simple than it might seem from the following code description (below ndi =
numpy.lib.index_tricks):
np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)]).
But this omits some subtleties. Here is a fully general summary:
Given an index array (a) of integers and a sequence of n arrays (choices), a and each choice array
are first broadcast, as necessary, to arrays of a common shape; calling these Ba and Bchoices[i], i =
0,...,n-1 we have that, necessarily, Ba.shape == Bchoices[i].shape for each i. Then, a new array with
shape Ba.shape is created as follows:
•if mode=raise (the default), then, first of all, each element of a (and thus Ba) must be in the range
[0, n-1]; now, suppose that i (in that range) is the value at the (j0, j1, ..., jm) position in Ba - then
the value at the same position in the new array is the value in Bchoices[i] at that same position;
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•if mode=wrap, values in a (and thus Ba) may be any (signed) integer; modular arithmetic is
used to map integers outside the range [0, n-1] back into that range; and then the new array is
constructed as above;
•if mode=clip, values in a (and thus Ba) may be any (signed) integer; negative integers are mapped
to 0; values greater than n-1 are mapped to n-1; and then the new array is constructed as above.
Parameters
• a (int array) – This array must contain integers in [0, n-1], where n is the
number of choices, unless mode=wrap or mode=clip, in which cases any integers
are permissible.
• choices (sequence of arrays) – Choice arrays. a and all of the choices
must be broadcastable to the same shape. If choices is itself an array (not
recommended), then its outermost dimension (i.e., the one corresponding to
choices.shape[0]) is taken as defining the sequence.
• out (array, optional) – If provided, the result will be inserted into this
array. It should be of the appropriate shape and dtype.
• mode ({raise (default), wrap, clip}, optional) – Specifies how indices outside [0, n-1] will be treated: raise : an exception is raised wrap : value becomes value mod n clip : values < 0 are mapped to 0, values > n-1 are mapped
to n-1
Returns The merged result.
Return type merged_array - array
Raises ValueError - shape mismatch – If a and each choice array are not all broadcastable
to the same shape.
Reductions
theano.tensor.max(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the maximum
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns maximum of x along axis
axis can be:
• None - in which case the maximum is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
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theano.tensor.argmax(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis along which to compute the index of the maximum
Parameter keepdims - (boolean) If this is set to True, the axis which is reduced is left
in the result as a dimension with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns the index of the maximum value along a given axis
if axis=None, Theano 0.5rc1 or later: argmax over the flattened tensor (like numpy) older: then
axis is assumed to be ndim(x)-1
theano.tensor.max_and_argmax(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis along which to compute the maximum and its index
Parameter keepdims - (boolean) If this is set to True, the axis which is reduced is left
in the result as a dimension with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns the maxium value along a given axis and its index.
if axis=None, Theano 0.5rc1 or later: max_and_argmax over the flattened tensor (like numpy)
older: then axis is assumed to be ndim(x)-1
theano.tensor.min(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the minimum
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns minimum of x along axis
axis can be:
• None - in which case the minimum is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.argmin(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis along which to compute the index of the minimum
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Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns the index of the minimum value along a given axis
if axis=None, Theano 0.5rc1 or later: argmin over the flattened tensor (like numpy) older: then
axis is assumed to be ndim(x)-1
theano.tensor.sum(x, axis=None, dtype=None, keepdims=False, acc_dtype=None)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the sum
Parameter dtype - The dtype of the returned tensor. If None, then we use the default dtype
which is the same as the input tensor’s dtype except when:
• the input dtype is a signed integer of precision < 64 bit, in which case we use int64
• the input dtype is an unsigned integer of precision < 64 bit, in which case we use
uint64
This default dtype does _not_ depend on the value of “acc_dtype”.
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Parameter acc_dtype - The dtype of the internal accumulator. If None (default), we use
the dtype in the list below, or the input dtype if its precision is higher:
• for int dtypes, we use at least int64;
• for uint dtypes, we use at least uint64;
• for float dtypes, we use at least float64;
• for complex dtypes, we use at least complex128.
Returns sum of x along axis
axis can be:
• None - in which case the sum is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.prod(x, axis=None, dtype=None,
no_zeros_in_input=False)
keepdims=False,
acc_dtype=None,
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the product
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Parameter dtype - The dtype of the returned tensor. If None, then we use the default dtype
which is the same as the input tensor’s dtype except when:
• the input dtype is a signed integer of precision < 64 bit, in which case we use int64
• the input dtype is an unsigned integer of precision < 64 bit, in which case we use
uint64
This default dtype does _not_ depend on the value of “acc_dtype”.
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Parameter acc_dtype - The dtype of the internal accumulator. If None (default), we use
the dtype in the list below, or the input dtype if its precision is higher:
• for int dtypes, we use at least int64;
• for uint dtypes, we use at least uint64;
• for float dtypes, we use at least float64;
• for complex dtypes, we use at least complex128.
Parameter no_zeros_in_input - The grad of prod is complicated as we need to handle 3
different cases: without zeros in the input reduced group, with 1 zero or with more
zeros.
This could slow you down, but more importantly, we currently don’t support the second derivative of the 3 cases. So you cannot take the second derivative of the default
prod().
To remove the handling of the special cases of 0 and so get some small speed up and
allow second derivative set no_zeros_in_inputs to True. It defaults to False.
It is the user responsibility to make sure there are no zeros in the inputs. If there
are, the grad will be wrong.
Returns product of every term in x along axis
axis can be:
• None - in which case the sum is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.mean(x, axis=None, dtype=None, keepdims=False, acc_dtype=None)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the mean
Parameter dtype - The dtype to cast the result of the inner summation into. For instance,
by default, a sum of a float32 tensor will be done in float64 (acc_dtype would be
float64 by default), but that result will be casted back in float32.
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Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Parameter acc_dtype - The dtype of the internal accumulator of the inner summation.
This will not necessarily be the dtype of the output (in particular if it is a discrete
(int/uint) dtype, the output will be in a float type). If None, then we use the same rules
as sum().
Returns mean value of x along axis
axis can be:
• None - in which case the mean is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.var(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the variance
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns variance of x along axis
axis can be:
• None - in which case the variance is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.std(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to compute the standard deviation
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns variance of x along axis
axis can be:
• None - in which case the standard deviation is computed along all axes (like numpy)
• an int - computed along this axis
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• a list of ints - computed along these axes
theano.tensor.all(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to apply ‘bitwise and’
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns bitwise and of x along axis
axis can be:
• None - in which case the ‘bitwise and’ is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.any(x, axis=None, keepdims=False)
Parameter x - symbolic Tensor (or compatible)
Parameter axis - axis or axes along which to apply bitwise or
Parameter keepdims - (boolean) If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option, the result will broadcast
correctly against the original tensor.
Returns bitwise or of x along axis
axis can be:
• None - in which case the ‘bitwise or’ is computed along all axes (like numpy)
• an int - computed along this axis
• a list of ints - computed along these axes
theano.tensor.ptp(x, axis = None)
Range of values (maximum - minimum) along an axis. The name of the function comes from the
acronym for peak to peak.
Parameter x Input tensor.
Parameter axis Axis along which to find the peaks. By default, flatten the array.
Returns A new array holding the result.
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Indexing
Like NumPy, Theano distinguishes between basic and advanced indexing. Theano fully supports basic
indexing (see NumPy’s indexing).
Integer advanced indexing will be supported in 0.6rc4 (or the development version). We do not support
boolean masks, as Theano does not have a boolean type (we use int8 for the output of logic operators).
NumPy with a mask:
>>> n = np.arange(9).reshape(3,3)
>>> n[n > 4]
array([5, 6, 7, 8])
Theano indexing with a “mask” (incorrect approach):
>>> t = theano.tensor.arange(9).reshape((3,3))
>>> t[t > 4].eval() # an array with shape (3, 3, 3)
array([[[0, 1, 2],
[0, 1, 2],
[0, 1, 2]],
[[0, 1, 2],
[0, 1, 2],
[3, 4, 5]],
[[3, 4, 5],
[3, 4, 5],
[3, 4, 5]]])
Getting a Theano result like NumPy:
>>> t[(t > 4).nonzero()].eval()
array([5, 6, 7, 8])
The gradient of Advanced indexing needs in many cases NumPy 1.8. It is not released yet as of April 30th,
2013. You can use NumPy development version to have this feature now.
Index-assignment is not supported. If you want to do something like a[5] = b or a[5]+=b, see
theano.tensor.set_subtensor() and theano.tensor.inc_subtensor() below.
theano.tensor.set_subtensor(x, y, inplace=False, tolerate_inplace_aliasing=False)
Return x with the given subtensor overwritten by y.
Parameters
• x – Symbolic variable for the lvalue of = operation.
• y – Symbolic variable for the rvalue of = operation.
• tolerate_inplace_aliasing – See inc_subtensor for documentation.
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Examples
To replicate the numpy expression “r[10:] = 5”, type
>>> r = ivector()
>>> new_r = set_subtensor(r[10:], 5)
theano.tensor.inc_subtensor(x, y, inplace=False, set_instead_of_inc=False, tolerate_inplace_aliasing=False)
Return x with the given subtensor incremented by y.
Parameters
• x – The symbolic result of a Subtensor operation.
• y – The amount by which to increment the subtensor in question.
• inplace – Don’t use. Theano will do it when possible.
• set_instead_of_inc – If True, do a set_subtensor instead.
• tolerate_inplace_aliasing – Allow x and y to be views of a single
underlying array even while working inplace. For correct results, x and y must
not be overlapping views; if they overlap, the result of this Op will generally be
incorrect. This value has no effect if inplace=False.
Examples
To replicate the numpy expression “r[10:] += 5”, type
>>> r = ivector()
>>> new_r = inc_subtensor(r[10:], 5)
Operator Support
Many Python operators are supported.
>>> a, b = T.itensor3(), T.itensor3() # example inputs
Arithmetic
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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a + 3
3 - a
a * 3.5
2.2 / a
2.2 // a
2.2**a
b % a
#
#
#
#
#
#
#
T.add(a, 3) -> itensor3
T.sub(3, a)
T.mul(a, 3.5) -> ftensor3 or dtensor3 (depending on casting)
T.truediv(2.2, a)
T.intdiv(2.2, a)
T.pow(2.2, a)
T.mod(b, a)
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Bitwise
>>>
>>>
>>>
>>>
a & b
a ^ 1
a | b
~a
#
#
#
#
T.and_(a,b)
T.xor(a,1)
T.or_(a,b)
T.invert(a)
bitwise
bitwise
bitwise
bitwise
and (alias T.bitwise_and)
xor (alias T.bitwise_xor)
or (alias T.bitwise_or)
invert (alias T.bitwise_not)
Inplace
In-place operators are not supported. Theano’s graph-optimizations will determine which intermediate values to use for in-place computations. If you would like to update the value of a shared variable, consider
using the updates argument to theano.function().
Elementwise
Casting
theano.tensor.cast(x, dtype)
Cast any tensor x to a Tensor of the same shape, but with a different numerical type dtype.
This is not a reinterpret cast, but a coersion cast, similar to numpy.asarray(x,
dtype=dtype).
import theano.tensor as T
x = T.matrix()
x_as_int = T.cast(x, 'int32')
Attempting to casting a complex value to a real value is ambiguous and will raise an exception. Use
real(), imag(), abs(), or angle().
theano.tensor.real(x)
Return the real (not imaginary) components of Tensor x. For non-complex x this function returns x.
theano.tensor.imag(x)
Return the imaginary components of Tensor x. For non-complex x this function returns zeros_like(x).
Comparisons
The six usual equality and inequality operators share the same interface.
Parameter a - symbolic Tensor (or compatible)
Parameter b - symbolic Tensor (or compatible)
Return type symbolic Tensor
Returns a symbolic tensor representing the application of the logical elementwise operator.
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Note: Theano has no boolean dtype. Instead, all boolean tensors are represented in 'int8'.
Here is an example with the less-than operator.
import theano.tensor as T
x,y = T.dmatrices('x','y')
z = T.le(x,y)
theano.tensor.lt(a, b)
Returns a symbolic 'int8' tensor representing the result of logical less-than (a<b).
Also available using syntax a < b
theano.tensor.gt(a, b)
Returns a symbolic 'int8' tensor representing the result of logical greater-than (a>b).
Also available using syntax a > b
theano.tensor.le(a, b)
Returns a variable representing the result of logical less than or equal (a<=b).
Also available using syntax a <= b
theano.tensor.ge(a, b)
Returns a variable representing the result of logical greater or equal than (a>=b).
Also available using syntax a >= b
theano.tensor.eq(a, b)
Returns a variable representing the result of logical equality (a==b).
theano.tensor.neq(a, b)
Returns a variable representing the result of logical inequality (a!=b).
theano.tensor.isnan(a)
Returns a variable representing the comparison of a elements with nan.
This is equivalent to numpy.isnan.
theano.tensor.isinf(a)
Returns a variable representing the comparison of a elements with inf or -inf.
This is equivalent to numpy.isinf.
theano.tensor.isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)
Returns a symbolic 'int8' tensor representing where two tensors are equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b))
and the absolute difference atol are added together to compare against the absolute difference between
a and b.
For finite values, isclose uses the following equation to test whether two floating point values are
equivalent: |a - b| <= (atol + rtol * |b|)
For infinite values, isclose checks if both values are the same signed inf value.
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If equal_nan is True, isclose considers NaN values in the same position to be close. Otherwise, NaN
values are not considered close.
This is equivalent to numpy.isclose.
theano.tensor.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)
Returns a symbolic 'int8' value representing if all elements in two tensors are equal within a
tolerance.
See notes in isclose for determining values equal within a tolerance.
This is equivalent to numpy.allclose.
Condition
theano.tensor.switch(cond, ift, iff )
Returns a variable representing a switch between ift (iftrue) and iff (iffalse) based on the condition cond. This is the theano equivalent of numpy.where.
Parameter cond - symbolic Tensor (or compatible)
Parameter ift - symbolic Tensor (or compatible)
Parameter iff - symbolic Tensor (or compatible)
Return type symbolic Tensor
import theano.tensor as T
a,b = T.dmatrices('a','b')
x,y = T.dmatrices('x','y')
z = T.switch(T.lt(a,b), x, y)
theano.tensor.where(cond, ift, iff )
Alias for switch. where is the numpy name.
theano.tensor.clip(x, min, max)
Return a variable representing x, but with all elements greater than max clipped to max and all elements less than min clipped to min.
Normal broadcasting rules apply to each of x, min, and max.
Bit-wise
The bitwise operators possess this interface:
Parameter a - symbolic Tensor of integer type.
Parameter b - symbolic Tensor of integer type.
Note: The bitwise operators must have an integer type as input.
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The bit-wise not (invert) takes only one parameter.
Return type symbolic Tensor with corresponding dtype.
theano.tensor.and_(a, b)
Returns a variable representing the result of the bitwise and.
theano.tensor.or_(a, b)
Returns a variable representing the result of the bitwise or.
theano.tensor.xor(a, b)
Returns a variable representing the result of the bitwise xor.
theano.tensor.invert(a)
Returns a variable representing the result of the bitwise not.
theano.tensor.bitwise_and(a, b)
Alias for and_. bitwise_and is the numpy name.
theano.tensor.bitwise_or(a, b)
Alias for or_. bitwise_or is the numpy name.
theano.tensor.bitwise_xor(a, b)
Alias for xor_. bitwise_xor is the numpy name.
theano.tensor.bitwise_not(a, b)
Alias for invert. invert is the numpy name.
Here is an example using the bit-wise and_ via the & operator:
import theano.tensor as T
x,y = T.imatrices('x','y')
z = x & y
Mathematical
theano.tensor.abs_(a)
Returns a variable representingthe absolute of a, ie |a|.
Note: Can also be accessed with abs(a).
theano.tensor.angle(a)
Returns a variable representing angular component of complex-valued Tensor a.
theano.tensor.exp(a)
Returns a variable representing the exponential of a, ie e^a.
theano.tensor.maximum(a, b)
Returns a variable representing the maximum element by element of a and b
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theano.tensor.minimum(a, b)
Returns a variable representing the minimum element by element of a and b
theano.tensor.neg(a)
Returns a variable representing the negation of a (also -a).
theano.tensor.inv(a)
Returns a variable representing the inverse of a, ie 1.0/a. Also called reciprocal.
theano.tensor.log(a), log2(a), log10(a)
Returns a variable representing the base e, 2 or 10 logarithm of a.
theano.tensor.sgn(a)
Returns a variable representing the sign of a.
theano.tensor.ceil(a)
Returns a variable representing the ceiling of a (for example ceil(2.1) is 3).
theano.tensor.floor(a)
Returns a variable representing the floor of a (for example floor(2.9) is 2).
theano.tensor.round(a, mode=”half_away_from_zero”)
Returns a variable representing the rounding of a in the same dtype as a. Implemented rounding mode
are half_away_from_zero and half_to_even.
theano.tensor.iround(a, mode=”half_away_from_zero”)
Short hand for cast(round(a, mode),’int64’).
theano.tensor.sqr(a)
Returns a variable representing the square of a, ie a^2.
theano.tensor.sqrt(a)
Returns a variable representing the of a, ie a^0.5.
theano.tensor.cos(a), sin(a), tan(a)
Returns a variable representing the trigonometric functions of a (cosine, sine and tangent).
theano.tensor.cosh(a), sinh(a), tanh(a)
Returns a variable representing the hyperbolic trigonometric functions of a (hyperbolic cosine, sine
and tangent).
theano.tensor.erf(a), erfc(a)
Returns a variable representing the error function or the complementary error function. wikipedia
theano.tensor.erfinv(a), erfcinv(a)
Returns a variable representing the inverse error function or the inverse complementary error function.
wikipedia
theano.tensor.gamma(a)
Returns a variable representing the gamma function.
theano.tensor.gammaln(a)
Returns a variable representing the logarithm of the gamma function.
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theano.tensor.psi(a)
Returns a variable representing the derivative of the logarithm of the gamma function (also called the
digamma function).
theano.tensor.chi2sf(a, df )
Returns a variable representing the survival function (1-cdf — sometimes more accurate).
C code is provided in the Theano_lgpl repository. This makes it faster.
https://github.com/Theano/Theano_lgpl.git
Broadcasting in Theano vs. Numpy
Broadcasting is a mechanism which allows tensors with different numbers of dimensions to be added or
multiplied together by (virtually) replicating the smaller tensor along the dimensions that it is lacking.
Broadcasting is the mechanism by which a scalar may be added to a matrix, a vector to a matrix or a scalar
to a vector.
Broadcasting a row matrix. T and F respectively stand for True and False and indicate along which dimensions we allow broadcasting.
If the second argument were a vector, its shape would be (2,) and its broadcastable pattern (F,). They
would be automatically expanded to the left to match the dimensions of the matrix (adding 1 to the shape
and T to the pattern), resulting in (1, 2) and (T, F). It would then behave just like the example above.
Unlike numpy which does broadcasting dynamically, Theano needs to know, for any operation which supports broadcasting, which dimensions will need to be broadcasted. When applicable, this information is
given in the Type of a Variable.
See also:
• SciPy documentation about numpy’s broadcasting
• OnLamp article about numpy’s broadcasting
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Linear Algebra
theano.tensor.dot(X, Y)
For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product
of vectors (without complex conjugation). For N dimensions it is a sum product over the
last axis of a and the second-to-last of b:
Parameters
• X (symbolic tensor) – left term
• Y (symbolic tensor) – right term
Return type symbolic matrix or vector
Returns the inner product of X and Y.
theano.tensor.outer(X, Y)
Parameters
• X (symbolic vector) – left term
• Y (symbolic vector) – right term
Return type symbolic matrix
Returns vector-vector outer product
theano.tensor.tensordot(a, b, axes=2)
Given two tensors a and b,tensordot computes a generalized dot product over the provided axes.
Theano’s implementation reduces all expressions to matrix or vector dot products and is based on
code from Tijmen Tieleman’s gnumpy (http://www.cs.toronto.edu/~tijmen/gnumpy.html).
Parameters
• a (symbolic tensor) – the first tensor variable
• b (symbolic tensor) – the second tensor variable
• axes (int or array-like of length 2) – an integer or array. If an integer, the number of axes to sum over. If an array, it must have two array elements
containing the axes to sum over in each tensor.
Note that the default value of 2 is not guaranteed to work for all values of a and b,
and an error will be raised if that is the case. The reason for keeping the default
is to maintain the same signature as numpy’s tensordot function (and np.tensordot
raises analogous errors for non-compatible inputs).
If an integer i, it is converted to an array containing the last i dimensions of the
first tensor and the first i dimensions of the second tensor:
axes = [range(a.ndim - i, b.ndim), range(i)]
If an array, its two elements must contain compatible axes of the two tensors. For
example, [[1, 2], [2, 0]] means sum over the 2nd and 3rd axes of a and the 3rd and
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1st axes of b. (Remember axes are zero-indexed!) The 2nd axis of a and the 3rd
axis of b must have the same shape; the same is true for the 3rd axis of a and the
1st axis of b.
Returns a tensor with shape equal to the concatenation of a’s shape (less any dimensions
that were summed over) and b’s shape (less any dimensions that were summed over).
Return type symbolic tensor
It may be helpful to consider an example to see what tensordot does. Theano’s implementation is
identical to NumPy’s. Here a has shape (2, 3, 4) and b has shape (5, 6, 4, 3). The axes to sum over
are [[1, 2], [3, 2]] – note that a.shape[1] == b.shape[3] and a.shape[2] == b.shape[2]; these axes are
compatible. The resulting tensor will have shape (2, 5, 6) – the dimensions that are not being summed:
import numpy as np
a = np.random.random((2,3,4))
b = np.random.random((5,6,4,3))
#tensordot
c = np.tensordot(a, b, [[1,2],[3,2]])
#loop replicating tensordot
a0, a1, a2 = a.shape
b0, b1, _, _ = b.shape
cloop = np.zeros((a0,b0,b1))
#loop over non-summed indices -- these exist
#in the tensor product.
for i in range(a0):
for j in range(b0):
for k in range(b1):
#loop over summed indices -- these don't exist
#in the tensor product.
for l in range(a1):
for m in range(a2):
cloop[i,j,k] += a[i,l,m] * b[j,k,m,l]
assert np.allclose(c, cloop)
This specific implementation avoids a loop by transposing a and b such that the summed axes of a are
last and the summed axes of b are first. The resulting arrays are reshaped to 2 dimensions (or left as
vectors, if appropriate) and a matrix or vector dot product is taken. The result is reshaped back to the
required output dimensions.
In an extreme case, no axes may be specified. The resulting tensor will have shape equal to the
concatenation of the shapes of a and b:
>>>
>>>
(2,
>>>
(5,
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a.shape
3, 4)
b.shape
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>>> print(c.shape)
(2, 3, 4, 5, 6, 4, 3)
Note See the documentation of numpy.tensordot for more examples.
theano.tensor.batched_dot(X, Y)
Parameters
• x – A Tensor with sizes e.g.: for 3D (dim1, dim3, dim2)
• y – A Tensor with sizes e.g.: for 3D (dim1, dim2, dim4)
This function computes the dot product between the two tensors, by iterating over the first dimension
using scan. Returns a tensor of size e.g. if it is 3D: (dim1, dim3, dim4) Example:
>>> first = T.tensor3('first')
>>> second = T.tensor3('second')
>>> result = batched_dot(first, second)
Note This is a subset of numpy.einsum, but we do not provide it for now. But
numpy einsum is slower than dot or tensordot: http://mail.scipy.org/pipermail/
numpy-discussion/2012-October/064259.html
Parameters
• X (symbolic tensor) – left term
• Y (symbolic tensor) – right term
Returns tensor of products
theano.tensor.batched_tensordot(X, Y, axes=2)
Parameters
• x – A Tensor with sizes e.g.: for 3D (dim1, dim3, dim2)
• y – A Tensor with sizes e.g.: for 3D (dim1, dim2, dim4)
• axes (int or array-like of length 2) – an integer or array. If an integer, the number of axes to sum over. If an array, it must have two array elements
containing the axes to sum over in each tensor.
If an integer i, it is converted to an array containing the last i dimensions of the first
tensor and the first i dimensions of the second tensor (excluding the first (batch)
dimension):
axes = [range(a.ndim - i, b.ndim), range(1,i+1)]
If an array, its two elements must contain compatible axes of the two tensors. For
example, [[1, 2], [2, 4]] means sum over the 2nd and 3rd axes of a and the 3rd and
5th axes of b. (Remember axes are zero-indexed!) The 2nd axis of a and the 3rd
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axis of b must have the same shape; the same is true for the 3rd axis of a and the
5th axis of b.
Returns a tensor with shape equal to the concatenation of a’s shape (less any dimensions
that were summed over) and b’s shape (less first dimension and any dimensions that
were summed over).
Return type tensor of tensordots
A hybrid of batch_dot and tensordot, this function computes the tensordot product between the two
tensors, by iterating over the first dimension using scan to perform a sequence of tensordots.
Note See tensordot() and batched_dot() for supplementary documentation.
theano.tensor.mgrid()
Returns an instance which returns a dense (or fleshed out) mesh-grid when indexed, so
that each returned argument has the same shape. The dimensions and number of the
output arrays are equal to the number of indexing dimensions. If the step length is not
a complex number, then the stop is not inclusive.
Example:
>>> a = T.mgrid[0:5, 0:3]
>>> a[0].eval()
array([[0, 0, 0],
[1, 1, 1],
[2, 2, 2],
[3, 3, 3],
[4, 4, 4]])
>>> a[1].eval()
array([[0, 1, 2],
[0, 1, 2],
[0, 1, 2],
[0, 1, 2],
[0, 1, 2]])
theano.tensor.ogrid()
Returns an instance which returns an open (i.e. not fleshed out) mesh-grid when indexed,
so that only one dimension of each returned array is greater than 1. The dimension
and number of the output arrays are equal to the number of indexing dimensions. If
the step length is not a complex number, then the stop is not inclusive.
Example:
>>> b = T.ogrid[0:5, 0:3]
>>> b[0].eval()
array([[0],
[1],
[2],
[3],
[4]])
>>> b[1].eval()
array([[0, 1, 2]])
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Gradient / Differentiation
Driver for gradient calculations.
theano.gradient.grad(cost, wrt, consider_constant=None, disconnected_inputs=’raise’,
add_names=True, known_grads=None, return_disconnected=’zero’,
null_gradients=’raise’)
Return symbolic gradients for one or more variables with respect to some cost.
For more information about how automatic differentiation works in Theano, see gradient. For
information on how to implement the gradient of a certain Op, see grad().
Parameters
• cost (Variable scalar (0-dimensional) tensor variable or None) – Value with
respect to which we are differentiating. May be None if known_grads is provided.
• wrt (Variable or list of Variables) – term[s] for which we want gradients
• consider_constant (list of variables) – expressions not to backpropagate through
• disconnected_inputs ({'ignore', 'warn', 'raise'}) – Defines
the behaviour if some of the variables in wrt are not part of the computational
graph computing cost (or if all links are non-differentiable). The possible values
are:
– ‘ignore’: considers that the gradient on these parameters is zero.
– ‘warn’: consider the gradient zero, and print a warning.
– ‘raise’: raise DisconnectedInputError.
• add_names (bool) – If True, variables generated by grad will be named
(d<cost.name>/d<wrt.name>) provided that both cost and wrt have names
• known_grads (dict, optional) – A dictionary mapping variables to their
gradients. This is useful in the case where you know the gradient on some variables but do not know the original cost.
• return_disconnected ({'zero', 'None', 'Disconnected'}) –
– ‘zero’ [If wrt[i] is disconnected, return value i will be] wrt[i].zeros_like()
– ‘None’ [If wrt[i] is disconnected, return value i will be] None
– ‘Disconnected’ : returns variables of type DisconnectedType
• null_gradients ({'raise', 'return'}) – Defines the behaviour if
some of the variables in wrt have a null gradient. The possibles values are:
– ‘raise’ : raise a NullTypeGradError exception
– ‘return’ : return the null gradients
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Returns symbolic expression of gradient of cost with respect to each of the wrt terms. If
an element of wrt is not differentiable with respect to the output, then a zero variable
is returned.
Return type variable or list/tuple of variables (matches wrt)
See the gradient page for complete documentation of the gradient module.
nnet – Ops related to neural networks
Theano was originally developped for machine learning applications, particularly for the topic of deep learning. As such, our lab has developed many functions and ops which are particular to neural networks and
deep learning.
conv – Ops for convolutional neural nets
Note: Two similar implementation exists for conv2d:
signal.conv2d and nnet.conv2d.
The former implements a traditional 2D convolution, while the latter implements the convolutional layers
present in convolutional neural networks (where filters are 3D and pool over several input channels).
Note: As of December 2015, a new conv2d interface has been introduced. nnet.conv2d defines an
abstract theano graph convolution operation (nnet.abstract_conv.AbstractConv2d) that will be
replaced by an actual convolution implementation during the optimization phase.
Since the abstract Op does not have any implementation, it will prevent computations in the un-optimized
graph, and cause problems with DebugMode, test values, and when compiling with optimizer=None.
By default, if cuDNN is available, we will use it, otherwise we will fall back to using the gemm version
(slower then cuDNN in most cases and uses more memory).
Either cuDNN and the gemm version can be disabled using the Theano flags
optimizer_excluding=conv_dnn and optimizer_excluding=conv_gemm,
respectively. In this case, we will fall back to using the legacy convolution code, which is slower, but
does not require extra memory. To verify that cuDNN is used, you can supply the Theano flag
optimizer_including=cudnn. This will raise an error if cuDNN is unavailable.
It is not advised to ever disable cuDNN, as this is usually the fastest option. Disabling the gemm version is
only useful if cuDNN is unavailable and you run out of GPU memory.
There are two other implementations: An FFT-based convolution integrated into Theano, and an implementation by Alex Krizhevsky available via Pylearn2. See the documentation below on how to use them.
Old conv2d interface is still accessible through nnet.conv.conv2d.
TODO: Give examples on how to use these things! They are pretty complicated.
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• Implemented operators for neural network 2D / image convolution:
– nnet.conv.conv2d. CPU convolution implementation, previously used as the convolution interface. This is the standard operator for convolutional neural networks working
with batches of multi-channel 2D images, available. It computes a convolution, i.e., it flips
the kernel. Most of the more efficient GPU implementations listed below can be inserted automatically as a replacement for nnet.conv.conv2d via graph optimizations. Some of these
graph optimizations are enabled by default, others can be enabled via Theano flags. Since
November 24th, 2014, you can also use a meta-optimizer to automatically choose the fastest
implementation for each specific convolution in your graph using the old interface. For each
instance, it will compile and benchmark each applicable implementation of the ones listed
below and choose the fastest one. As performance is dependent on input and filter shapes,
this only works for operations introduced via nnet.conv.conv2d with fully specified shape
information. Enable it via the Theano flag optimizer_including=conv_meta, and
optionally set it to verbose mode via the flag metaopt.verbose=1.
– conv2d_fft This is a GPU-only version of nnet.conv2d that uses an FFT transform to perform the work. It flips the kernel just like conv2d. conv2d_fft should
not be used directly as it does not provide a gradient. Instead, use nnet.conv2d
and allow Theano’s graph optimizer to replace it by the FFT version by setting
‘THEANO_FLAGS=optimizer_including=conv_fft’ in your environment. If enabled, it
will take precedence over cuDNN and the gemm version. It is not enabled by default
because it has some restrictions on input and uses a lot more memory. Also note that it
requires CUDA >= 5.0, scikits.cuda >= 0.5.0 and PyCUDA to run. To deactivate the FFT
optimization on a specific nnet.conv2d while the optimization flag is active, you can set its
version parameter to 'no_fft'. To enable it for just one Theano function:
mode = theano.compile.get_default_mode()
mode = mode.including('conv_fft')
f = theano.function(..., mode=mode)
– cuda-convnet wrapper for 2d correlation
Wrapper for an open-source GPU-only implementation of conv2d by Alex Krizhevsky, very
fast, but with several restrictions on input and kernel shapes, and with a different memory
layout for the input. It does not flip the kernel.
This is in Pylearn2, where it is normally called from the linear transform implementation, but it can also be used directly from within Theano as a manual replacement for
nnet.conv2d.
– GpuCorrMM This is a GPU-only 2d correlation implementation taken from caffe’s CUDA
implementation and also used by Torch. It does not flip the kernel.
For each element in a batch, it first creates a Toeplitz matrix in a CUDA kernel. Then, it
performs a gemm call to multiply this Toeplitz matrix and the filters (hence the name: MM
is for matrix multiplication). It needs extra memory for the Toeplitz matrix, which is a
2D matrix of shape (no of channels * filter width * filter height,
output width * output height).
As it provides a gradient, you can use it as a replacement for nnet.conv2d. But usually, you
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will just use nnet.conv2d and allow Theano’s graph optimizer to automatically replace it by
the GEMM version if cuDNN is not available. To explicitly disable the graph optimizer,
set THEANO_FLAGS=optimizer_excluding=conv_gemm in your environment. If
using it, please see the warning about a bug in CUDA 5.0 to 6.0 below.
– CorrMM This is a CPU-only 2d correlation implementation taken from caffe’s cpp
implementation and also used by Torch. It does not flip the kernel. As it provides a gradient, you can use it as a replacement for nnet.conv2d. For convolutions
done on CPU, nnet.conv2d will be replaced by CorrMM. To explicitly disable it, set
THEANO_FLAGS=optimizer_excluding=conv_gemm in your environment.
– dnn_conv GPU-only convolution using NVIDIA’s cuDNN library. This requires that you
have cuDNN installed and available, which in turn requires CUDA 6.5 and a GPU with
compute capability 3.0 or more.
If
cuDNN
is
available,
by
default,
Theano
will
replace
all
nnet.conv2d operations with dnn_conv.
To explicitly disable it, set
THEANO_FLAGS=optimizer_excluding=conv_dnn in your environment.
As dnn_conv has a gradient defined, you can also use it manually.
• Implemented operators for neural network 3D / video convolution:
– conv3D 3D Convolution applying multi-channel 3D filters to batches of multi-channel 3D
images. It does not flip the kernel.
– conv3d_fft GPU-only version of conv3D using FFT transform.
conv3d_fft
should not be called directly as it does not provide a gradient. Instead, use conv3D
and allow Theano’s graph optimizer to replace it by the FFT version by setting
THEANO_FLAGS=optimizer_including=conv3d_fft:convgrad3d_fft:convtransp3d_
in your environment. This is not enabled by default because it does not support strides and
uses more memory. Also note that it requires CUDA >= 5.0, scikits.cuda >= 0.5.0 and
PyCUDA to run. To enable for just one Theano function:
mode = theano.compile.get_default_mode()
mode = mode.including('conv3d_fft', 'convgrad3d_fft',
˓→'convtransp3d_fft')
f = theano.function(..., mode=mode)
– GpuCorr3dMM This is a GPU-only 3d correlation relying on a Toeplitz matrix and gemm implementation (see GpuCorrMM ) It needs extra memory for
the Toeplitz matrix, which is a 2D matrix of shape (no of channels *
filter width * filter height * filter depth, output width
As it provides a gradient, you can
* output height * output depth).
use it as a replacement for nnet.conv3d. Alternatively, you can use nnet.conv3d
and allow Theano’s graph optimizer to replace it by the GEMM version by setting
THEANO_FLAGS=optimizer_including=conv3d_gemm:convgrad3d_gemm:convtransp3
in your environment. This is not enabled by default because it uses some extra memory, but
the overhead is small compared to conv3d_fft, there are no restrictions on input or kernel
shapes and strides are supported. If using it, please see the warning about a bug in CUDA
5.0 to 6.0 in GpuCorrMM .
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– conv3d2d Another conv3d implementation that uses the conv2d with data reshaping. It is
faster in some cases than conv3d, and work on the GPU. It flip the kernel.
theano.tensor.nnet.conv2d(input, filters, input_shape=None, filter_shape=None, border_mode=’valid’, subsample=(1, 1), filter_flip=True, image_shape=None, **kwargs)
This function will build the symbolic graph for convolving a mini-batch of a stack of 2D inputs with
a set of 2D filters. The implementation is modelled after Convolutional Neural Networks (CNN).
Parameters
• input (symbolic 4D tensor) – Mini-batch of feature map stacks, of shape
(batch size, input channels, input rows, input columns). See the optional parameter input_shape.
• filters (symbolic 4D tensor) – Set of filters used in CNN layer of
shape (output channels, input channels, filter rows, filter columns). See the optional parameter filter_shape.
• input_shape
(None, tuple/list of len 4 of int or
Constant variable) – The shape of the input parameter. Optional,
possibly used to choose an optimal implementation. You can give None for any
element of the list to specify that this element is not known at compile time.
• filter_shape
(None, tuple/list of len 4 of int or
Constant variable) – The shape of the filters parameter. Optional,
possibly used to choose an optimal implementation. You can give None for any
element of the list to specify that this element is not known at compile time.
• border_mode (str, int or tuple of two int) – Either of the following:
'valid': apply filter wherever it completely overlaps with the input. Generates output of shape: input shape - filter shape + 1
'full': apply filter wherever it partly overlaps with the input. Generates
output of shape: input shape + filter shape - 1
'half': pad input with a symmetric border of filter rows // 2
rows and filter columns // 2 columns, then perform a valid convolution. For filters with an odd number of rows and columns, this leads to the
output shape being equal to the input shape.
int: pad input with a symmetric border of zeros of the given width,
perform a valid convolution.
then
(int1, int2): pad input with a symmetric border of int1 rows and
int2 columns, then perform a valid convolution.
• subsample (tuple of len 2) – Factor by which to subsample the output.
Also called strides elsewhere.
• filter_flip (bool) – If True, will flip the filter rows and columns before
sliding them over the input. This operation is normally referred to as a convolu-
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tion, and this is the default. If False, the filters are not flipped and the operation
is referred to as a cross-correlation.
• image_shape
(None, tuple/list of len 4 of int or
Constant variable) – Deprecated alias for input_shape.
• kwargs
(Any other keyword arguments are accepted for
backwards) – compatibility, but will be ignored.
Returns Set of feature maps generated by convolutional layer. Tensor is of shape (batch
size, output channels, output rows, output columns)
Return type Symbolic 4D tensor
Notes
If cuDNN is available, it will be used on the GPU. Otherwise, it is the CorrMM convolution that will
be used “caffe style convolution”.
This is only supported in Theano 0.8 or the development version until it is released.
theano.sandbox.cuda.fftconv.conv2d_fft(input, filters, image_shape=None, filter_shape=None, border_mode=’valid’,
pad_last_dim=False)
Perform a convolution through fft.
Only support input which will be even on the last dimension (width). All other dimensions can be
anything and the filters can have an even or odd width.
If you must use input which has an odd width, you can either pad it or use the pad_last_dim argument
which will do it for you and take care to strip the padding before returning. Don’t use this argument
if you are not sure the input is odd since the padding is unconditional and will make even input odd,
thus leading to problems.
On valid mode the filters must be smaller than the input.
Parameters
• input – (b, ic, i0, i1).
• filters – (oc, ic, f0, f1).
• border_mode ({'valid', 'full'}) –
• pad_last_dim – Unconditionally pad the last dimension of the input to to turn
it from odd to even. Will strip the padding before returning the result.
theano.tensor.nnet.Conv3D.conv3D(V, W, b, d)
3D “convolution” of multiple filters on a minibatch.
(does not flip the kernel, moves kernel with a user specified stride)
Parameters
• V – Visible unit, input. Dimensions: (batch, row, column, time, in channel).
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• W – Weights, filter. Dimensions: (out channel, row, column, time ,in channel).
• b – Bias, shape == (W.shape[0],).
• d – Strides when moving the filter over the input(dx, dy, dt).
Notes
The order of dimensions does not correspond to the one in conv2d. This is for optimization.
The GPU implementation is very slow. You should use conv3d2d or conv3d_fft for a GPU
graph instead.
See also:
Someone(), between(), the()
theano.sandbox.cuda.fftconv.conv3d_fft(input, filters, image_shape=None, filter_shape=None, border_mode=’valid’,
pad_last_dim=False)
Perform a convolution through fft.
Only supports input whose shape is even on the last dimension. All other dimensions can be anything
and the filters can have an even or odd last dimension.
The semantics associated with the last three dimensions are not important as long as they are in
the same order between the inputs and the filters. For example, when the convolution is done on a
sequence of images, they could be either (duration, height, width) or (height, width, duration).
If you must use input which has an odd width, you can either pad it or use the pad_last_dim argument
which will do it for you and take care to strip the padding before returning. pad_last_dim checks that
the last dimension is odd before the actual paddding
On valid mode the filters must be smaller than the input.
Parameters
• input – (b, ic, i0, i1, i2).
• filters – (oc, ic, f0, f1, i2).
• border_mode ({'valid', 'full'}.) –
• pad_last_dim – Unconditionally pad the last dimension of the input to to turn
it from odd to even. Will strip the padding before returning the result.
theano.tensor.nnet.conv3d2d.conv3d(signals, filters, signals_shape=None,
ters_shape=None, border_mode=’valid’)
Convolve spatio-temporal filters with a movie.
fil-
It flips the filters.
Parameters
• signals – Timeseries of images whose pixels have color channels. Shape: [Ns,
Ts, C, Hs, Ws].
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• filters – Spatio-temporal filters. Shape: [Nf, Tf, C, Hf, Wf].
• signals_shape – None or a tuple/list with the shape of signals.
• filters_shape – None or a tuple/list with the shape of filters.
• border_mode – The only one tested is ‘valid’.
Notes
Another way to define signals: (batch, time, in channel, row, column) Another way to define filters:
(out channel,time,in channel, row, column)
For the GPU, you can use this implementation or conv3d_fft.
See also:
Someone made a script that shows how to swap the axes between both 3d convolution implementations
in Theano. See the last attachment
theano.tensor.nnet.conv.conv2d(input, filters, image_shape=None, filter_shape=None,
border_mode=’valid’, subsample=(1, 1), **kargs)
Deprecated, old conv2d interface. This function will build the symbolic graph for convolving a stack
of input images with a set of filters. The implementation is modelled after Convolutional Neural
Networks (CNN). It is simply a wrapper to the ConvOp but provides a much cleaner interface.
Parameters
• input (symbolic 4D tensor) – Mini-batch of feature map stacks, of shape
(batch size, stack size, nb row, nb col) see the optional parameter image_shape
• filters (symbolic 4D tensor) – Set of filters used in CNN layer of
shape (nb filters, stack size, nb row, nb col) see the optional parameter filter_shape
• border_mode ({'valid', 'full'}) – ‘valid’only apply filter to complete
patches of the image. Generates output of shape: image_shape - filter_shape +
1. ‘full’ zero-pads image to multiple of filter shape to generate output of shape:
image_shape + filter_shape - 1.
• subsample (tuple of len 2) – Factor by which to subsample the output.
Also called strides elsewhere.
• image_shape (None, tuple/list of len 4 of int, None or
Constant variable) – The shape of the input parameter. Optional, used
for optimization like loop unrolling You can put None for any element of the list
to tell that this element is not constant.
• filter_shape (None, tuple/list of len 4 of int, None or
Constant variable) – Optional, used for optimization like loop unrolling
You can put None for any element of the list to tell that this element is not constant.
• kwargs – Kwargs are passed onto ConvOp. Can be used to set the following:
unroll_batch, unroll_kern, unroll_patch, openmp (see ConvOp doc).
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openmp: By default have the same value as config.openmp. For small image,
filter, batch size, nkern and stack size, it can be faster to disable manually
openmp. A fast and incomplete test show that with image size 6x6, filter size
4x4, batch size==1, n kern==1 and stack size==1, it is faster to disable it in
valid mode. But if we grow the batch size to 10, it is faster with openmp on a
core 2 duo.
Returns Set of feature maps generated by convolutional layer. Tensor is of shape (batch
size, nb filters, output row, output col).
Return type symbolic 4D tensor
Abstract conv interface
class theano.tensor.nnet.abstract_conv.AbstractConv2d(imshp=None,
kshp=None,
border_mode=’valid’,
subsample=(1,
1),
filter_flip=True)
Abstract Op for the forward convolution. Refer to BaseAbstractConv2d for a more detailed
documentation.
class theano.tensor.nnet.abstract_conv.AbstractConv2d_gradInputs(imshp=None,
kshp=None,
border_mode=’valid’,
subsample=(1,
1), filter_flip=True)
Gradient wrt. inputs for AbstractConv2d. Refer to BaseAbstractConv2d for a more detailed
documentation.
Note You will not want to use this directly, but rely on Theano’s automatic differentiation
or graph optimization to use it as needed.
class theano.tensor.nnet.abstract_conv.AbstractConv2d_gradWeights(imshp=None,
kshp=None,
border_mode=’valid’,
subsample=(1,
1),
filter_flip=True)
Gradient wrt. filters for AbstractConv2d. Refer to BaseAbstractConv2d for a more detailed
documentation.
Note You will not want to use this directly, but rely on Theano’s automatic differentiation
or graph optimization to use it as needed.
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class theano.tensor.nnet.abstract_conv.BaseAbstractConv2d(imshp=None,
kshp=None, border_mode=’valid’,
subsample=(1,
1),
filter_flip=True)
Base class for AbstractConv
Define an abstract convolution op that will be replaced with the appropriate implementation
Parameters
• imshp
(None, tuple/list of len 4 of int or Constant
variable) – The shape of the input parameter. Optional, possibly used to
choose an optimal implementation. You can give None for any element of the
list to specify that this element is not known at compile time. imshp is defined
w.r.t the forward conv.
• kshp
(None, tuple/list of len 4 of int or Constant
variable) – The shape of the filters parameter. Optional, possibly used to
choose an optimal implementation. You can give None for any element of the
list to specify that this element is not known at compile time. kshp is defined w.r.t
the forward conv.
• border_mode (str, int or tuple of two int) – Either of the following:
'valid': apply filter wherever it completely overlaps with the input. Generates output of shape: input shape - filter shape + 1
'full': apply filter wherever it partly overlaps with the input. Generates
output of shape: input shape + filter shape - 1
'half': pad input with a symmetric border of filter rows // 2
rows and filter columns // 2 columns, then perform a valid convolution. For filters with an odd number of rows and columns, this leads to the
output shape being equal to the input shape.
int: pad input with a symmetric border of zeros of the given width,
perform a valid convolution.
then
(int1, int2): pad input with a symmetric border of int1 rows and
int2 columns, then perform a valid convolution.
subsample: tuple of len 2 Factor by which to subsample the output. Also called strides elsewhere.
filter_flip: bool If True, will flip the filter rows and columns before sliding them over the input.
This operation is normally referred to as a convolution, and this is the default. If False, the
filters are not flipped and the operation is referred to as a cross-correlation.
conv2d(img, kern, mode=’valid’)
Basic slow python implementatation for DebugMode
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flops(inp, outp)
Useful with the hack in profilemode to print the MFlops
theano.tensor.nnet.abstract_conv.bilinear_kernel_1D(ratio,
ize=True)
Compute 1D kernel for bilinear upsampling
normal-
This function builds the 1D kernel that can be used to upsample a tensor by the given ratio using
bilinear interpolation.
Parameters
• ratio
(int or Constant/Scalar Theano tensor of int*
dtype) – the ratio by which an image will be upsampled by the returned filter in
the 2D space.
• normalize (bool) – param normalize: indicates whether to normalize the kernel or not. Default is True.
Returns the 1D kernels that can be applied to any given image to upsample it by the
indicated ratio using bilinear interpolation in one dimension.
Return type symbolic 1D tensor
theano.tensor.nnet.abstract_conv.bilinear_kernel_2D(ratio,
ize=True)
Compute 2D kernel for bilinear upsampling
normal-
This function builds the 2D kernel that can be used to upsample a tensor by the given ratio using
bilinear interpolation.
Parameters
• ratio
(int or Constant/Scalar Theano tensor of int*
dtype) – the ratio by which an image will be upsampled by the returned filter in
the 2D space.
• normalize (bool) – param normalize: indicates whether to normalize the kernel or not. Default is True.
Returns the 2D kernels that can be applied to any given image to upsample it by the
indicated ratio using bilinear interpolation in two dimensions.
Return type symbolic 2D tensor
theano.tensor.nnet.abstract_conv.bilinear_upsampling(input,
ratio,
batch_size=None,
num_input_channels=None,
use_1D_kernel=True)
Compute bilinear upsampling
This function will build the symbolic graph for upsampling a tensor by the given ratio using bilinear
interpolation.
Parameters
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• input (symbolic 4D tensor) – mini-batch of feature map stacks, of shape
(batch size, input channels, input rows, input columns) that will be upsampled.
• ratio (int or Constant or Scalar Tensor of int* dtype) – the ratio by which the
input is upsampled in the 2D space (row and col size).
• batch_size (None, int or Constant variable) – The size of the
first dimension of the input variable. Optional, possibly used to choose an optimal
implementation. batch_size will be used only if num_input_channels is not None.
• num_input_channels (None, int or Constant variable) – The
size of the second dimension of the input variable. Optional, possibly used to
choose an optimal implementation. num_input_channels will be used only if
batch_size is not None.
• use_1D_kernel (bool) – if set to true, row and column will be upsampled
seperately by 1D kernels, otherwise they are upsampled together using a 2D kernel. The final result is the same, only the speed can differ, given factors such as
upsampling ratio.
Returns set of feature maps generated by bilinear upsampling. Tensor is of shape (batch
size, num_input_channels, input row size * ratio, input column size * ratio)
Return type symbolic 4D tensor
Notes
Note The kernel used for bilinear interpolation is fixed (not learned).
Note When the upsampling ratio is even, the last row and column is repeated one extra
time compared to the first row and column which makes the upsampled tensor asymmetrical on both sides. This does not happen when the upsampling ratio is odd.
theano.tensor.nnet.abstract_conv.conv2d(input, filters, input_shape=None, filter_shape=None, border_mode=’valid’,
subsample=(1, 1), filter_flip=True)
This function will build the symbolic graph for convolving a mini-batch of a stack of 2D inputs with
a set of 2D filters. The implementation is modelled after Convolutional Neural Networks (CNN).
Refer to nnet.conv2d for a more detailed documentation.
theano.tensor.nnet.abstract_conv.conv2d_grad_wrt_inputs(output_grad,
filters,
input_shape, filter_shape=None,
border_mode=’valid’,
subsample=(1,
1),
filter_flip=True)
Compute conv output gradient w.r.t its inputs
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This function builds the symbolic graph for getting the gradient of the output of a convolution (namely
output_grad) w.r.t the input of the convolution, given a set of 2D filters used by the convolution, such
that the output_grad is upsampled to the input_shape.
Parameters
• output_grad (symbolic 4D tensor) – mini-batch of feature map stacks,
of shape (batch size, input channels, input rows, input columns). This is the tensor
that will be upsampled or the output gradient of the convolution whose gradient
will be taken with respect to the input of the convolution.
• filters (symbolic 4D tensor) – set of filters used in CNN layer of shape
(output channels, input channels, filter rows, filter columns). See the optional
parameter filter_shape.
• input_shape
([None/int/Constant] * 2 + [Tensor/int/
Constant] * 2) – The shape of the input (upsampled) parameter. A tuple/list
of len 4, with the first two dimensions being None or int or Constant and the
last two dimensions being Tensor or int or Constant. Not Optional, since given
the output_grad shape and the subsample values, multiple input_shape may be
plausible.
• filter_shape (None or [None/int/Constant] * 4) – The shape
of the filters parameter. None or a tuple/list of len 4. Optional, possibly used to
choose an optimal implementation. You can give None for any element of the list
to specify that this element is not known at compile time.
• border_mode (str, int or tuple of two int) – Either of the following:
'valid' apply filter wherever it completely overlaps with the input. Generates output of shape: input shape - filter shape + 1
'full' apply filter wherever it partly overlaps with the input. Generates
output of shape: input shape + filter shape - 1
'half' pad input with a symmetric border of filter rows // 2
rows and filter columns // 2 columns, then perform a valid convolution. For filters with an odd number of rows and columns, this leads
to the output shape being equal to the input shape. It is known as ‘same’
elsewhere.
int pad input with a symmetric border of zeros of the given width, then
perform a valid convolution.
(int1, int2) pad input with a symmetric border of int1 rows and
int2 columns, then perform a valid convolution.
• subsample (tuple of len 2) – The subsampling used in the forward pass.
Also called strides elsewhere.
• filter_flip (bool) – If True, will flip the filter rows and columns before
sliding them over the input. This operation is normally referred to as a convolu-
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tion, and this is the default. If False, the filters are not flipped and the operation
is referred to as a cross-correlation.
Returns set of feature maps generated by convolutional layer. Tensor is of shape (batch
size, output channels, output rows, output columns)
Return type symbolic 4D tensor
Notes
Note If cuDNN is available, it will be used on the GPU. Otherwise, it is the CorrMM
convolution that will be used “caffe style convolution”.
Note This is only supported in Theano 0.8 or the development version until it is released.
theano.tensor.nnet.abstract_conv.conv2d_grad_wrt_weights(input,
output_grad, filter_shape, input_shape=None,
border_mode=’valid’,
subsample=(1, 1), filter_flip=True)
Compute conv output gradient w.r.t its weights
This function will build the symbolic graph for getting the gradient of the output of a convolution
(output_grad) w.r.t its wights.
Parameters
• input (symbolic 4D tensor) – mini-batch of feature map stacks, of shape
(batch size, input channels, input rows, input columns). This is the input of the
convolution in the forward pass.
• output_grad (symbolic 4D tensor) – mini-batch of feature map stacks,
of shape (batch size, input channels, input rows, input columns). This is the gradient of the output of convolution.
• filter_shape
([None/int/Constant] * 2 + [Tensor/int/
Constant] * 2) – The shape of the filter parameter. A tuple/list of len 4,
with the first two dimensions being None or int or Constant and the last two
dimensions being Tensor or int or Constant. Not Optional, since given the
output_grad shape and the input_shape, multiple filter_shape may be plausible.
• input_shape (None or [None/int/Constant] * 4) – The shape of
the input parameter. None or a tuple/list of len 4. Optional, possibly used to
choose an optimal implementation. You can give None for any element of the list
to specify that this element is not known at compile time.
• border_mode (str, int or tuple of two ints) – Either of the following:
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'valid' apply filter wherever it completely overlaps with the input. Generates output of shape: input shape - filter shape + 1
'full' apply filter wherever it partly overlaps with the input. Generates
output of shape: input shape + filter shape - 1
'half' pad input with a symmetric border of filter rows // 2
rows and filter columns // 2 columns, then perform a valid convolution. For filters with an odd number of rows and columns, this leads
to the output shape being equal to the input shape. It is known as ‘same’
elsewhere.
int pad input with a symmetric border of zeros of the given width, then
perform a valid convolution.
(int1, int2) pad input with a symmetric border of int1 rows and
int2 columns, then perform a valid convolution.
• subsample (tuple of len 2) – The subsampling used in the forward pass
of the convolutional operation. Also called strides elsewhere.
• filter_flip (bool) – If True, will flip the filter rows and columns before
sliding them over the input. This operation is normally referred to as a convolution, and this is the default. If False, the filters are not flipped and the operation
is referred to as a cross-correlation.
Returns set of feature maps generated by convolutional layer. Tensor is of shape (batch
size, output channels, output rows, output columns)
Return type symbolic 4D tensor
Notes
Note If cuDNN is available, it will be used on the GPU. Otherwise, it is the CorrMM
convolution that will be used “caffe style convolution”.
Note This is only supported in Theano 0.8 or the development version until it is released.
theano.tensor.nnet.abstract_conv.get_conv_output_shape(image_shape,
kernel_shape,
border_mode,
subsample)
This function compute the output shape of convolution operation.
Parameters
• image_shape
(tuple of int (symbolic or numeric)
corresponding to the input) – image shape. Its four (or five) element must correspond respectively to: batch size, number of input channels,
height and width (and possibly depth) of the image. None where undefined.
• kernel_shape
(tuple of int (symbolic or numeric)
corresponding to the) – kernel shape. Its four (or five) elements
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must correspond respectively to: number of output channels, number of input
channels, height and width (and possibly depth) of the kernel. None where
undefined.
• border_mode
(string, int (symbolic or numeric) or
tuple of int (symbolic) – or numeric). If it is a string, it must be
‘valid’, ‘half’ or ‘full’. If it is a tuple, its two (or three) elements respectively
correspond to the padding on height and width (and possibly depth) axis.
• subsample
(tuple of int (symbolic or numeric) Its or
three elements) – espectively correspond to the subsampling on height and
width (and possibly depth) axis.
Returns output_shape – four element must correspond respectively to: batch size, number of output channels, height and width of the image. None where undefined.
Return type tuple of int corresponding to the output image shape. Its
theano.tensor.nnet.abstract_conv.get_conv_shape_1axis(image_shape,
kernel_shape,
border_mode,
subsample)
This function compute the output shape of convolution operation.
Parameters
• image_shape
(int or None. Corresponds to the input
image shape on a) – given axis. None if undefined.
• kernel_shape
(int or None. Corresponds to the kernel
shape on a given) – axis. None if undefined.
• border_mode (string or int. If it is a string, it must
be) – ‘valid’, ‘half’ or ‘full’. If it is an integer, it must correspond to the padding
on the considered axis.
• subsample (int. It must correspond to the subsampling
on the) – considered axis.
Returns out_shp – considered axis. None if undefined.
Return type int corresponding to the output image shape on the
nnet – Ops for neural networks
• Sigmoid
– sigmoid()
– ultra_fast_sigmoid()
– hard_sigmoid()
• Others
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– softplus()
– softmax()
– relu()
– binary_crossentropy()
– categorical_crossentropy()
– h_softmax()
theano.tensor.nnet.nnet.sigmoid(x)
Returns the standard sigmoid nonlinearity applied to x
Parameters x - symbolic Tensor (or compatible)
Return type same as x
Returns element-wise sigmoid: 𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑥) =
1
1+exp(−𝑥) .
note see ultra_fast_sigmoid() or hard_sigmoid() for faster versions.
Speed comparison for 100M float64 elements on a Core2 Duo @ 3.16 GHz:
• hard_sigmoid: 1.0s
• ultra_fast_sigmoid: 1.3s
• sigmoid (with amdlibm): 2.3s
• sigmoid (without amdlibm): 3.7s
Precision:
sigmoid(with or without amdlibm) > ultra_fast_sigmoid >
hard_sigmoid.
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Example:
import theano.tensor as T
x, y, b = T.dvectors('x', 'y', 'b')
W = T.dmatrix('W')
y = T.nnet.sigmoid(T.dot(W, x) + b)
Note: The underlying code will return an exact 0 or 1 if an element of x is too small or too big.
theano.tensor.nnet.nnet.ultra_fast_sigmoid(x)
Returns the approximated standard sigmoid() nonlinearity applied to x.
Parameters x - symbolic Tensor (or compatible)
Return type same as x
Returns approximated element-wise sigmoid: 𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑥) =
1
1+exp(−𝑥) .
note To automatically change all sigmoid() ops to this version, use the Theano optimization local_ultra_fast_sigmoid. This can be done with the Theano
flag optimizer_including=local_ultra_fast_sigmoid. This optimization is done late, so it should not affect stabilization optimization.
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Note:
The underlying code will return 0.00247262315663 as the minimum value and
0.997527376843 as the maximum value. So it never returns 0 or 1.
Note: Using directly the ultra_fast_sigmoid in the graph will disable stabilization optimization associated with it. But using the optimization to insert them won’t disable the stability optimization.
theano.tensor.nnet.nnet.hard_sigmoid(x)
Returns the approximated standard sigmoid() nonlinearity applied to x.
Parameters x - symbolic Tensor (or compatible)
Return type same as x
Returns approximated element-wise sigmoid: 𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑥) =
1
1+exp(−𝑥) .
note To automatically change all sigmoid() ops to this version, use the Theano
optimization local_hard_sigmoid. This can be done with the Theano
flag optimizer_including=local_hard_sigmoid. This optimization
is done late, so it should not affect stabilization optimization.
Note: The underlying code will return an exact 0 or 1 if an element of x is too small or too big.
Note: Using directly the ultra_fast_sigmoid in the graph will disable stabilization optimization associated with it. But using the optimization to insert them won’t disable the stability optimization.
theano.tensor.nnet.nnet.softplus(x)
Returns the softplus nonlinearity applied to x
Parameter x - symbolic Tensor (or compatible)
Return type same as x
Returns elementwise softplus: 𝑠𝑜𝑓 𝑡𝑝𝑙𝑢𝑠(𝑥) = log𝑒 (1 + exp(𝑥)).
Note: The underlying code will return an exact 0 if an element of x is too small.
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softplus(T.dot(W,x) + b)
theano.tensor.nnet.nnet.softmax(x)
Returns the softmax function of x:
Parameter x symbolic 2D Tensor (or compatible).
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Return type same as x
Returns a symbolic 2D tensor whose ijth element is 𝑠𝑜𝑓 𝑡𝑚𝑎𝑥𝑖𝑗 (𝑥) =
∑︀ exp 𝑥𝑖𝑗
.
𝑘 exp(𝑥𝑖𝑘 )
The softmax function will, when applied to a matrix, compute the softmax values row-wise.
note this supports hessian free as well. The code of the softmax op is more
numerically stable because it uses this code:
e_x = exp(x - x.max(axis=1, keepdims=True))
out = e_x / e_x.sum(axis=1, keepdims=True)
Example of use:
x,y,b = T.dvectors('x','y','b')
W = T.dmatrix('W')
y = T.nnet.softmax(T.dot(W,x) + b)
theano.tensor.nnet.relu(x, alpha=0)
Compute the element-wise rectified linear activation function.
New in version 0.7.1.
Parameters
• x (symbolic tensor) – Tensor to compute the activation function for.
• alpha (scalar or tensor, optional) – Slope for negative input, usually between
0 and 1. The default value of 0 will lead to the standard rectifier, 1 will lead to
a linear activation function, and any value in between will give a leaky rectifier.
A shared variable (broadcastable against x) will result in a parameterized rectifier
with learnable slope(s).
Returns Element-wise rectifier applied to x.
Return type symbolic tensor
Notes
This is numerically equivalent to T.switch(x > 0, x, alpha * x) (or T.maximum(x,
alpha * x) for alpha < 1), but uses a faster formulation or an optimized Op, so we encourage
to use this function.
theano.tensor.nnet.nnet.binary_crossentropy(output, target)
Computes the binary cross-entropy between a target and an output:
Parameters
• target - symbolic Tensor (or compatible)
• output - symbolic Tensor (or compatible)
Return type same as target
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Returns a symbolic tensor, where the following is applied elementwise
𝑐𝑟𝑜𝑠𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑦(𝑡, 𝑜) = −(𝑡 · 𝑙𝑜𝑔(𝑜) + (1 − 𝑡) · 𝑙𝑜𝑔(1 − 𝑜)).
The following block implements a simple auto-associator with a sigmoid nonlinearity and a reconstruction error which corresponds to the binary cross-entropy (note that this assumes that x will contain
values between 0 and 1):
x, y, b, c = T.dvectors('x', 'y', 'b', 'c')
W = T.dmatrix('W')
V = T.dmatrix('V')
h = T.nnet.sigmoid(T.dot(W, x) + b)
x_recons = T.nnet.sigmoid(T.dot(V, h) + c)
recon_cost = T.nnet.binary_crossentropy(x_recons, x).mean()
theano.tensor.nnet.nnet.categorical_crossentropy(coding_dist, true_dist)
Return the cross-entropy between an approximating distribution and a true distribution.
The cross entropy between two probability distributions measures the average number of
bits needed to identify an event from a set of possibilities, if a coding scheme is used
based on a given probability distribution q, rather
∑︀ than the “true” distribution p. Mathematically, this function computes 𝐻(𝑝, 𝑞) = − 𝑥 𝑝(𝑥) log(𝑞(𝑥)), where p=true_dist and
q=coding_dist.
Parameters
• coding_dist - symbolic 2D Tensor (or compatible). Each row represents a
distribution.
• true_dist - symbolic 2D Tensor OR symbolic vector of ints. In the case of
an integer vector argument, each element represents the position of the ‘1’
in a 1-of-N encoding (aka “one-hot” encoding)
Return type tensor of rank one-less-than coding_dist
Note: An application of the scenario where true_dist has a 1-of-N representation is in classification
with softmax outputs. If coding_dist is the output of the softmax and true_dist is a vector of correct
labels, then the function will compute y_i = - \log(coding_dist[i, one_of_n[i]]),
which corresponds to computing the neg-log-probability of the correct class (which is typically the
training criterion in classification settings).
y = T.nnet.softmax(T.dot(W, x) + b)
cost = T.nnet.categorical_crossentropy(y, o)
# o is either the above-mentioned 1-of-N vector or 2D tensor
theano.tensor.nnet.h_softmax(x, batch_size, n_outputs, n_classes, n_outputs_per_class,
W1, b1, W2, b2, target=None)
Two-level hierarchical softmax.
The architecture is composed of two softmax layers: the first predicts the class of the input x while
the second predicts the output of the input x in the predicted class. More explanations can be found in
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the original paper1 .
If target is specified, it will only compute the outputs of the corresponding targets. Otherwise, if target
is None, it will compute all the outputs.
The outputs are grouped in the same order as they are initially defined.
New in version 0.7.1.
Parameters
• x (tensor of shape (batch_size, number of features)) – the
minibatch input of the two-layer hierarchical softmax.
• batch_size (int) – the size of the minibatch input x.
• n_outputs (int) – the number of outputs.
• n_classes (int) – the number of classes of the two-layer hierarchical softmax.
It corresponds to the number of outputs of the first softmax. See note at the end.
• n_outputs_per_class (int) – the number of outputs per class. See note at
the end.
• W1 (tensor of shape (number of features of the input x,
n_classes)) – the weight matrix of the first softmax, which maps the input x
to the probabilities of the classes.
• b1 (tensor of shape (n_classes,)) – the bias vector of the first softmax layer.
• W2 (tensor of shape (n_classes, number of features of
the input x, n_outputs_per_class)) – the weight matrix of the
second softmax, which maps the input x to the probabilities of the outputs.
• b2 (tensor of shape (n_classes, n_outputs_per_class)) –
the bias vector of the second softmax layer.
• target
(tensor of shape either (batch_size,) or
(batch_size, 1)) – (optional, default None) contains the indices of
the targets for the minibatch input x. For each input, the function computes the
output for its corresponding target. If target is None, then all the outputs are
computed for each input.
Returns output_probs – Output of the two-layer hierarchical softmax for input x. If target is not specified (None), then all the outputs are computed and the returned tensor
has shape (batch_size, n_outputs). Otherwise, when target is specified, only the corresponding outputs are computed and the returned tensor has thus shape (batch_size,
1).
Return type tensor of shape (batch_size, n_outputs) or (batch_size, 1)
1
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Notes
The product of n_outputs_per_class and n_classes has to be greater or equal to n_outputs. If it is
strictly greater, then the irrelevant outputs will be ignored. n_outputs_per_class and n_classes have to
be the same as the corresponding dimensions of the tensors of W1, b1, W2 and b2. The most computational efficient configuration is when n_outputs_per_class and n_classes are equal to the square root
of n_outputs.
References
neighbours – Ops for working with images in convolutional nets
Functions
theano.tensor.nnet.neighbours.images2neibs(ten4, neib_shape, neib_step=None,
mode=’valid’)
Function images2neibs allows to apply a sliding window operation to a tensor containing images
or other two-dimensional objects. The sliding window operation loops over points in input data and
stores a rectangular neighbourhood of each point. It is possible to assign a step of selecting patches
(parameter neib_step).
Parameters
• ten4 (A 4d tensor-like) – A 4-dimensional tensor which represents a list
of lists of images. It should have shape (list 1 dim, list 2 dim, row, col). The first
two dimensions can be useful to store different channels and batches.
• neib_shape (A 1d tensor-like of 2 values) – A tuple containing
two values: height and width of the neighbourhood. It should have shape (r,c)
where r is the height of the neighborhood in rows and c is the width of the neighborhood in columns.
• neib_step (A 1d tensor-like of 2 values) – (dr,dc) where dr is
the number of rows to skip between patch and dc is the number of columns. The
parameter should be a tuple of two elements: number of rows and number of
columns to skip each iteration. Basically, when the step is 1, the neighbourhood
of every first element is taken and every possible rectangular subset is returned.
By default it is equal to neib_shape in other words, the patches are disjoint. When
the step is greater than neib_shape, some elements are omitted. When None, this
is the same as neib_shape (patch are disjoint).
• mode ({'valid', 'ignore_borders', 'wrap_centered'}) –
valid Requires an input that is a multiple of the pooling factor (in each direction).
ignore_borders Same as valid, but will ignore the borders if the shape(s) of
the input is not a multiple of the pooling factor(s).
wrap_centered ?? TODO comment
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Returns
Reshapes the input as a 2D tensor where each row is an pooling example. Pseudo-code
of the output:
idx = 0
for i in xrange(list 1 dim):
for j in xrange(list 2 dim):
for k in <image column coordinates>:
for l in <image row coordinates>:
output[idx,:]
= flattened version of ten4[i,j,
˓→l:l+r,k:k+c]
idx += 1
Note: The operation isn’t necessarily implemented internally with these for
loops, they’re just the easiest way to describe the output pattern.
Return type object
Notes
Note: Currently the step size should be chosen in the way that the corresponding dimension 𝑖 (width
or height) is equal to 𝑛 * 𝑠𝑡𝑒𝑝_𝑠𝑖𝑧𝑒𝑖 + 𝑛𝑒𝑖𝑏_𝑠ℎ𝑎𝑝𝑒𝑖 for some 𝑛.
Examples
# Defining variables
images = T.tensor4('images')
neibs = images2neibs(images, neib_shape=(5, 5))
# Constructing theano function
window_function = theano.function([images], neibs)
# Input tensor (one image 10x10)
im_val = np.arange(100.).reshape((1, 1, 10, 10))
# Function application
neibs_val = window_function(im_val)
Note: The underlying code will construct a 2D tensor of disjoint patches 5x5. The output has shape
4x25.
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theano.tensor.nnet.neighbours.neibs2images(neibs, neib_shape, original_shape,
mode=’valid’)
Function neibs2images performs the inverse operation of images2neibs. It inputs the output
of images2neibs and reconstructs its input.
Parameters
• neibs (2d tensor) – Like the one obtained by images2neibs.
• neib_shape – neib_shape that was used in images2neibs.
• original_shape – Original shape of the 4d tensor given to images2neibs
Returns Reconstructs the input of images2neibs, a 4d tensor of shape original_shape.
Return type object
Notes
Currently, the function doesn’t support tensors created with neib_step different from default
value. This means that it may be impossible to compute the gradient of a variable gained by
images2neibs w.r.t. its inputs in this case, because it uses images2neibs for gradient computation.
Examples
Example, which uses a tensor gained in example for images2neibs:
im_new = neibs2images(neibs, (5, 5), im_val.shape)
# Theano function definition
inv_window = theano.function([neibs], im_new)
# Function application
im_new_val = inv_window(neibs_val)
Note: The code will output the initial image array.
See also
• Indexing
• scan – Looping in Theano
bn – Batch Normalization
theano.tensor.nnet.bn.batch_normalization(inputs, gamma, beta, mean, std,
mode=’low_mem’)
This function will build the symbolic graph for applying batch normalization to a set of activations.
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Also works on GPUs
New in version 0.7.1.
Parameters
• inputs (symbolic tensor) – Mini-batch of activations
• gamma (symbolic tensor) – BN scale parameter, must be of same dimensionality as inputs and broadcastable against it
• beta (symbolic tensor) – BN shift parameter, must be of same dimensionality as inputs and broadcastable against it
• mean (symbolic tensor) – inputs means, must be of same dimensionality
as inputs and broadcastable against it
• std (symbolic tensor) – inputs standard deviation, must be of same dimensionality as inputs and broadcastable against it
• mode ('low_mem' or 'high_mem') – Specify which batch_normalization
implementation that will be used. As no intermediate representations are stored
for the back-propagation, ‘low_mem’ implementation lower the memory usage,
however, it is 5-10% slower than ‘high_mem’ implementation. Note that 5-10%
computation time difference compare the batch_normalization operation only,
time difference between implementation is likely to be less important on the full
model fprop/bprop.
blocksparse – Block sparse dot operations (gemv and outer)
class theano.tensor.nnet.blocksparse.SparseBlockGemv(inplace=False)
This op computes the dot product of specified pieces of vectors and matrices, returning pieces of
vectors:
for b in range(batch_size):
for j in range(o.shape[1]):
for i in range(h.shape[1]):
o[b, j, :] += numpy.dot(h[b, i], W[iIdx[b, i], oIdx[b, j]])
where b, h, W, o iIdx, oIdx are defined in the docstring of make_node.
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make_node(o, W, h, inputIdx, outputIdx)
Compute the dot product of the specified pieces of vectors and matrices.
The parameter types are actually their expected shapes relative to each other.
Parameters
• o (batch, oWin, oSize) – output vector
• W (iBlocks, oBlocks, iSize, oSize) – weight matrix
• h (batch, iWin, iSize) – input from lower layer (sparse)
• inputIdx (batch, iWin) – indexes of the input blocks
• outputIdx (batch, oWin) – indexes of the output blocks
Returns dot(W[i, j], h[i]) + o[j]
Return type (batch, oWin, oSize)
Notes
•batch is the number of examples in a minibatch (batch size).
•iBlocks is the total number of blocks in the input (from lower layer).
•iSize is the size of each of these input blocks.
•iWin is the number of blocks that will be used as inputs. Which blocks will be used is
specified in inputIdx.
•oBlocks is the number or possible output blocks.
•oSize is the size of each of these output blocks.
•oWin is the number of output blocks that will actually be computed. Which
will be computed is specified in outputIdx.
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class theano.tensor.nnet.blocksparse.SparseBlockOuter(inplace=False)
This computes the outer product of two sets of pieces of vectors updating a full matrix with the results:
for b in range(batch_size):
o[xIdx[b, i], yIdx[b, j]] += (alpha * outer(x[b, i], y[b, j]))
This op is involved in the gradient of SparseBlockGemv.
make_node(o, x, y, xIdx, yIdx, alpha=None)
Compute the dot product of the specified pieces of vectors and matrices.
The parameter types are actually their expected shapes relative to each other.
Parameters
• o (xBlocks, yBlocks, xSize, ySize) –
• x (batch, xWin, xSize) –
• y (batch, yWin, ySize) –
• xIdx (batch, iWin) – indexes of the x blocks
• yIdx (batch, oWin) – indexes of the y blocks
Returns outer(x[i], y[j]) + o[i, j]
Return type (xBlocks, yBlocks, xSize, ySize)
Notes
•batch is the number of examples in a minibatch (batch size).
•xBlocks is the total number of blocks in x.
•xSize is the size of each of these x blocks.
•xWin is the number of blocks that will be used as x. Which blocks will be used is specified
in xIdx.
•yBlocks is the number or possible y blocks.
•ySize is the size of each of these y blocks.
•yWin is the number of y blocks that will actually be computed. Which blocks will be
computed is specified in yIdx.
theano.tensor.nnet.blocksparse.sparse_block_dot(W, h, inputIdx, b, outputIdx)
Compute the dot product (plus bias) of the specified pieces of vectors and matrices. See SparseBlockGemv to get more information.
The parameter types are actually their expected shapes relative to each other.
Parameters
• W (iBlocks, oBlocks, iSize, oSize) – weight matrix
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• h (batch, iWin, iSize) – input from lower layer (sparse)
• inputIdx (batch, iWin) – indexes of the input blocks
• b (oBlocks, oSize) – bias vector
• outputIdx (batch, oWin) – indexes of the output blocks
Returns dot(W[i, j], h[i]) + b[j] but b[j] is only added once
Return type (batch, oWin, oSize)
Notes
•batch is the number of examples in a minibatch (batch size).
•iBlocks is the total number of blocks in the input (from lower layer).
•iSize is the size of each of these input blocks.
•iWin is the number of blocks that will be used as inputs. Which blocks will be used is specified in inputIdx.
•oBlocks is the number or possible output blocks.
•oSize is the size of each of these output blocks.
•oWin is the number of output blocks that will actually be computed. Which blocks will be
computed is specified in outputIdx.
raw_random – Low-level random numbers
Raw random provides the random-number drawing functionality, that underlies the friendlier
RandomStreams interface.
Reference
class theano.tensor.raw_random.RandomStreamsBase(object)
This is the interface for the theano.tensor.shared_randomstreams.RandomStreams
subclass
binomial(self, size=(), n=1, p=0.5, ndim=None):
Sample n times with probability of success p for each trial and return the number of successes.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This wraps the numpy implementation, so it has the same behavior.
uniform(self, size=(), low=0.0, high=1.0, ndim=None):
Sample a tensor of the given size whose elements come from a uniform distribution between low
and high.
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If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This wraps the numpy implementation, so it has the same bounds: [low, high[.
normal(self, size=(), avg=0.0, std=1.0, ndim=None):
Sample from a normal distribution centered on avg with the specified standard deviation (std)
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This wrap numpy implementation, so it have the same behavior.
random_integers(self, size=(), low=0, high=1, ndim=None):
Sample a random integer between low and high, both inclusive.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This is a generalization of numpy.random.random_integers() to the case where low
and high are tensors. Otherwise it behaves the same.
choice(self, size=(), a=2, replace=True, p=None, ndim=None, dtype='int64'):
Choose values from a with or without replacement. a can be a 1-D array or a positive scalar. If
a is a scalar, the samples are drawn from the range [0, a[.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This wraps the numpy implementation so it has the same behavior.
poisson(self, size=(), lam=None, ndim=None, dtype='int64'):
Draw samples from a Poisson distribution.
The Poisson distribution is the limit of the Binomial distribution for large N.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement
the missing information.
This wraps the numpy implementation so it has the same behavior.
permutation(self, size=(), n=1, ndim=None):
Returns permutations of the integers between 0 and n-1, as many times as required by size.
For instance, if size=(p,q), p*q permutations will be generated, and the output shape will
be (p,q,n), because each permutation is of size n.
Theano tries to infer the number of dimensions from the length of size, but you may always
specify it with ndim.
Note: The output will have ndim+1 dimensions.
This is a generalization of numpy.random.permutation() to tensors. Otherwise it behaves the same.
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multinomial(self, size=(), n=1, pvals=[0.5, 0.5], ndim=None):
Sample n times from a multinomial distribution defined by probabilities pvals, as many times
as required by size. For instance, if size=(p,q), p*q samples will be drawn, and the output
shape will be (p,q,len(pvals)).
Theano tries to infer the number of dimensions from the length of size, but you may always
specify it with ndim.
Note: The output will have ndim+1 dimensions.
This is a generalization of numpy.random.multinomial() to the case where n and
pvals are tensors. Otherwise it behaves the same.
shuffle_row_elements(self, input):
Return a variable with every row (rightmost index) shuffled.
This uses a permutation random variable internally, available via the .permutation attribute
of the return value.
class theano.tensor.raw_random.RandomStateType(gof.Type)
A Type for variables that will take numpy.random.RandomState values.
theano.tensor.raw_random.random_state_type(name=None)
Return a new Variable whose .type is random_state_type.
class theano.tensor.raw_random.RandomFunction(gof.Op)
Op that draws random numbers from a numpy.RandomState object. This Op is parametrized to draw
numbers from many possible distributions.
theano.tensor.raw_random.uniform(random_state, size=None, low=0.0, high=1.0,
ndim=None, dtype=None)
Sample from a uniform distribution between low and high.
If the size argument is ambiguous on the number of dimensions, the first argument may be a plain
integer to supplement the missing information.
Returns RandomVariable, NewRandomState
theano.tensor.raw_random.binomial(random_state,
size=None,
n=1,
p=0.5,
ndim=None, dtype=’int64’)
Sample n times with probability of success p for each trial and return the number of successes.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement the
missing information.
Returns RandomVariable, NewRandomState
theano.tensor.raw_random.normal(random_state, size=None, avg=0.0, std=1.0,
ndim=None, dtype=None)
Sample from a normal distribution centered on avg with the specified standard deviation (std).
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement the
missing information.
Returns RandomVariable, NewRandomState
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theano.tensor.raw_random.random_integers(random_state, size=None, low=0,
high=1, ndim=None, dtype=’int64’)
Sample random integers in [low, high] to fill up size.
If size is ambiguous on the number of dimensions, ndim may be a plain integer to supplement the
missing information.
Returns RandomVariable, NewRandomState
theano.tensor.raw_random.permutation(random_state, size=None, n=1, ndim=None,
dtype=’int64’)
Returns permutations of the integers in [0, n[, as many times as required by size. For instance, if
size=(p,q), p*q permutations will be generated, and the output shape will be (p,q,n), because
each permutation is of size n.
If size is ambiguous on the number of dimensions, ndim may be a plain integer, which should
correspond to len(size).
Note: The output will have ndim+1 dimensions.
Returns RandomVariable, NewRandomState
theano.tensor.raw_random.multinomial(random_state, size=None, p_vals=[0.5, 0.5],
ndim=None, dtype=’int64’)
Sample from a multinomial distribution defined by probabilities pvals, as many times as required
by size. For instance, if size=(p,q), p*q samples will be drawn, and the output shape will be
(p,q,len(pvals)).
If size is ambiguous on the number of dimensions, ndim may be a plain integer, which should
correspond to len(size).
Note: The output will have ndim+1 dimensions.
Returns RandomVariable, NewRandomState
shared_randomstreams – Friendly random numbers
Guide
Since Theano uses a functional design, producing pseudo-random numbers in a graph is not quite as straightforward as it is in numpy.
The way to think about putting randomness into Theano’s computations is to put random variables in your
graph. Theano will allocate a numpy RandomState object for each such variable, and draw from it as
necessary. We will call this sort of sequence of random numbers a random stream.
For an example of how to use random numbers, see Using Random Numbers.
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Reference
class theano.tensor.shared_randomstreams.RandomStreams(raw_random.RandomStreamsBase)
This is a symbolic stand-in for numpy.random.RandomState. Random variables of various
distributions are instantiated by calls to parent class raw_random.RandomStreamsBase.
updates()
Returns a list of all the (state, new_state) update pairs for the random variables created
by this object
This can be a convenient shortcut to enumerating all the random variables in a large graph in the
update parameter of function.
seed(meta_seed)
meta_seed will be used to seed a temporary random number generator, that will in turn generate
seeds for all random variables created by this object (via gen).
Returns None
gen(op, *args, **kwargs)
Return the random variable from op(*args, **kwargs), but also install special attributes (.rng
and update, see RandomVariable ) into it.
This function also adds the returned variable to an internal list so that it can be seeded later by a
call to seed.
uniform, normal, binomial, multinomial, random_integers, ...
See raw_random.RandomStreamsBase.
class theano.tensor.shared_randomstreams.RandomVariable(object)
rng
The shared variable whose .value is the numpy RandomState generator feeding this random
variable.
update
A pair whose first element is a shared variable whose value is a numpy RandomState, and whose
second element is an [symbolic] expression for the next value of that RandomState after drawing
samples. Including this pair in the‘‘updates‘‘ list to function will cause the function to update
the random number generator feeding this variable.
signal – Signal Processing
Signal Processing
The signal subpackage contains ops which are useful for performing various forms of signal processing.
conv – Convolution
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Note: Two similar implementation exists for conv2d:
signal.conv2d and nnet.conv2d.
The former implements a traditional 2D convolution, while the latter implements the convolutional layers
present in convolutional neural networks (where filters are 3D and pool over several input channels).
theano.tensor.signal.conv.conv2d(input,
filters,
image_shape=None,
filter_shape=None, border_mode=’valid’, subsample=(1, 1), **kargs)
signal.conv.conv2d performs a basic 2D convolution of the input with the given filters. The input
parameter can be a single 2D image or a 3D tensor, containing a set of images. Similarly, filters can
be a single 2D filter or a 3D tensor, corresponding to a set of 2D filters.
Shape parameters are optional and will result in faster execution.
Parameters
• input (dmatrix of dtensor3) – Symbolic variable for images to be filtered.
• filters (dmatrix of dtensor3) – Symbolic variable containing filter
values.
• border_mode ({'valid', 'full'}) – See scipy.signal.convolve2d.
• subsample – Factor by which to subsample output.
• image_shape (tuple of length 2 or 3) – ([number images,] image
height, image width).
• filter_shape (tuple of length 2 or 3) – ([number filters,] filter
height, filter width).
• kwargs – See theano.tensor.nnet.conv.conv2d.
Returns Tensor of filtered images, with shape ([number images,] [number filters,] image
height, image width).
Return type symbolic 2D,3D or 4D tensor
conv.fft(*todo)
[James has some code for this, but hasn’t gotten it into the source tree yet.]
downsample – Down-Sampling
See also:
theano.tensor.nnet.neighbours.images2neibs()
downsample.fft(*todo)
[James has some code for this, but hasn’t gotten it into the source tree yet.]
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pool – Down-Sampling
See also:
theano.tensor.nnet.neighbours.images2neibs()
theano.tensor.signal.pool.pool_2d(input, ds, ignore_border=None,
padding=(0, 0), mode=’max’)
Downscale the input by a specified factor
st=None,
Takes as input a N-D tensor, where N >= 2. It downscales the input image by the specified factor, by
keeping only the maximum value of non-overlapping patches of size (ds[0],ds[1])
Parameters
• input (N-D theano tensor of input images) – Input images. Max
pooling will be done over the 2 last dimensions.
• ds (tuple of length 2) – Factor by which to downscale (vertical ds, horizontal ds). (2,2) will halve the image in each dimension.
• ignore_border (bool (default None, will print a warning
and set to False)) – When True, (5,5) input with ds=(2,2) will generate a
(2,2) output. (3,3) otherwise.
• st (tuple of two ints) – Stride size, which is the number of shifts over
rows/cols to get the next pool region. If st is None, it is considered equal to ds (no
overlap on pooling regions).
• padding (tuple of two ints) – (pad_h, pad_w), pad zeros to extend beyond four borders of the images, pad_h is the size of the top and bottom margins,
and pad_w is the size of the left and right margins.
• mode
({'max', 'sum', 'average_inc_pad',
'average_exc_pad'}) – Operation executed on each window.
max
and sum always exclude the padding in the computation. average gives you the
choice to include or exclude it.
theano.tensor.signal.pool.max_pool_2d_same_size(input, patch_size)
Takes as input a 4-D tensor. It sets all non maximum values of non-overlapping patches of size
(patch_size[0],patch_size[1]) to zero, keeping only the maximum values. The output has the same
dimensions as the input.
Parameters
• input (4-D theano tensor of input images) – Input images. Max
pooling will be done over the 2 last dimensions.
• patch_size (tuple of length 2) – Size of the patch (patch height,
patch width). (2,2) will retain only one non-zero value per patch of 4 values.
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tensor.utils – Tensor Utils
theano.tensor.utils.hash_from_ndarray(data)
Return a hash from an ndarray.
It takes care of the data, shapes, strides and dtype.
theano.tensor.utils.shape_of_variables(fgraph, input_shapes)
Compute the numeric shape of all intermediate variables given input shapes.
Parameters
• fgraph – The theano.FunctionGraph in question.
• input_shapes (dict) – A dict mapping input to shape.
Returns
• shapes (dict) – A dict mapping variable to shape
• .. warning:: This modifies the fgraph. Not pure.
Examples
>>> import theano
>>> x = theano.tensor.matrix('x')
>>> y = x[512:]; y.name = 'y'
>>> fgraph = theano.FunctionGraph([x], [y], clone=False)
>>> d = shape_of_variables(fgraph, {x: (1024, 1024)})
>>> d[y]
(array(512), array(1024))
>>> d[x]
(array(1024), array(1024))
tensor.elemwise – Tensor Elemwise
class theano.tensor.elemwise.All(axis=None)
Applies bitwise and to all the values of a tensor along the specified axis(es).
Equivalent to CAReduce(scalar.and_, axis=axis).
class theano.tensor.elemwise.Any(axis=None)
Applies bitwise or to all the values of a tensor along the specified axis(es).
Equivalent to CAReduce(scalar.or_, axis=axis).
class theano.tensor.elemwise.CAReduce(scalar_op, axis=None)
CAReduce = Commutative Associative Reduce Reduces a scalar operation along the specified
axis(es). (The scalar op should be both commutative and assocative)
The output will have the same shape as the input minus the reduced dimensions. It will contain the
variable of accumulating all values over the reduced dimensions using the specified scalar op.
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Parameters
• scalar_op – A binary scalar op with only one output. It must be commutative
and associative.
• axis –
– The dimension along which we want to reduce
– List of dimensions that we want to reduce
– If None, all dimensions are reduced
Note:
CAReduce(add)
CAReduce(mul)
CAReduce(maximum)
CAReduce(minimum)
CAReduce(or_)
CAReduce(and_)
CAReduce(xor)
#
#
#
#
#
#
#
#
#
sum (ie, acts like the numpy sum operation)
product
max
min
any # not lazy
all # not lazy
a bit at 1 tell that there was an odd number of
bit at that position that where 1. 0 it was an
even number ...
In order to (eventually) optimize memory usage patterns, CAReduce makes zero guarantees on the
order in which it iterates over the dimensions and the elements of the array(s). Therefore, to ensure
consistent variables, the scalar operation represented by the reduction must be both commutative and
associative (eg add, multiply, maximum, binary or/and/xor - but not subtract, divide or power).
class theano.tensor.elemwise.CAReduceDtype(scalar_op, axis=None, dtype=None,
acc_dtype=None)
Reduces a scalar operation along the specified axis(es).
This subclass of CAReduce accepts an additional “dtype” parameter, that specifies which dtype the
output should be.
It also accepts an optional “acc_dtype”, which specify the dtype that will be used for the accumulation.
So, the accumulation will be done into a tensor of dtype “acc_dtype”, then it will be casted into
“dtype” and returned.
If no dtype is provided, one will be inferred so as not to lose too much precision.
Parameters
• scalar_op – A binary scalar op with only one output. It must be commutative
and associative.
• axis –
– the dimension along which we want to reduce
– list of dimensions that we want to reduce
– if None, all dimensions are reduced
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• dtype – The dtype of the returned tensor. If None, then we use the default dtype
which is the same as the input tensor’s dtype except when:
– the input dtype is a signed integer of precision < 64 bit, in which case we use
int64
– the input dtype is an unsigned integer of precision < 64 bit, in which case we
use uint64
This default dtype does _not_ depend on the value of “acc_dtype”. This behavior
is similar in spirit to that of numpy (except numpy uses the default machine integer
while we always use 64 bit integers to avoid platform-dependent behavior).
• acc_dtype – The dtype of the internal accumulator. If None (default), we use
the dtype in the list below, or the input dtype if its precision is higher:
– for int dtypes, we use at least int64;
– for uint dtypes, we use at least uint64;
– for float dtypes, we use at least float64;
– for complex dtypes, we use at least complex128.
class theano.tensor.elemwise.DimShuffle(input_broadcastable,
new_order,
inplace=False)
Allows to reorder the dimensions of a tensor or insert or remove broadcastable dimensions.
In the following examples, ‘x’ means that we insert a broadcastable dimension and a numerical index
represents the dimension of the same rank in the tensor passed to perform.
Parameters
• input_broadcastable – The expected broadcastable pattern of the input
• new_order – A list representing the relationship between the input’s dimensions and the output’s dimensions. Each element of the list can either be an index
or ‘x’. Indices must be encoded as python integers, not theano symbolic integers.
• inplace (bool, optional) – If True, the output will be a view of the input.
If False (default), the output will be a copy of the input.
Note: If j = new_order[i] is an index, the output’s ith dimension will be the input’s jth dimension. If
new_order[i] is x, the output’s ith dimension will be 1 and Broadcast operations will be allowed to do
broadcasting over that dimension.
If input.broadcastable[i] == False then i must be found in new_order. Broadcastable dimensions, on
the other hand, can be discarded.
Note:
DimShuffle((False, False, False), ['x', 2, 'x', 0, 1])
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This op will only work on 3d tensors with no broadcastable dimensions. The first dimension will be
broadcastable, then we will have the third dimension of the input tensor as the second of the resulting
tensor, etc. If the tensor has shape (20, 30, 40), the resulting tensor will have dimensions (1, 40, 1, 20,
30). (AxBxC tensor is mapped to 1xCx1xAxB tensor)
DimShuffle((True, False), [1])
This op will only work on 2d tensors with the first dimension broadcastable. The second dimension
of the input tensor will be the first dimension of the resulting tensor. If the tensor has shape (1, 20),
the resulting tensor will have shape (20, ).
Example
DimShuffle((), ['x']) # make a 0d (scalar) into a 1d vector
DimShuffle((False, False), [0, 1]) # identity
DimShuffle((False, False), [1, 0]) # inverts the 1st and 2nd dimensions
DimShuffle((False,), ['x', 0]) # make a row out of a 1d vector
# (N to 1xN)
DimShuffle((False,), [0, 'x']) # make a column out of a 1d vector
# (N to Nx1)
DimShuffle((False, False, False), [2, 0, 1]) # AxBxC to CxAxB
DimShuffle((False, False), [0, 'x', 1]) # AxB to Ax1xB
DimShuffle((False, False), [1, 'x', 0]) # AxB to Bx1xA
The reordering of the dimensions can be done with the numpy.transpose function. Adding, subtracting
dimensions can be done with reshape.
class theano.tensor.elemwise.Elemwise(scalar_op,
name=None,
openmp=None)
Generalizes a scalar op to tensors.
inplace_pattern=None,
nfunc_spec=None,
All the inputs must have the same number of dimensions. When the Op is performed, for each
dimension, each input’s size for that dimension must be the same. As a special case, it can also be
1 but only if the input’s broadcastable flag is True for that dimension. In that case, the tensor is
(virtually) replicated along that dimension to match the size of the others.
The dtypes of the outputs mirror those of the scalar Op that is being generalized to tensors. In particular, if the calculations for an output are done inplace on an input, the output type must be the same as
the corresponding input type (see the doc of scalar.ScalarOp to get help about controlling the output
type)
Parameters
• scalar_op – An instance of a subclass of scalar.ScalarOp which works
uniquely on scalars.
• inplace_pattern – A dictionary that maps the index of an output to the index
of an input so the output is calculated inplace using the input’s storage. (Just like
destroymap, but without the lists.)
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• nfunc_spec – Either None or a tuple of three elements, (nfunc_name, nin,
nout) such that getattr(numpy, nfunc_name) implements this operation, takes nin
inputs and nout outputs. Note that nin cannot always be inferred from the scalar
op’s own nin field because that value is sometimes 0 (meaning a variable number
of inputs), whereas the numpy function may not have varargs.
Note:
Elemwise(add) represents + on tensors (x + y)
Elemwise(add, {0 : 0}) represents the += operation (x += y)
Elemwise(add, {0 : 1}) represents += on the second argument (y += x)
Elemwise(mul)(rand(10, 5), rand(1, 5)) the second input is completed along the first dimension to
match the first input
Elemwise(true_div)(rand(10, 5), rand(10, 1)) same but along the second dimension
Elemwise(int_div)(rand(1, 5), rand(10, 1)) the output has size (10, 5)
Elemwise(log)(rand(3, 4, 5))
make_node(*inputs)
If the inputs have different number of dimensions, their shape is left-completed to the greatest
number of dimensions with 1s using DimShuffle.
python_constant_folding(node)
Return True if we do not want to compile c code when doing constant folding of this node.
class theano.tensor.elemwise.Prod(axis=None,
dtype=None,
no_zeros_in_input=False)
Multiplies all the values of a tensor along the specified axis(es).
acc_dtype=None,
Equivalent to CAReduce(scalar.prod, axis = axis), with the difference that this defines the gradient of
prod wrt its tensor input.
grad(inp, grads)
The grad of this Op could be very easy, if it is was not for the case where zeros are present in a
given “group” (ie. elements reduced together to form the product).
If no zeros are found in the elements of the product, then the partial derivative of the product
relative to one of the elements (one of the inputs) is simply the product of the other elements.
That’s easy to see from the chain rule.
Now the trick (with no zeros) is to take the overall product, then for every original element, the
partial derivative is given by this product divided by the element itself (which equals the product
of the other terms). This is easy to do by broadcasting the original product.
(Note that we also need to broadcast-multiply by the “incoming gradient”, ie. the gradient of the
cost relative to the output/product).
With zeros, things get more complicated. For a given group, we have 3 cases:
•No zeros in the group. Use previous trick.
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•If only one zero is present, then the gradient for that element is non-zero, but is zero
for all others.
•If more than one zero is present, then all the derivatives are zero.
For the last two cases (with 1 or more zeros), we can’t use the division trick, as this gives
divisions by 0.
Implementing that case-by-case logic is not as trivial, so a bunch of hacks are piled down here
to do it. Notably, for the “only one zero” case, there’s a special Op that computes the product
of the elements in the group, minus the zero (see ProdWithoutZero). The trick is then to use the
division trick for groups with no zero, to use the ProdWithoutZeros op where there’s only one
zero, and to output a derivative of zero for any element part of a group with more than one zero.
I do this by first counting the number of zeros in each group (see the “T.eq()” bits), then taking
this or that behavior (see T.switch) based on the result of this count.
class theano.tensor.elemwise.Sum(axis=None, dtype=None, acc_dtype=None)
Sums all the values of a tensor along the specified axis(es).
Equivalent to CAReduceDtype(scalar.add, axis=axis, dtype=dtype), with the difference that this defines the gradient of sum wrt its tensor input.
Parameters
• axis – Axis(es) along which the tensor should be summed (use None to sum
over all axes, and a list or tuple to sum along more than one axis).
• dtype – The dtype of the internal accumulator and returned tensor. If None,
then we use the default dtype which is the same as the input tensor’s dtype except
when: - the input dtype is a signed integer of precision < 64 bit, in which case we
use int64 - the input dtype is an unsigned integer of precision < 64 bit, in which
case we use uint64 This value does not depend on the value of “acc_dtype”.
• acc_dtype – The dtype of the internal accumulator. If None (default), we use
the dtype in the list below, or the input dtype if its precision is higher: - for int
dtypes, we use at least int64; - for uint dtypes, we use at least uint64; - for float
dtypes, we use at least float64; - for complex dtypes, we use at least complex128.
tensor.extra_ops – Tensor Extra Ops
class theano.tensor.extra_ops.BinCountOp(minlength=None)
Note: Deprecated Use bincount() instead. See function bincount for docstring.
compatible_type = (‘int8’, ‘int16’, ‘int32’, ‘int64’, ‘uint8’, ‘uint16’, ‘uint32’, ‘uint64’)
Tuple of all compatible dtype for the parameter of this op.
class theano.tensor.extra_ops.CpuContiguous(use_c_code=’/usr/bin/g++’)
Check to see if the input is c-contiguous, if it is, do nothing, else return a contiguous array.
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class theano.tensor.extra_ops.Unique(return_index=False, return_inverse=False, return_counts=False)
Wraps numpy.unique. This op is not implemented on the GPU.
Examples
>>> import numpy as np
>>> import theano
>>> x = theano.tensor.vector()
>>> f = theano.function([x], Unique(True, True, False)(x))
>>> f([1, 2., 3, 4, 3, 2, 1.])
[array([ 1., 2., 3., 4.]), array([0, 1, 2, 3]), array([0, 1, 2, 3, 2,
˓→1, 0])]
>>> y = theano.tensor.matrix()
>>> g = theano.function([y], Unique(True, True, False)(y))
>>> g([[1, 1, 1.0], (2, 3, 3.0)])
[array([ 1., 2., 3.]), array([0, 3, 4]), array([0, 0, 0, 1, 2, 2])]
theano.tensor.extra_ops.bartlett(M)
An instance of this class returns the Bartlett spectral window in the time-domain. The Bartlett window
is very similar to a triangular window, except that the end points are at zero. It is often used in signal
processing for tapering a signal, without generating too much ripple in the frequency domain.
New in version 0.6.
Parameters M (integer scalar) – Number of points in the output window. If zero
or less, an empty vector is returned.
Returns The triangular window, with the maximum value normalized to one (the value
one appears only if the number of samples is odd), with the first and last samples
equal to zero.
Return type vector of doubles
theano.tensor.extra_ops.bincount(x,
weights=None,
sert_nonneg=False)
Count number of occurrences of each value in array of ints.
minlength=None,
as-
The number of bins (of size 1) is one larger than the largest value in x. If minlength is specified, there
will be at least this number of bins in the output array (though it will be longer if necessary, depending
on the contents of x). Each bin gives the number of occurrences of its index value in x. If weights is
specified the input array is weighted by it, i.e. if a value n is found at position i, out[n] += weight[i]
instead of out[n] += 1.
Parameters
• x (1 dimension, nonnegative ints) –
• weights
(array of the same shape as x with
corresponding weights.) – Optional.
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• minlength
(A minimum number of bins for the output
array.) – Optional.
• assert_nonneg
(A flag that inserts an assert_op to
check if) – every input x is nonnegative. Optional.
New in version 0.6.
theano.tensor.extra_ops.compress(condition, x, axis=None)
Return selected slices of an array along given axis.
It returns the input tensor, but with selected slices along a given axis retained. If no axis is provided,
the tensor is flattened. Corresponds to numpy.compress
New in version 0.7.
Parameters
• x – Input data, tensor variable.
• condition – 1 dimensional array of non-zero and zero values corresponding to
indices of slices along a selected axis.
Returns x with selected slices.
Return type object
theano.tensor.extra_ops.cumprod(x, axis=None)
Return the cumulative product of the elements along a given axis.
Wraping of numpy.cumprod.
Parameters
• x – Input tensor variable.
• axis – The axis along which the cumulative product is computed. The default
(None) is to compute the cumprod over the flattened array.
New in version 0.7.
theano.tensor.extra_ops.cumsum(x, axis=None)
Return the cumulative sum of the elements along a given axis.
Wraping of numpy.cumsum.
Parameters
• x – Input tensor variable.
• axis – The axis along which the cumulative sum is computed. The default
(None) is to compute the cumsum over the flattened array.
New in version 0.7.
theano.tensor.extra_ops.diff(x, n=1, axis=-1)
Calculate the n-th order discrete difference along given axis.
The first order difference is given by out[i] = a[i + 1] - a[i] along the given axis, higher order differences are calculated by using diff recursively. Wraping of numpy.diff.
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Parameters
• x – Input tensor variable.
• n – The number of times values are differenced, default is 1.
• axis – The axis along which the difference is taken, default is the last axis.
New in version 0.6.
theano.tensor.extra_ops.fill_diagonal(a, val)
Returns a copy of an array with all elements of the main diagonal set to a specified scalar value.
New in version 0.6.
Parameters
• a – Rectangular array of at least two dimensions.
• val – Scalar value to fill the diagonal whose type must be compatible with that
of array ‘a’ (i.e. ‘val’ cannot be viewed as an upcast of ‘a’).
Returns
• array – An array identical to ‘a’ except that its main diagonal is filled with scalar
‘val’. (For an array ‘a’ with a.ndim >= 2, the main diagonal is the list of locations
a[i, i, ..., i] (i.e. with indices all identical).)
• Support rectangular matrix and tensor with more than 2 dimensions
• if the later have all dimensions are equals.
theano.tensor.extra_ops.fill_diagonal_offset(a, val, offset)
Returns a copy of an array with all elements of the main diagonal set to a specified scalar value.
Parameters
• a – Rectangular array of two dimensions.
• val – Scalar value to fill the diagonal whose type must be compatible with that
of array ‘a’ (i.e. ‘val’ cannot be viewed as an upcast of ‘a’).
• offset – Scalar value Offset of the diagonal from the main diagonal. Can be
positive or negative integer.
Returns An array identical to ‘a’ except that its offset diagonal is filled with scalar ‘val’.
The output is unwrapped.
Return type array
theano.tensor.extra_ops.repeat(x, repeats, axis=None)
Repeat elements of an array.
It returns an array which has the same shape as x, except along the given axis. The axis is used to
speficy along which axis to repeat values. By default, use the flattened input array, and return a flat
output array.
The number of repetitions for each element is repeat. repeats is broadcasted to fit the length of the
given axis.
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Parameters
• x – Input data, tensor variable.
• repeats – int, scalar or tensor variable
• axis (int, optional) –
See also:
tensor.tile(), ()
theano.tensor.extra_ops.squeeze(x)
Remove broadcastable dimensions from the shape of an array.
It returns the input array, but with the broadcastable dimensions removed. This is always x itself or a
view into x.
New in version 0.6.
Parameters x – Input data, tensor variable.
Returns x without its broadcastable dimensions.
Return type object
theano.tensor.extra_ops.to_one_hot(y, nb_class, dtype=None)
Return a matrix where each row correspond to the one hot encoding of each element in y.
Parameters
• y – A vector of integer value between 0 and nb_class - 1.
• nb_class (int) – The number of class in y.
• dtype (data-type) – The dtype of the returned matrix. Default floatX.
Returns A matrix of shape (y.shape[0], nb_class), where each row i is the one hot encoding of the corresponding y[i] value.
Return type object
tensor.io – Tensor IO Ops
File operation
• Load from disk with the function load and its associated op LoadFromDisk
MPI operation
• Non-blocking transfer: isend and irecv.
• Blocking transfer: send and recv
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Details
class theano.tensor.io.LoadFromDisk(dtype, broadcastable, mmap_mode=None)
An operation to load an array from disk.
See also:
load
Notes
Non-differentiable.
class theano.tensor.io.MPIRecv(source, tag, shape, dtype)
An operation to asynchronously receive an array to a remote host using MPI.
See also:
MPIRecv, MPIWait
Notes
Non-differentiable.
class theano.tensor.io.MPIRecvWait(tag)
An operation to wait on a previously received array using MPI.
See also:
MPIRecv
Notes
Non-differentiable.
class theano.tensor.io.MPISend(dest, tag)
An operation to asynchronously Send an array to a remote host using MPI.
See also:
MPIRecv, MPISendWait
Notes
Non-differentiable.
class theano.tensor.io.MPISendWait(tag)
An operation to wait on a previously sent array using MPI.
See also:
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MPISend
Notes
Non-differentiable.
theano.tensor.io.irecv(shape, dtype, source, tag)
Non-blocking receive.
theano.tensor.io.isend(var, dest, tag)
Non blocking send.
theano.tensor.io.load(path, dtype, broadcastable, mmap_mode=None)
Load an array from an .npy file.
Parameters
• path – A Generic symbolic variable, that will contain a string
• dtype (data-type) – The data type of the array to be read.
• broadcastable – The broadcastable pattern of the loaded array, for instance,
(False,) for a vector, (False, True) for a column, (False, False) for a matrix.
• mmap_mode – How the file will be loaded. None means that the data will be
copied into an array in memory, ‘c’ means that the file will be mapped into virtual
memory, so only the parts that are needed will be actually read from disk and put
into memory. Other modes supported by numpy.load (‘r’, ‘r+’, ‘w+’) cannot be
supported by Theano.
Examples
>>> from theano import *
>>> path = Variable(Generic())
>>> x = tensor.load(path, 'int64', (False,))
>>> y = x*2
>>> fn = function([path], y)
>>> fn("stored-array.npy")
array([0, 2, 4, 6, 8], dtype=int64)
theano.tensor.io.mpi_send_wait_key(a)
Wait as long as possible on Waits, Start Send/Recvs early.
theano.tensor.io.mpi_tag_key(a)
Break MPI ties by using the variable tag - prefer lower tags first.
theano.tensor.io.recv(shape, dtype, source, tag)
Blocking receive.
theano.tensor.io.send(var, dest, tag)
Blocking send.
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tensor.opt – Tensor Optimizations
Tensor optimizations addressing the ops in basic.py.
class theano.tensor.opt.Assert(msg=’Theano Assert failed!’)
Implements assertion in a computational graph.
Returns the first parameter if the condition is true, otherwise, triggers AssertionError.
Notes
This Op is a debugging feature. It can be removed from the graph because of optimizations, and
can hide some possible optimizations to the optimizer. Specifically, removing happens if it can be
determined that condition will always be true. Also, the output of the Op must be used in the function
computing the graph, but it doesn’t have to be returned.
Examples
>>>
>>>
>>>
>>>
>>>
import theano
T = theano.tensor
x = T.vector('x')
assert_op = T.opt.Assert()
func = theano.function([x], assert_op(x, x.size<2))
class theano.tensor.opt.Canonizer(main,
inverse,
reciprocal,
calculate,
use_reciprocal=True)
Simplification tool. The variable is a local_optimizer. It is best used with a TopoOptimizer in
in_to_out order.
Usage: Canonizer(main, inverse, reciprocal, calculate)
Parameters
• main – A suitable Op class that is commutative, associative and takes one to an
arbitrary number of inputs, e.g. add or mul
• inverse – An Op class such that inverse(main(x, y), y) == x e.g. sub or true_div
• reciprocal – A function such that main(x, reciprocal(y)) == inverse(x, y) e.g.
neg or inv
• calculate – Function that takes a list of numpy.ndarray instances for the numerator, another list for the denumerator, and calculates inverse(main(*num),
main(*denum)). It takes a keyword argument, aslist. If True, the value should
be returned as a list of one element, unless the value is such that value = main().
In that case, the return value should be an empty list.
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Examples
>>>
>>>
>>>
...
>>>
...
import theano.tensor as T
from theano.tensor.opt import Canonizer
add_canonizer = Canonizer(T.add, T.sub, T.neg, \
lambda n, d: sum(n) - sum(d))
mul_canonizer = Canonizer(T.mul, T.true_div, T.inv, \
lambda n, d: prod(n) / prod(d))
Examples of optimizations mul_canonizer can perform:
x / x -> 1
(x * y) / x -> y
x / y / x -> 1 / y
x / y / z -> x / (y * z)
x / (y / z) -> (x * z) / y
(a / b) * (b / c) * (c / d) -> a / d
(2.0 * x) / (4.0 * y) -> (0.5 * x) / y
2 * x / 2 -> x
x * y * z -> Elemwise(T.mul){x,y,z} #only one pass over the memory.
!-> Elemwise(T.mul){x,Elemwise(T.mul){y,z}}
static get_constant(v)
Returns A numeric constant if v is a Constant or, well, a numeric constant. If v is a
plain Variable, returns None.
Return type object
get_num_denum(input)
This extract two lists, num and denum, such that the input is: self.inverse(self.main(*num),
self.main(*denum)). It returns the two lists in a (num, denum) pair.
For example, for main, inverse and reciprocal = *, / and inv(),
input -> returned value (num, denum)
x*y -> ([x, y], [])
inv(x) -> ([], [x])
inv(x) * inv(y) -> ([], [x, y])
x*y/z -> ([x, y], [z])
log(x) / y * (z + x) / y -> ([log(x), z + x], [y, y])
(((a / b) * c) / d) -> ([a, c], [b, d])
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a / (b / c) -> ([a, c], [b])
log(x) -> ([log(x)], [])
x**y -> ([x**y], [])
x * y * z -> ([x, y, z], [])
merge_num_denum(num, denum)
Utility function which takes two lists, num and denum, and returns something which is equivalent to inverse(main(*num), main(*denum)), but depends on the length of num and the length
of denum (in order to minimize the number of operations).
Let n = len(num) and d = len(denum):
n=0, d=0: neutral element (given by self.calculate([], []))
(for example, this would be 0 if main is addition
and 1 if main is multiplication)
n=1, d=0: num[0]
n=0, d=1: reciprocal(denum[0])
n=1, d=1: inverse(num[0], denum[0])
n=0, d>1: reciprocal(main(*denum))
n>1, d=0: main(*num)
n=1, d>1: inverse(num[0], main(*denum))
n>1, d=1: inverse(main(*num), denum[0])
n>1, d>1: inverse(main(*num), main(*denum))
Given the values of n and d to which they are associated, all of the above are equivalent to:
inverse(main(*num), main(*denum))
simplify(num, denum, out_type)
Shorthand for:
self.simplify_constants(*self.simplify_factors(num, denum))
simplify_constants(orig_num, orig_denum, out_type=None)
Find all constants and put them together into a single constant.
Finds all constants in orig_num and orig_denum (using get_constant) and puts them together
into a single constant. The constant is inserted as the first element of the numerator. If the
constant is the neutral element, it is removed from the numerator.
Examples
Let main be multiplication:
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[2, 3, x], [] -> [6, x], []
[x, y, 2], [4, z] -> [0.5, x, y], [z]
[x, 2, y], [z, 2] -> [x, y], [z]
simplify_factors(num, denum)
For any Variable r which is both in num and denum, removes it from both lists. Modifies the
lists inplace. Returns the modified lists. For example:
[x], [x] -> [], []
[x, y], [x] -> [y], []
[a, b], [c, d] -> [a, b], [c, d]
class theano.tensor.opt.FusionOptimizer(local_optimizer)
Graph optimizer for Fusion of elemwise operations.
class theano.tensor.opt.MakeVector(dtype=’int64’)
Concatenate a number of scalars together into a vector.
This is a simple version of stack() that introduces far less cruft into the graph. Should work with 0
inputs. The constant_folding optimization will remove it.
class theano.tensor.opt.ShapeFeature
Graph optimizer for removing all calls to shape().
This optimizer replaces all Shapes and Subtensors of Shapes with Shape_i and MakeVector Ops.
This optimizer has several goals:
1.to ‘lift’ Shapes to as close to the inputs as possible.
2.to infer the shape of every node in the graph in terms of the input shapes.
3.remove all fills (T.second, T.fill) from the graph
Lifting shapes as close to the inputs as possible is important for canonicalization because it is very
bad form to have to compute something just to know how big it will be. Firstly, it is a waste of time
to compute such outputs. But it is important to get rid of these outputs as early as possible in the
compilation process because the extra computations make it appear as if many internal graph nodes
have multiple clients. Many optimizations refuse to work on nodes with multiple clients.
Lifting is done by using an <Op>.infer_shape function if one is present, or else using a conservative default. An Op that supports shape-lifting should define a infer_shape(self, node, input_shapes)
function. The argument input_shapes is a tuple of tuples... there is an interior tuple for each input
to the node. The tuple has as many elements as dimensions. The element in position i of tuple j
represents the i’th shape component of the j’th input. The function should return a tuple of tuples.
One output tuple for each node.output. Again, the i’th element of the j’th output tuple represents the
output[j].shape[i] of the function. If an output is not a TensorType, then None should be returned
instead of a tuple for that output.
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For example the infer_shape for a matrix-matrix product would accept input_shapes=((x0,x1),
(y0,y1)) and return ((x0, y1),).
Inferring the shape of internal nodes in the graph is important for doing size-driven optimizations.
If we know how big various intermediate results will be, we can estimate the cost of many Ops
accurately, and generate c-code that is specific [e.g. unrolled] to particular sizes.
In cases where you cannot figure out the shape, raise a ShapeError.
Notes
Right now there is only the ConvOp that could really take advantage of this shape inference, but it
is worth it even just for the ConvOp. All that’s necessary to do shape inference is 1) to mark shared
inputs as having a particular shape, either via a .tag or some similar hacking; and 2) to add an optional
In() argument to promise that inputs will have a certain shape (or even to have certain shapes in certain
dimensions). We can’t automatically infer the shape of shared variables as they can change of shape
during the execution by default. (NOT IMPLEMENTED YET, BUT IS IN TRAC)
Using Shape information in Optimizations
To use this shape information in OPTIMIZATIONS, use the shape_of dictionary.
For example:
try:
shape_of = node.fgraph.shape_feature.shape_of
except AttributeError:
# This can happen when the mode doesn't include the ShapeFeature.
return
shape_of_output_zero = shape_of[node.output[0]]
The shape_of_output_zero symbol will contain a tuple, whose elements are either integers or
symbolic integers.
TODO: check to see if the symbols are necessarily non-constant... or are integer literals sometimes
Theano constants?? That would be confusing.
default_infer_shape(node, i_shapes)
Return a list of shape tuple or None for the outputs of node.
This function is used for Ops that don’t implement infer_shape. Ops that do implement infer_shape should use the i_shapes parameter, but this default implementation ignores it.
get_shape(var, idx)
Optimization can call this to get the current shape_i
It is better to call this then use directly shape_of[var][idx] as this method should update shape_of
if needed.
TODO: Up to now, we don’t update it in all cases. Update in all cases.
init_r(r)
Register r’s shape in the shape_of dictionary.
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same_shape(x, y, dim_x=None, dim_y=None)
Return True if we are able to assert that x and y have the same shape.
dim_x and dim_y are optional. If used, they should be an index to compare only 1 dimension of
x and y.
set_shape(r, s, override=False)
Assign the shape s to previously un-shaped variable r.
Parameters
• r (a variable) –
• s (None or a tuple of symbolic integers) –
• override (If False, it mean r is a new object in the
fgraph.) – If True, it mean r is already in the fgraph and we want to override
its shape.
set_shape_i(r, i, s_i)
Replace element i of shape_of[r] by s_i
shape_ir(i, r)
Return symbolic r.shape[i] for tensor variable r, int i.
shape_tuple(r)
Return a tuple of symbolic shape vars for tensor variable r.
unpack(s_i)
Return a symbolic integer scalar for the shape element s_i.
The s_i argument was produced by the infer_shape() of an Op subclass.
update_shape(r, other_r)
Replace shape of r by shape of other_r.
If, on some dimensions, the shape of other_r is not informative, keep the shape of r on those
dimensions.
class theano.tensor.opt.ShapeOptimizer
Optimizer that serves to add ShapeFeature as an fgraph feature.
theano.tensor.opt.apply_rebroadcast_opt(rval)
Apply as many times as required the optimization local_useless_rebroadcast and local_rebroadcast_lift.
Parameters rval (a Variable) –
Returns
Return type A Variable (the same if no optimization can be applied)
theano.tensor.opt.broadcast_like(value, template, fgraph, dtype=None)
Return a Variable with the same shape and dtype as the template, filled by broadcasting value through
it. value will be cast as necessary.
theano.tensor.opt.check_for_x_over_absX(numerators, denominators)
Convert x/abs(x) into sign(x).
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theano.tensor.opt.copy_stack_trace(from_var, to_var)
Copies the stack trace from one or more tensor variables to one or more tensor variables.
Parameters
• from_var – Tensor variable or list of tensor variables to copy stack traces from.
• to_var – Tensor variable or list of tensor variables to copy stack traces to.
Notes
The stacktrace is assumed to be of the form of a list of lists of tuples. Each tuple contains the filename,
line number, function name and so on. Each list of tuples contains the truples belonging to a particular
variable.
theano.tensor.opt.encompasses_broadcastable(b1, b2)
Parameters
• b1 – The broadcastable attribute of a tensor type.
• b2 – The broadcastable attribute of a tensor type.
Returns True if the broadcastable patterns b1 and b2 are such that b2 is broadcasted to
b1’s shape and not the opposite.
Return type bool
theano.tensor.opt.get_clients(node)
Used by erf/erfc opt to track less frequent op.
theano.tensor.opt.get_clients2(node)
Used by erf/erfc opt to track less frequent op.
theano.tensor.opt.in2out(*local_opts, **kwargs)
WRITEME
theano.tensor.opt.inplace_elemwise_optimizer_op(OP)
We parametrise it to make it work for Elemwise and GpuElemwise op.
theano.tensor.opt.is_inverse_pair(node_op, prev_op, inv_pair)
Given two consecutive operations, check if they are the provided pair of inverse functions.
theano.tensor.opt.local_add_mul_fusion(node)
Fuse consecutive add or mul in one such node with more inputs.
It is better to fuse add/mul that way then in a Composite node as this make the inner graph of the
Compiste smaller. This allow to put more computation in a Composite before hitting the max recusion
limit when pickling Composite.
theano.tensor.opt.local_elemwise_fusion(node)
As part of specialization, we fuse two consecutive elemwise Ops of the same shape.
For mixed dtype, we let the Composite op do the cast. It lets the C compiler do the cast. The number
of dimensions is validated at call time by theano itself.
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theano.tensor.opt.local_elemwise_fusion_op(OP,
max_input_fct=<function
<lambda>>, maker=None)
We parametrize it to make it work for Elemwise and GpuElemwise op.
Parameters
• OP – GpuElemwise or Elemwise class (the one that we want to fuse)
• max_input_fct – A function that returns the maximum number of inputs that
this elemwise can take (useful for GpuElemwise). GPU kernel currently has a
limit of 256 bytes for the size of all parameters passed to it. As currently we
pass many information only by parameter, we must limit how many ops we fuse
together to avoid busting that 256 limit.
On the CPU we limit to 32 input variables since that is the maximum numpy
support.
theano.tensor.opt.merge_two_slices(slice1, len1, slice2, len2)
This function merges two slices into a single slice. The code works on the assumption that:
1.slice1 is actually a slice and not an index, while slice2 can be just an index.
2.the two slices have been applied consecutively on the same tensor
The output slice is not in canonical form, but actually just a slice that can be applied to a tensor to
produce the same output as applying the two consecutive slices. len1 is the length of the tensor
before applying the first slice, while len2 is the length after applying the first slice.
theano.tensor.opt.out2in(*local_opts, **kwargs)
WRITEME
theano.tensor.opt.scalarconsts_rest(inputs)
Partition a list of variables into two kinds: scalar constants, and the rest.
tensor.slinalg – Linear Algebra Ops Using Scipy
Note: This module is not imported by default. You need to import it to use it.
API
class theano.tensor.slinalg.Cholesky(lower=True)
Return a triangular matrix square root of positive semi-definite x.
L = cholesky(X, lower=True) implies dot(L, L.T) == X.
class theano.tensor.slinalg.CholeskyGrad(lower=True)
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perform(node, inputs, outputs)
Implements the “reverse-mode” gradient1 for the Cholesky factorization of a positive-definite
matrix.
References
class theano.tensor.slinalg.Eigvalsh(lower=True)
Generalized eigenvalues of a Hermitian positive definite eigensystem.
class theano.tensor.slinalg.EigvalshGrad(lower=True)
Gradient of generalized eigenvalues of a Hermitian positive definite eigensystem.
class theano.tensor.slinalg.Expm(use_c_code=’/usr/bin/g++’)
Compute the matrix exponential of a square array.
class theano.tensor.slinalg.ExpmGrad(use_c_code=’/usr/bin/g++’)
Gradient of the matrix exponential of a square array.
class theano.tensor.slinalg.Solve(A_structure=’general’,
lower=False,
write_A=False, overwrite_b=False)
Solve a system of linear equations.
over-
theano.tensor.slinalg.kron(a, b)
Kronecker product.
Same as scipy.linalg.kron(a, b).
Parameters
• a (array_like) –
• b (array_like) –
Returns
Return type array_like with a.ndim + b.ndim - 2 dimensions
Notes
numpy.kron(a, b) != scipy.linalg.kron(a, b)! They don’t have the same shape and order when a.ndim
!= b.ndim != 2.
tensor.nlinalg – Linear Algebra Ops Using Numpy
Note: This module is not imported by default. You need to import it to use it.
1
S. P. Smith. “Differentiation of the Cholesky Algorithm”. Journal of Computational and Graphical Statistics, Vol. 4, No. 2
(Jun.,1995), pp. 134-147 http://www.jstor.org/stable/1390762
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API
class theano.tensor.nlinalg.AllocDiag(use_c_code=’/usr/bin/g++’)
Allocates a square matrix with the given vector as its diagonal.
class theano.tensor.nlinalg.Det(use_c_code=’/usr/bin/g++’)
Matrix determinant. Input should be a square matrix.
class theano.tensor.nlinalg.Eig(use_c_code=’/usr/bin/g++’)
Compute the eigenvalues and right eigenvectors of a square array.
class theano.tensor.nlinalg.Eigh(UPLO=’L’)
Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix.
grad(inputs, g_outputs)
The gradient function should return
(︃
∑︁
𝑛
𝜕 𝑤𝑛 ∑︁
𝜕 𝑣𝑛𝑘
𝑊𝑛
+
𝑉𝑛𝑘
𝜕𝑎𝑖𝑗
𝜕𝑎𝑖𝑗
)︃
,
𝑘
where [𝑊 , 𝑉 ] corresponds to g_outputs, 𝑎 to inputs, and (𝑤, 𝑣) = eig(𝑎).
Analytic formulae for eigensystem gradients are well-known in perturbation theory:
𝜕 𝑤𝑛
= 𝑣𝑖𝑛 𝑣𝑗𝑛
𝜕𝑎𝑖𝑗
∑︁ 𝑣𝑘𝑚 𝑣𝑗𝑛
𝜕 𝑣𝑘𝑛
=
𝜕𝑎𝑖𝑗
𝑤𝑛 − 𝑤𝑚
𝑚̸=𝑛
class theano.tensor.nlinalg.EighGrad(UPLO=’L’)
Gradient of an eigensystem of a Hermitian matrix.
perform(node, inputs, outputs)
Implements the “reverse-mode” gradient for the eigensystem of a square matrix.
class theano.tensor.nlinalg.ExtractDiag(view=False)
Return the diagonal of a matrix.
Notes
Works on the GPU.
perform(node, ins, outs)
For some reason numpy.diag(x) is really slow, so we implemented our own.
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class theano.tensor.nlinalg.MatrixInverse
Computes the inverse of a matrix 𝐴.
Given a square matrix 𝐴, matrix_inverse returns a square matrix 𝐴𝑖𝑛𝑣 such that the dot product
𝐴 · 𝐴𝑖𝑛𝑣 and 𝐴𝑖𝑛𝑣 · 𝐴 equals the identity matrix 𝐼.
Notes
When possible, the call to this op will be optimized to the call of solve.
R_op(inputs, eval_points)
The gradient function should return
𝜕𝑋 −1
𝑉,
𝜕𝑋
where 𝑉 corresponds to g_outputs and 𝑋 to inputs. Using the matrix cookbook, one can
deduce that the relation corresponds to
𝑋 −1 · 𝑉 · 𝑋 −1 .
grad(inputs, g_outputs)
The gradient function should return
𝑉
𝜕𝑋 −1
,
𝜕𝑋
where 𝑉 corresponds to g_outputs and 𝑋 to inputs. Using the matrix cookbook, one can
deduce that the relation corresponds to
(𝑋 −1 · 𝑉 𝑇 · 𝑋 −1 )𝑇 .
class theano.tensor.nlinalg.MatrixPinv
Computes the pseudo-inverse of a matrix 𝐴.
The pseudo-inverse of a matrix 𝐴, denoted 𝐴+ , is defined as: “the matrix that ‘solves’ [the leastsquares problem] 𝐴𝑥 = 𝑏,” i.e., if 𝑥
¯ is said solution, then 𝐴+ is that matrix such that 𝑥
¯ = 𝐴+ 𝑏.
Note that 𝐴𝑥 = 𝐴𝐴+ 𝑏, so 𝐴𝐴+ is close to the identity matrix. This method is not faster than
matrix_inverse. Its strength comes from that it works for non-square matrices. If you have a square
matrix though, matrix_inverse can be both more exact and faster to compute. Also this op does not
get optimized into a solve op.
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class theano.tensor.nlinalg.QRFull(mode)
Full QR Decomposition.
Computes the QR decompos