Neuromorphic Implementation of Orientation Hypercolumns

Neuromorphic Implementation of Orientation Hypercolumns
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 6, JUNE 2005
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Neuromorphic Implementation of
Orientation Hypercolumns
Thomas Yu Wing Choi, Paul A. Merolla, John V. Arthur, Kwabena A. Boahen, and Bertram E. Shi
Abstract—Neurons in the mammalian primary visual cortex
are selective along multiple stimulus dimensions, including retinal
position, spatial frequency, and orientation. Neurons tuned to different stimulus features but the same retinal position are grouped
into retinotopic arrays of hypercolumns. This paper describes
a neuromorphic implementation of orientation hypercolumns,
which consists of a single silicon retina feeding multiple chips,
each of which contains an array of neurons tuned to the same
orientation and spatial frequency, but different retinal locations.
All chips operate in continuous time, and communicate with each
other using spikes transmitted by the address-event representation protocol. This system is modular in the sense that orientation
coverage can be increased simply by adding more chips, and
expandable in the sense that its output can be used to construct
neurons tuned to other stimulus dimensions. We present measured
results from the system, demonstrating neuronal selectivity along
position, spatial frequency and orientation. We also demonstrate
that the system supports recurrent feedback between neurons
within one hypercolumn, even though they reside on different
chips. The measured results from the system are in excellent
concordance with theoretical predictions.
Index Terms—Address-event representation (AER), Gabor
filter, image processing, mixed analog–digital integrated circuits,
neural chips, neuromorphic engineering, visual cortex.
I. INTRODUCTION
N
EUROMORPHIC engineering is the design and construction of systems that replicate the capabilities of biological systems, as well as their advantages, such as robustness and
power efficiency by mimicking both functional and structural
characteristics of biological systems [1].
We describe here a neuromorphic multichip implementation
of orientation hypercolumns in the mammalian primary visual
cortex (V1). In their “ice-cube” model, illustrated in Fig. 1(a),
Hubel and Wiesel suggested that the visual cortex can be
thought of as a two-dimensional (2-D) sheet with limited extent
in depth [4]. At any point on this sheet, all of the neurons are
tuned to the same orientation and location regardless of depth.
An orientation tuned neuron’s response to a bar is strongest
when it is located at a preferred retinal location and with a
preferred orientation, and weakens as the bar is moved or
Manuscript received April 8, 2004; revised September 22, 2004. This work
was supported by the Hong Kong Research Grants Council under Grant
HKUST6218/01E and by the National Science Foundation under CAREER
Grant ECS00-93851. This paper was recommended by Associate Editor G.
Cauwenberghs.
T. Y. W. Choi and B. E. Shi are with the Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hong
Kong (e-mail: [email protected]).
P. Merolla, J. Arthur, and K. Boahen are with the Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104-6392 USA.
Digital Object Identifier 10.1109/TCSI.2005.849136
Fig. 1. (a) The “ice-cube” model of the visual cortex. Hypercolumns are
divided by thick lines and subdivided by thin lines into columns of neurons
tuned to different orientations as indicated by the oriented bars. (b) The
multichip architecture used to implement the ice-cube model. Each layer
represents one chip containing neurons tuned to the same orientation but
different retinal positions. Vertically aligned neurons receive inputs from the
same retinal locations.
rotated. Neurons tuned to the same orientation and retinal
location are grouped into columns, which are depicted as cubes
in Fig. 1(a). Neighboring columns that serve the same retinal
location, but with different preferred orientations, are grouped
into hypercolumns. Bold lines in Fig. 1(a) represent divisions
between hypercolumns. These hypercolumns are arranged
retinotopically, with neighboring hypercolumns serving neighboring retinal locations.
This work is an initial step in the construction of a neuromorphic system containing retinotopic arrays of continuous-time
spiking silicon neurons exhibiting the same multidimensional
stimulus selectivity observed in visual cortical neurons. Neurons in V1 are selective along the dimensions of retinal position,
spatial frequency, temporal frequency, color, orientation, direction of motion, and binocular disparity [2]. Our goals in constructing this system are both to investigate hypotheses about
the way biological system fuse information from different visual cues into a coherent perception of the environment, and to
build biologically inspired systems for artificial perception. Our
system operates in continuous-time to facilitate the incorporation of feedback interconnections between neurons, which appear to be critical for perception [3].
We have started by constructing orientation-tuned neurons
because orientation selectivity is one of the predominant distinguishing characteristics of neurons in V1 [4]. Due to the processing by the retina, the input to cortex is already selective
along the dimensions of retinal position, spatial frequency, temporal frequency, and color. In addition, selectivity along other
stimulus dimensions commonly associated with V1, such as direction of motion and binocular disparity, can be obtained by
combining the outputs of orientation-tuned neurons [5]–[7].
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Our system, illustrated in Fig. 1(b), consists of a number of
silicon chips. Each chip, called a Gabor chip, contains a 2-D
array of silicon neurons, which are arranged retinotopically.
However, unlike the biological cortex, all of the neurons in
one chip have the same preferred orientation. To cover the
orientation dimension, we use different chips, each containing
neurons tuned to different orientations. Each chip in the system
processes signals internally pixel-parallel and in continuous
time using a combination of analog and asynchronous digital
processing circuits. The chips interact with each other by
spike-encoded inputs and outputs, which are communicated
using the digital asynchronous address-event representation
(AER) communication protocol [8]–[10].
We have previously described the circuit design of the Gabor
chips used in this system, and characterized their operation in
isolation with test input provided by a pattern generator [11].
This paper extends that work in several important directions.
First, it describes experimental measurements of the output of
the Gabor chips with optical input provided through a separate silicon retina chip. Second, it characterizes experimentally
the operation of reconfigurable multichip systems of two to five
chips linked by point-to-point AER routing circuits included in
each chip. Third, it demonstrates experimentally that the AER
protocol can be used effectively to implement continuous time
feedback interactions between large arrays of spiking neurons
on different chips.
This approach has several advantages over previous approaches to implementing orientation selectivity.
First, orientation resolution and spatial resolution can be
controlled independently. Orientation resolution (the number
of different orientation tuned neurons serving the same retinal
location) can be increased by adding more Gabor chips. Spatial
resolution (the number of retinal locations processed) can be
increased by tiling more processing pixels in each chip. Since
each neuron has the same orientation selectivity, its structure
is identical to the other neurons on the chip, except for an
offset due to the difference in the retinal position. In contrast,
approaches that follow the ice-cube model by allocating different
regions of silicon to different retinal locations and then further
subdividing these regions for different orientations [12], [13],
must trade off orientation resolution and spatial resolution.
Although placing neurons tuned to different orientations on
the same chip facilitates feedback interactions between them,
we demonstrate here that our approach also supports such
feedback interactions. However, the amount of interaction is
limited by inter-chip bandwidth, which is slower and costlier
in power than intra-chip bandwidth.
Second, the approach is expandable to include selectivity
along more stimulus dimensions. We can combine the spatial
filtering of these chips with temporal filtering to obtain velocity
and direction tuned neurons [14] or combine the outputs of two
chips processing left and right eye inputs to obtain binocular
disparity tuned neurons [15]. Another approach to computing
multiple feature maps is to time multiplex the same processing
circuits and store the results of different maps in local pixel
memories, as adopted by the Cellular Neural Network Universal Machine [16] or the computation on readout architecture
[17]. However, multiplexing the computation of different
feature maps in time makes it impossible to incorporate continuous-time recurrent interconnections between neurons with
different stimulus selectivity.
Our approach is most similar to those reported by Serrano–Gotarredona et al. [18] and Venier et al. [19]. It differs
primarily in the orientation selective receptive fields of the
neurons, and in that we have been able to demonstrate feedback
interactions between neurons tuned to different orientations
experimentally. The approach proposed in [18] can implement
only spatial filters with separable convolution kernels. Therefore, only horizontal or vertical orientation selectivity could be
implemented. The system reported in [19] implements neurons
with purely excitatory and even symmetric RF profiles. Thus,
it cannot implement pairs of neurons with phase quadrature
Gabor-like receptive fields.
The above discussion focused on architectures that are orientation selective, i.e., their responses vary according to the difference between the input orientation and a preferred orientation.
Very large-scale integration (VLSI) architectures that measure
feature orientation have also been proposed [20], [21]. However, we do not discuss them here, as the computations are quite
different. For example, measurement assumes that each image
point has a unique orientation. However, an orientation-selective architecture can support multiple orientation hypotheses at
each point, e.g., the junction of two oriented edges.
In the following, Section II describes our multichip architecture. Section III gives measured results from our system demonstrating selectivity along three stimulus dimensions associated
with V1: retinal position, spatial frequency, and orientation. We
also demonstrate that our system supports recurrent interactions
between neurons. Finally, Section IV concludes with summary
and a description of the next steps in incorporating additional
cortical functionality into this system.
II. MULTICHIP ARCHITECTURE
This section describes both a feedforward implementation of
orientation hypercolumns, where the Gabor chips operate independently, and a feedback implementation, where the Gabor
chips interact with each other.
Fig. 2(a) shows the block diagram of the feedforward implementation. The output of a silicon retina chip is fanned out
to several Gabor chips. Fig. 2(b) shows a photograph of the
feedforward system. Each Gabor chip is mounted on a separate
printed circuit board, which also holds the circuits required to
bias it. Each Gabor board dissipates 44 mW at 3 Kspike/s. Most
mW
% of the power consumption on the board is
due to circuits that supply constant bias voltages to the chip and
that power light emitting diodes (LEDs) that are used as status
indicators.
The silicon retina, which is described in [22], [23], contains
a 60 96 array of phototransistors and processing circuits that
generate spike outputs that mimic the responses of ON-sustained
and OFF-sustained retinal ganglion cells at a 30 48 array of
retinal positions. ON and OFF neurons encode positive and negative contrasts relative to the local background intensity. Sustained retinal ganglion cells respond to inputs that vary slowly
in time.
CHOI et al.: NEUROMORPHIC IMPLEMENTATION OF ORIENTATION HYPERCOLUMNS
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Fig. 2. (a) Feedforward implementation of orientation selective hypercolumns. Each box with the double line border represents a chip containing a retinotopic
array of neurons. Gabor chips are represented by the larger boxes with the dark bar indicating the tuned orientation of the neurons on the chip. Boxes with single
line borders indicate circuits that manipulate AER encoded spike trains. The “flip image” circuit remaps spike addresses to flip the input and output images of the
fourth chip horizontally, resulting in neurons tuned to 135 . The chip select circuits pass only spikes originating from a desired chip. (b) Photo of the feedforward
implementation. The silicon retina and Gabor chips are mounted on separate printed circuit boards with biasing circuits. The display board connects to a VGA
monitor (not shown) for visualizing the chip outputs. The logic analyzer collects spikes for analysis. (c) Feedback implementation. The “flip ON/OFF” circuit inverts
the image passing through it by mapping ON spikes to OFF spikes and vice versa. The missing bar in the right-most chip indicates that its spatial filtering is disabled.
Each Gabor chip can process ON and OFF spike input from a
32 64 array of retinal positions [11]. Each retinal position has
four neurons associated with it. Each of those neurons computes
a weighted sum of the spike rates from the ON and OFF ganglion
cells in a small neighborhood of that retinal position, half-wave
rectifies it, and encodes the result as an output spike rate. We
refer to the weighting function used in the sum as the neurons
receptive field (RF) profile. The four neurons are denoted by
EVEN-ON, EVEN-OFF, ODD-ON, and ODD-OFF, and differ according
to their RF symmetry (EVEN-ODD) and polarity (ON-OFF). The
ON and OFF neurons encode the positive and negative half-wave
rectified sums.
The RF symmetry with respect to the origin is determined by
a phase parameter . Each neuron’s RF profile is a Gabor-like
function given by
(1)
where
and
denote the horizontal and vertical distance
from the neuron’s position. The parameters
, and are
(described
real valued constants. Because the function
below) is even symmetric with respect to the origin, the RF is
EVEN symmetric if
and ODD symmetric if
.
When presented with a sine wave grating, the neurons will
respond maximally to a grating with spatial frequency
, orientation
and phase offset .
Vertical orientations correspond to
. The spatial frequency
bandwidth is determined by the function
, whose Fourier
transform is given by
where
, and
are positive constants. The paramcontrols the gain of the neuron. The parameters
eter
and
control the spatial frequency bandwidth in the and
directions. Although we do not have an exact closed form ex, we know that it decays with distance from
pression for
the origin and that the decay can be approximated by a zeroth
order Bessel function of the second kind [24]. The parameters,
, and
, are controllable via external bias
voltages applied to the chip.
The neurons in our system capture many of the important
characteristics of orientation tuned cortical neurons. The model
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 6, JUNE 2005
of linear filtering followed by nonlinearity has been shown to
account for the responses of a large proportion of V1 neurons
[25]–[27]. The receptive field profile (1) has the same form as
the Gabor functions commonly used to model orientation selective cortical neurons [28], [29], except that the modulating
is not Gaussian. Pairs of EVEN and ODD neufunction
rons are critical in energy models of cortical function, and have
been observed in cortex [30].
In contrast to conventional digital image processing systems
where array readout is synchronized according to a pre-defined
frame rate, output spike activity in our system is asynchronous.
Each neuron in the array determines the time of its next spike
output based upon the array’s input and its last spike time. Neurons operate in continuous time and are free to generate a spike
at any time. There is no clock synchronizing the activity in the
array or its readout. Because the output activity depends upon
the input activity, there is no well defined “frame” during which
all neurons are read out.
We use the AER protocol [8]–[10] to communicate spike
activity between chips. An AER link consists of a transmitter
and a receiver connected by asynchronous digital lines. The
transmitter signals that a neuron has spiked by sending an
address event: a sequence of binary words identifying the
spatial location (address) of the spiking neuron. Each spike
is specified by three words that identify the chip, row and
column that the spiking neuron resides in. The spike time is
not encoded explicitly, but is taken to be the time at which the
address event appears on the link. Simultaneous spikes from
neurons in the same row and the same chip are transmitted
in a single burst, which consists of the chip address, the row
address, followed by the column addresses of the neurons that
spiked. Simultaneous spikes from different rows are sequenced
by arbitration. Since link bandwidth is allocated to the most
active neurons, AER is more efficient than scanning when spike
activity is sparse [31]. The Appendix describes the word-serial
protocol we use, as well as the way in which the four types
of neurons are addressed.
Since all spikes from one chip are transmitted via the same
digital link, the total spike rate in the array is limited by the
time which it takes to transmit one address event, which we
measured to be
ns. Subsequent events encoded in
the same burst require only
ns. For low loads where
each burst contains only one address event, the link capacity
million spikes per second. The link capacity
is
in burst-mode is
million spikes per second. This
burst rate does not indicate the true performance of the inter-chip
links, as latches were interspersed between chips to correct for
a design error in the communication protocol circuits.
Our architecture routes spikes between chips using point-topoint links, rather than a global bus connecting a number of
transmitters and receivers. This avoids the need for complex circuits that control bus access and perform routing. Instead, we
use two basic routing circuits, the split and the merge, which
are included in each Gabor chip, and determine spike routing
by the way that we link the chips together. Using this approach,
routing circuit complexity expands automatically to accommodate the number of chips in the system. In addition, unique chip
addresses are generated and updated automatically by the split
and merge circuits, so that we can distinguish spikes from different chips in one AER address stream. The implementation of
this network architecture will be described in detail in a forthcoming publication.
The split circuit makes two copies of the AER events appearing at its input. One copy is sent into the neuron array
through a decoder that reads the originating address of the each
spike and sends a spike to the neuron with the same row and
column address, irrespective of the chip address. The other
copy has its chip address incremented by one and is sent off
chip via a transmitter.
Our system uses the split circuit for signal fan out. By daisy
chaining the Gabor chips by connecting the split output of one
with the split input of the next, we can distribute the same silicon
retina output to all chips.
The merge circuit combines the address events at its input
with address events generated by the neuron array and sends
them off chip via a transmitter. Collisions between events at the
input and the neuron array are handled by arbitration. Events
coming from the neuron array are assigned a chip address of
zero. Events coming from the input have their chip address incremented by one.
In our system, we use the merge circuits to collect the activity
from all of the chips in the system, by daisy chaining the merge
output of one chip with the merge input of the next. The merge
output of each chip encodes all of the spike activity in the chips
up to that point in the chain. Because it increments the chip address of input events, the merge circuit enables us to distinguish
spikes originating in different chips. The “chip select” circuit is
a filter that passes only spikes from a desired chip.
To minimize pixel size, we designed the Gabor chips so that
they can only be tuned to orientations between 0 and 90 .
However, the system can contain neurons tuned to orientations
greater than 90 , since the AER protocol makes it easy to
flip images horizontally and/or vertically before and after
processing. The Appendix describes the design of the “Flip
Image” circuit.
Fig. 2(c) shows the block diagram of the feedback implementation of orientation hypercolumns. Each neuron on each
Gabor chip is driven by a residual signal, which is the difference
between the input from the silicon retina at its corresponding
retinal location and the sum across orientation of the outputs
of all the Gabor neurons serving the same retinal location with
the same polarity and RF symmetry. The feedback system uses
the merge and split circuits as well as a “combination chip” to
compute the residual signal. The system first computes the inverted sum of the outputs of the Gabor chips, and then sums the
input from the silicon retina with the inverted sum to compute
the difference.
To compute the inverted sum across orientation, the system
first collects the output spike activity from all of the Gabor chips
at the input to the “flip ON/OFF” circuit by cascading the Gabor
chips’ merge circuits as in the feedforward system. The “flip
ON/OFF” circuit, whose design is described in the Appendix, inverts the polarity of the Gabor chips’ outputs by mapping ON
spikes to OFF spikes and vice versa. The output of the “flip
ON/OFF” circuit is fed to the split input of the combination chip,
which sums the spike activity. The combination chip is simply
CHOI et al.: NEUROMORPHIC IMPLEMENTATION OF ORIENTATION HYPERCOLUMNS
a Gabor chip with its spatial filtering disabled. Its neurons integrate spikes corresponding to the same retinal location, polarity
and symmetry but irrespective of orientation, since the decoder
sends all spikes received at the split input into the neuron array
irrespective of the chip address. For each retinal position and
RF symmetry, the output spike rates of the ON and OFF neurons
are approximately proportional to the half wave rectified differences between their input spike rates.
The combination chip’s merge circuit combines the input
spike activity from the silicon retina with the output of the
combination chip, which represents the inverted sum of the
Gabor chips’ outputs. These spikes are distributed to each of
the Gabor chips by cascading the split circuits as in the feedforward system. Although spikes from the silicon retina and the
combination chip can be distinguished by their chip addresses,
they are summed by the Gabor chips since the decoder ignores
the chip addresses when routing spikes from the split input into
the neuron array.
Intuitively, the net effect of this feedback connectivity is that
the system automatically adjusts the Gabor chip outputs so that
their sum at each location best fits the input from the silicon
retina at that location. The residual measures the quality of the
fit. If the residual has a large component near the tuned orientation of Gabor chip, that chip increases its response since
the residual signal is fed into its input. The interaction between
neurons tuned to different orientations is inhibitory, since if the
neurons tuned to one orientation are providing a good fit to the
input, they decrease the input to neurons tuned to other orientations. The extensive feedback interconnectivity in this system
might raise concern about its stability. However, we have not observed any unstable or oscillatory behavior in our experiments.
In addition, it is possible to prove that a similar system where
the spiking interactions are replaced by graded interactions is
stable, since its dynamics can be characterized as gradient descent on a Lyapunov function similar to that presented in [33].
III. EXPERIMENTAL RESULTS
This section describes experimental measurements from both
the feedforward and feedback implementations of the orientation selective hypercolumns. We demonstrate the position, spatial frequency, and orientation selectivity of the neurons using
the feedforward system. In the feedback system, we focus on the
effect of the competitive interactions on the orientation tuning,
which is the primary difference in the response characteristics
of neurons in the two systems.
A. Feedforward System
We tuned the four Gabor-type chips in the feedforward
system to similar spatial frequencies and bandwidths, but different orientations 0 , 45 , 90 , and 135 , with 135 achieved
by tuning the chip to 45 and then flipping the input and output
images horizontally. In total, this system contains 32 768 orientation tuned neurons tuned to four orientations, two spatial
phases, two polarities (ON/OFF) and 32 64 retinal positions.
Including the retina, the system contains 35 648 spiking neu, and
rons. We estimated the tuning parameters
for each chip by applying a spatial impulse input to the
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TABLE I
TUNING PARAMETERS ESTIMATED VIA IMPULSE RESPONSE FITTING
center pixel using a pattern generator and measuring the output
across the array, and finding the parameters that minimized the
squared error between the measured and theoretically predicted
responses (Table I). This estimation assumes the tuning parameters of the neurons are identical. In fact, the tuning parameters
vary from neuron to neuron due to transistor mismatch, with
different parameters exhibiting different amounts of variability
[15].
Fig. 3 shows the responses of the neurons in response to a
dark ring on a bright background. Neurons from different chips
respond to parts of the ring, depending on where their tuned
orientation match the ring’s. The ODD neurons are more sharply
tuned in orientation than the EVEN neurons. We used a 4 mm
lens to focus images onto the surface of the silicon retina, and
presented visual stimuli to the system using an liquid crystal
display (LCD) monitor placed 25 cm away. Transistor mismatch
adds variation in the neural responses across position, due to
changes in the gain, tuning, and background firing rates of the
neurons [11], [15].
To evaluate spatial frequency and orientation tuning of the
neurons, we presented the system with Gabor patches with a
constant circularly symmetric Gaussian envelope but varying
orientation and spatial frequency. To avoid edge effects, we ensured that the Gabor patch was confined within the field of view
of the retina by choosing the standard deviation of the Gaussian
to span 5.4 of visual angle, which corresponded to the spacing
between the receptive field centers of 8.4 SUSTAINED cells in
the silicon retina. Fig. 4 shows images of Gabor patches plotted
with examples of the parameters used.
To evaluate the spatial frequency tuning of the system, we
varied the spatial frequency of the Gabor patch while keeping
the orientation constant at 90 and monitored the response of
the array tuned to 90 . By measuring the total spike rate from
all neurons irrespective of retinal position, RF symmetry and
polarity, we eliminate the dependency of the response on the
spatial phase of the stimulus, leaving only the dependency on
the spatial frequency. For each spatial frequency, we measured
the spike times of 600 spikes from the chip to compute the
spike rate. Fig. 5 shows the population response of the retinal
neurons and the orientation-tuned neurons plotted versus spatial frequency. The spatial frequency that gave the greatest response was 0.6 radians/pixel, which agrees with the results from
the impulse response fitting. This spatial frequency corresponds
to 0.16 cycles per degree of visual angle. Much of the spatial
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Fig. 3. Responses of e feedforward system to a black ring. Image on the left shows the output of the silicon retina. Each image position represents one retinal
position in the upper-left 30 30 corner of the array. The image intensity encodes the difference between the spike rates of the ON and OFF neurons at each position.
The eight remaining images show the outputs of the EVEN (top row) and ODD (bottom row) neurons on the Gabor chips. For the EVEN responses, black corresponds
Hz. White corresponds to differential spike greater than or equal to
Hz. The mean absolute differential
to differential spike rates less than or equal to
Hz. White corresponds to differential spike
spike rate is 10.8 Hz. For the ODD responses, black corresponds to differential spike rates less than or equal to
greater than or equal to
Hz. The mean absolute differential spike rate is 4.4 Hz.
2
040
+40
080
+40
Fig. 4. Examples of the Gabor patches used to characterize the system responses to orientation and spatial frequency. (a) Gabor patch with orientation 90 that
projects onto the retina with the optimal spatial frequency of 0.6 radians/pixel. The black rectangle delimits the visual field of the silicon retina. The black circle
delimits the receptive field of one V1 neuron. (b) Gabor patch with orientation 90 and spatial frequency 0.9 radians/pixel. (c) Gabor patch with orientation 45
spatial frequency 0.6 radians/pixel.
Fig. 5. Spatial frequency tuning of the neurons in the retina (x) and the Gabor
chip (o). To facilitate comparison, both curves are normalized by the peak
population spike rate.
frequency selectivity is due to bandpass filtering by the retina,
which is tuned to the same spatial frequencies as the orientation
tuned neurons, but is not orientation selective.
To characterize the orientation tuning of the neurons, we
fixed the spatial frequency of the Gabor patches at 0.6 radians/pixel, which yielded the maximum response in the
previous experiment, and varied the orientations from 0 to
180 in steps of 11.25 . Because we used stationary gratings,
orientations greater than or equal to 180 are equivalent to
orientations less than 180 . Fig. 6 shows the measured population responses from the EVEN and ODD neurons, which were
obtained by summing the responses from all neurons with the
same RF symmetry on each chip, irrespective of retinal position
or polarity. The polar plots show that neurons on different chips
are tuned to respond maximally to different orientations, and
that the ODD neurons are more sharply tuned in orientation than
the EVEN neurons.
Fig. 6 also compares the measured data with the theoretical
predictions. The equations used to generate the theoretical fits
are given in the Appendix. We assumed that the spatial frequency of the input sine wave gratings and the spatial frequency
tuning of all the chips was 0.6 radians/pixel, and that the neurons were tuned to orientations 0 , 45 , 90 , and 135 exactly.
and that they were identical
We also assumed that
in all chips. We estimated the common value to be 0.61 radians
per pixel by a least squares fit to the measured data. This estimated value is slightly larger than the value predicted by the
impulse response fits, primarily because the Gabor patches used
in the experimental characterization are spatially localized, and
therefore have broader spatial frequency content than the sine
wave grating assumed in the theoretical analysis. Although it
is possible to predict the responses to Gabor patches numerically, we do not do so here because the assumption of sine wave
grating inputs matches the measured responses quite closely and
gives a convenient closed form expression. Other contributing
factors include the fact that the impulse response data was measured by stimulating a single pixel, which is not an accurate
measure of the average tuning across the neurons in the array
due to transistor mismatch, as well as the additional spatial filtering performed by the silicon retina.
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Fig. 6. Orientation tuning of the feedforward system. Polar plots show the total spike rate from all neurons with the same RF symmetry from one chip. For
each point, the angle represents the input orientation and the distance from the origin represents the total spike rate in kilohertz minus the background spike rate
measured in response to a blank screen. Top row shows the response of the EVEN neurons. Bottom row shows the response of the ODD neurons. Each column shows
responses from a different chip. Discrete data points x indicate measured data. Solid lines show the theoretical fit. Labels at the top of each column indicate the
target uncoupled tuning. Label below each graph indicates the preferred orientation computed from the measured data.
TABLE II
SYSTEM CHARACTERISTICS
For each RF symmetry, we evaluated the quality of the theoretical fits using a goodness of fit index defined by
%
where is the observed response (in spikes per second) and
is the theoretically predicted response for measurement . The
summation is taken over all input orientations and over all chips.
%.
A perfect fit gives
The goodness of fit indexes for all of the systems are given in
Table II, which summarizes the system characteristics. In general, the fit between the predicted and measured responses from
the ODD neurons is worse than the fit for the EVEN neurons. The
degradation is largely due to the fact that the theory predicts zero
response to orthogonal orientations, which is not the case for the
measurements.
We define the preferred orientation (PO) of an orientation
where is the resultant [34]
tuning curve to be
(2)
and is the response to the input orientation . We double
in the complex exponential and subsequently halve the angle of
to take into account the fact that orientations that differ by
180 are equivalent. The preferred orientation computed from
the measured data and theoretical fit, which are given in Fig. 6,
are in good concordance with the target tuning.
Fig. 7. Orientation tuning of the self-coupled system. Polar plots generated as
in Fig. 6. Label below each graph indicates the preferred orientation computed
from the measured data.
B. Feedback System
We characterized several different configurations of the feedback system, which varied in the number of Gabor chips coupled
together. In the following, we refer to the responses of the
neurons in the feedforward system as uncoupled, and the responses of the neurons in the feedback system as coupled. The
simplest feedback system, which we refer to as self-coupled,
contains one Gabor chip coupled back to itself through the
combination chip. The next level of complexity couples two
Gabor chips tuned to different orientations, where the inhibitory
feedback shifts the orientation tuning curves for the two sets
of neurons away from each other. Finally, we characterized a
system with three Gabor chips. These experiments used the
same bias voltages to set the uncoupled tuning parameters as
used in the feedforward experiments.
We characterized the self-coupled system for the Gabor chips
tuned to orientations of 0, 45 , and 90 with the same bias
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 6, JUNE 2005
Fig. 8. Orientation tuning with two coupled orientations. Polar plots generated as in Fig. 6. Label below each graph indicates the preferred orientation computed
from the measured data and predicted theoretically (in parenthesis).
voltages as used in the feedforward system. Fig. 7 shows the
polar plots of the measured response and theoretical fit. The
experimental measurements were performed using the same
protocol as for the feedforward system. The theoretical fit was
obtained using the equations described in the Appendix, where
we model the feedback as linear with a gain , which we
estimated to be 0.41 by a least squares fit to the experimental
measurements. The remaining parameters were the same as
used to fit the responses of the feedforward system.
The primary difference between the responses of the neurons
in the feedforward and self-coupled system is a reduction in the
responses of the neurons of the self-coupled system. In the selfcoupled system, each neurons output is inverted and fed back
to its own input. Thus, each neuron inhibits itself, accounting
for the reduced response. There is no significant change in the
preferred orientation or the sharpness of the orientation tuning.
To characterize the two Gabor chip system, we fixed the
uncoupled tuning of one Gabor chip at 45 , and coupled it with
a second chip tuned to 0 or 90 . We measured orientation
tuning using the same protocol as our previous experiments. In
the following, we refer to the chips and the neurons according
to their uncoupled tunings. Fig. 8 shows the orientation tuning
curves and preferred orientations obtained. The theoretical
predictions are based upon the parameters estimated in our
previous experiments, and therefore are true predictions of the
effect of feedback.
Comparing the 45 neurons in the two cases (the two center
columns), we observe that their preferred orientations shift toward higher orientations when they are coupled with 0 tuned
neurons, and toward lower orientations when coupled with 90
tuned neurons. Similarly, we observe that the preferred orientation of the 0 neurons (the first column) shifts toward negative
orientations. The preferred orientation of the 90 neurons (the
last column) shifts toward orientations greater than 90 .
When two sets of orientation-tuned neurons are coupled together, their tuning curves shift away from each other so that
the coupled tuning curves are more separated than the uncoupled tuning curves. Intuitively, consider two neurons, labeled 1
Fig. 9. Orientation tuning with three coupled orientations, 0 , 45 , and
90 . Polar plots generated as in Fig. 6. The label below each graph indicates
the preferred orientation computed from the measured data and predicted
theoretically (in parenthesis).
and 2, that respond to the same retinal region but different orientations. Feedback interactions will enhance the difference in
orientation tuning because inhibition from Neuron 2 reduces the
response of Neuron 1 to orientations that are near the preferred
orientation of Neuron 2.
Fig. 9 shows the tuning curves and preferred orientations obtained when coupling three chips with uncoupled tunings of
0 /45 /90 . As in the previous experiment, the theoretical predictions are based upon the parameters identified in the feedforward and self-coupled experiments.
In this case, the prediction is not as good as the prediction
with only two coupled orientations. In particular, the magnitude
of the response is smaller for the EVEN neurons than predicted
theoretically, resulting in a much poorer fit than observed for
the other systems. It appears that inhibition by two competing
orientations is greater than that predicted by the linear model in
the Appendix. Because we have been unable to fit the responses
CHOI et al.: NEUROMORPHIC IMPLEMENTATION OF ORIENTATION HYPERCOLUMNS
accurately by increasing the strength of the feedback factor, we
speculate that nonlinearities introduced by the spike-based communication between chips, e.g., in spike generation and leaky
integration, may be responsible for the discrepancy between the
theoretical predictions and the measured data.
The net shift in the tuning curve for the 45 neurons is close to
zero, since the shifts introduced by 0 and 90 neurons cancel.
The tuning curves of the 0 and 90 neurons shift in the same direction as in the two Gabor chip system, but by a greater amount
due to the increased inhibition on the same side of the tuned
orientation.
IV. CONCLUSION
Based upon the columnar organization of orientation selective neurons in the mammalian primary visual cortex (V1), we
have constructed a silicon system consisting of retinotopic arrays of silicon neurons whose receptive field properties closely
match those of orientation selective visual cortical neurons. The
system uses a similar ON-OFF signal representation as used in
biological neural systems to encode signals above and below a
mean value.
We have built and characterized a feedforward system where
the output of a silicon retina is fanned out to several Gabor chips
that are tuned to different orientations, but which operate independently. Our measurements from the feedforward system
demonstrate that the neurons in this system exhibits stimulus selectivity along three dimensions commonly associated with neurons in V1: retinal position, spatial frequency, and orientation.
We have also demonstrated that even though we implement
neurons that normally reside within a single hypercolumn in the
biological cortex on different chips, our system can still support
feedback interactions between them. This is a critical feature of
a neuromorphic model of cortex since much of the input to cortical cells comes from other cortical cells [35]. Our results show
that a linear model can account for over 80% of the response
of a feedback system consisting of two populations of neurons
tuned to different orientations.
In our system, inhibitory feedback shifts the orientation
tuning. In the biological cortex, similar shifts in orientation
tuning due to changes in feedback can account for changes in
neuronal response due to adaptation and learning [36]–[38].
Another hypothesized role for intracortical inhibition is to
balance local recurrent cortical excitation, leading to orientation
sharpening and contrast invariant tuning [35]. In our system,
contrast invariant tuning is achieved in a different manner, via
push-pull interactions between ON and OFF neurons similar to
those proposed in [39]. However, although our current system
does not exhibit any significant orientation sharpening, with
the exception of the measured data from the even neurons in
Fig. 9, the next generation of our system should be able to be
configured to exhibit orientation sharpening. Our theoretical
analysis indicates that the lack of orientation sharpening in
our current system is primarily because each neuron inhibits
itself, since the residual signal fed back to each neuron contains
its own output. If we eliminate this inhibitory self feedback,
the analysis in [33] predicts that the resulting system will
exhibit sharpened orientation tuning. One reason it is difficult
1057
Fig. 10. Address protocol used by the Gabor-type filter chip. A chip and
row address is followed by one or more column addresses, depending upon
how many neurons in a given row of the chip spiked simultaneously. Since
the protocol is asynchronous, the transmitter and receiver use handshaking
signals to ensure addresses are communicated correctly. Two request signals,
ReqY and ReqX, identify the start and end of each burst, and the location of
each address within the burst. Transmitter raises ReqY to signal the validity of
the chip address. Receiver acknowledges that it has read the chip address by
raising the acknowledge Ack. The transmitter then lowers ReqX to signal
the validity of the row and column addresses. Receiver acknowledges receipt
by lowering Ack. Transmitter lowers ReqY to signal the end of the burst.
to implement this type of system using our current chips is
that the decoder at the split input sends all spikes into the array
irrespective of the chip address. However, our next generation
of routing circuits will include the capability to decide whether
or not to route spikes into the neuron array depending upon the
chip address. This will facilitate the construction of a system
that does not include inhibitory self-feedback.
APPENDIX
A. Word-Serial AER Format
The Gabor chips use the 7-bit word serial format for addresses
illustrated in Fig. 10. Spikes are sent in sequences of addresses,
called bursts. The first address identifies the chip, the second address identifies the row and the remaining addresses identify the
columns containing neurons in the row that spiked. This “burst
mode” improves efficiency when there is high activity in the
array, by eliminating the time needed to send the same chip and
row addresses for each column address. Because the AER protocol is asynchronous, we use handshaking signals to ensure addresses are received properly.
Within each Gabor neuron array, ON and OFF neurons are
addressed in alternate columns, while EVEN and ODD neurons
are addressed in alternate rows. Thus, the LSB of the column
address identifies the neuron’s polarity. The LSB of the row
address identifies the receptive field symmetry. In the silicon
retina, ON and OFF neurons are also addressed in alternate
columns. SUSTAINED and TRANSIENT neurons are addressed
in alternate rows. Thus, the SUSTAINED outputs of the retina
map directly to the inputs of the EVEN neurons with the same
polarity. In the feedforward system, the ODD neurons are driven
indirectly through recurrent feedback interconnections with the
EVEN neurons on each chip. In the feedback system, they are
also driven by the ODD component of the residual signal. In this
system, we disable the TRANSIENT retina outputs, which encode
quickly varying image components.
B. Spike Remapping and Filtering Circuits
The “flip image” circuit can flip an image horizontally and/or
vertically by remapping the row and/or column addresses within
each burst. We generate a flipped row or column address by
inverting all of the bits except for the LSB, which encodes the
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 6, JUNE 2005
assuming the feedback interactions between neurons is linear.
The analysis is similar to that in [33], but differs because the
residual signal sent to each neuron in [33] does not include its
own output.
Each Gabor chip contains four arrays of neurons labeled
EVEN/ON
, EVEN/OFF
, ODD/ON
and ODD/OFF
. For each spatial position
let
denote the
input spike rates of the four neurons
.
and
These differentially encode two real numbers
, where
and sim. These two real numbers can be expressed
ilarly for
as a single complex number
where
. Similarly, the output spike rates
encode numbers
and
. Internally,
the chip performs spatial filtering on arrays of input currents
to produce arrays of output currents. Assuming that the conversion from spike rate to current and vice versa is linear,
the steady-state input and output images are related by the
equations
(3)
Fig. 11. (a) Multiplexer control for the “image flip” circuit. The shift register
outputs are cleared when ReqY is low. Once ReqY goes high, signalling the
presence of a burst, high bits are clocked into the shift register at every low
transition of the ReqX. At the chip address, the outputs (Q0; Q1) are (0, 0).
For the row address, the outputs are (1, 0). For all of the column addresses, the
outputs are (1, 1). Switch determines how the SELECT input of the multiplexer
is controlled to flip the row and/or column address. (b) Schematic of a chip
select block. When ReqY_in goes high, the select input to the multiplexer is
latched high or low, depending on whether the chip address matches the desired
chip address. If the chip address matches, then the ReqY in; ReqX in,
and Ack in signals are passed to ReqY out; ReqX out, and Ack out.
Otherwise, the ReqY out signal stays low, the ReqX out signal stays high
and the ReqY in and ReqX in signals are used to generate the Ack out
signal to complete the communication cycle.
where capital letters denote discrete spatial Fourier Transforms
denotes spatial frequency, and
where
, and
are tuning parameters, which are
is a gain factor that deset by external bias voltages, and
pends upon the tuning parameters and constants of proportionality introduced by the spike rate to current conversion and vice
versa.
Solving (3), we obtain
(4)
symmetry or polarity. A multiplexer sends either the original or
the flipped address. The logic to generate the multiplexer select
signal is shown in the schematic of Fig. 11(a). The “flip on/off”
circuit is similar. It uses the column flip logic to select whether
to send the original address, or an address with the LSB inverted.
Both are implemented on Xilinx field programmable gate arrays
(FPGAs).
The “chip select” circuit is placed between a transmitter and
a receiver, and passes only bursts corresponding to a desired
chip. If the chip address of a burst matches that of the desired
, and
chip, then the circuit is transparent to the
signals
Ack signals. Otherwise, it blocks the ReqY and
from the transmitter, and generates Ack signal locally. There
is no need to block the address bits, since data on the address
lines is ignored unless a request is detected. Fig. 11(b) gives
the schematic of this circuit, which we implement on a Xilinx
FPGA.
C. Theoretical Fits to Neuronal Responses
This section gives the expressions used to fit the tuning curves
for the EVEN and ODD neurons measured in the feedforward
and feedback systems. We derive the spatial transfer function
of the orientation selective neurons in the feedback network by
where
(5)
The transfer function achieves its maximum at
where
and drops by half at
and
where
. By the
Fourier shift theorem, the filter kernel has the form
where
is the inverse Fourier transform of
when
,
which is a real valued function that decays with distance from
and
to be the real and imaginary
the origin. If we define
parts of , we have
which have Fourier transforms
CHOI et al.: NEUROMORPHIC IMPLEMENTATION OF ORIENTATION HYPERCOLUMNS
To find the response of the EVEN and ODD neurons, we first
note that
1059
We predict the responses of EVEN and ODD neurons using equations similar to those used for the feedforward system, except
is replaced by
.
(6)
are real,
and
, where the * superscript denotes complex
conjugation. This implies that
Since
and
(7)
Combining (6) and (7), we obtain
Expanding (4) to
and substituting into the equation above we obtain
,
In the feedforward system, the input to each chip is supplied
and
by the silicon retina alone. Thus,
, where
is the discrete spatial Fourier transform of the
, which is differentially
SUSTAINED silicon retina output
encoded on ON and OFF channels. Thus, the responses of the
and
EVEN and ODD neurons are
. If the retinal input is a sine-wave grating
with frequency , then the responses of the neurons will be
and
.
proportional to
For the feedback system, the input to each Gabor chip is the
residual signal
where
denotes the output of the Gabor chip tuned to orientation and is a feedback factor which determines how much
of the summed output is subtracted from the input in computing
the residual. From (4), the output of the Gabor chip tuned to
is
(8)
Summing over , we find that
(9)
where
Combining (8) and (9), we obtain
the “c” superscript denotes the transfer function from the retinal
input to the chip under coupling and
(10)
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Thomas Yu Wing Choi (S’03) was born in Hong
Kong in 1975. He received the B.S., M.S., and Ph.D.
degrees in electrical and electronic engineering
from the Hong Kong University of Science and
Technology, Hong Kong, in 1997, 1999, and 2003,
respectively.
He is currently employed by Hong Kong Science
and Technology Research Institute Limited as an
Analog Integrated Circuit Design Engineer. His
research interests include analog very large-scale
integration design and neural networks.
Paul A. Merolla received the B.S. degree with high
distinction in electrical engineering from the University of Virginia, Charlottesville, in 2000. He is currently working toward the Ph.D. degree in bioengineering at the University of Pennsylvania, Philadelphia.
His research interests include very large-scale integration models of cortical networks, vision systems,
and asynchronous digital interfaces for routing, and
interchip connectivity.
John V. Arthur received the B.S.E. degree (summa
cum laude) in electrical engineering from Arizona
State University, Phoenix, in 2000. He is currently
working toward the Ph.D. degree in bioengineering
at the University of Pennsylvania.
His research interests include mixed-mode very
large-scale integration, neuromorphic learning systems, and asynchronous interchip communication.
Kwabena A. Boahen B.S. and M.S.E. degrees
in electrical and computer engineering from the
Johns Hopkins University, Baltimore MD, in the
concurrent masters-bachelors program, both in 1989,
and the Ph.D. degree in computation and neural
systems from the California Institute of Technology
(Caltech), Pasadena, CA in 1997. He received the
He is an Associate Professor in the Bioengineering Department, University of Pennsylvania,
Philadelphia, where he holds a secondary appointment in Electrical Engineering. His current research
interests include mixed-mode multichip very large-scale integration models of
biological sensory and perceptual systems, and their epigenetic development,
and asynchronous digital interfaces for interchip connectivity.
Dr. Boahen held a Sloan Fellowship for Theoretical Neurobiology while at
Caltech. He was awarded a Packard Fellowship in 1999, a National Science
Foundation CAREER Award in 2001, and an Office of Naval Research YIP in
2002. He is a Member of Tau Beta Kappa.
Bertram E. Shi received the B.S. and M.S. degrees
in electrical engineering from Stanford University,
Stanford, CA, and the Ph.D. degree in electrical
engineering from the University of California at
Berkeley, in 1987, 1988, and 1994, respectively.
He then joined the faculty of the Department of
Electrical and Electronic Engineering at the Hong
Kong University of Science and Technology, where
he is currently an Associate Professor. His research
interests are in analog very large-scale integration
and cellular neural networks, bio-inspired and
neuromorphic engineering, machine vision, and image processing.
Dr. Shi’s IEEE activities have included Student Activities Chair of the IEEE
Hong Kong Section, Associate Editor for the IEEE TRANSACTIONS ON CIRCUITS
AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, Secretary and
Chair-elect for the IEEE Circuits and Systems Society Technical Committee on
Cellular Neural Networks, and Array Computing and Distinguished Lecturer
for the IEEE Circuits and Systems Society.
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