Motion Detection using an aVLSI Network of Spiking Neurons

Motion Detection using an aVLSI Network of Spiking Neurons
Motion Detection Using an aVLSI Network of
Spiking Neurons
Yingxue Wang and Shih-Chii Liu
Institute of Neuroinformatics
University of Zürich and ETH Zürich
Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
yingxue, [email protected]
The paper is structured as follows. Section II describes the
architecture of the spiking multi-neuron chip used in the
experiments and the generation of input spike trains. Section
III describes the implementation of the feedforward directionselective architecture. Section IV discusses the results from
an aVLSI spiking network implementation of a recurrent
direction-selective architecture proposed by Rao (2004) [8].
Abstract— We explore the benefits of using a spiking
neuronal network to generate direction-selectivity. The
experiments are performed using an aVLSI spike-based
network configured for two possible cortical architectures. We find that the direction-selective properties are
influenced by the various connections in the recurrent
network and that the network is sensitive to over almost
3 decades of stimulus speeds.
I.
II.
INTRODUCTION
A. Chip Architecture
The spiking multi-neuron chip used in these experiments
consists of a group of 16x16 spiking neurons each with totally
10 excitatory and inhibitory synapses. The spiking neuron is
implemented as an integrate-and-fire neuron. The local
weight of each synapse can be set through a global 5-bit DAC,
thus allowing for more flexibility in constructing different
network architectures [12] (see Figure 1). The chip is
fabricated in a 4 metal 2 poly 0.35 μm process and the details
of these circuits have been previously described in [12]. A
synapse is stimulated by sending an AER address associated
with it at a desired point in time. To set the local weight for a
particular synapse immediately before the stimulation, we
simply transmit two AER addresses for each synaptic input
spike; That is, the first address sets the bits of the on-chip
DAC which controls the weight of the synapse, followed by
the second synaptic AER address.
The recent development of aVLSI implementations of
spiking multi-neuron arrays has allowed researchers to study
the real-time properties of event-based networks [1–4]. In
these systems, every output spike of the neurons is
transmitted asynchronously off-chip in the form of a digital
address unique to each neuron. This transmission is based on
an
asynchronous
protocol
called
Address-EventRepresentation (AER) [2, 3]. An AER infrastructure
surrounding systems of spiking neuron chips allows the
creation of virtual connections between neurons on-chip and
across chips. Questions on how the architecture of eventbased neuronal networks contributes to commonly studied
properties in the cortical cells, for example, orientation
selectivity, can be investigated using these chips [2-4].
In this work, we explore the possible benefits of a spiking
network in producing direction selectivity by implementing
plausible cortical architectures on an aVLSI spiking multineuron chip. Direction-selectivity in a network depends on
the presence of asymmetry. Here, we describe results from
two architectures: a feedforward architecture, where the
asymmetry is introduced in the feedforward input
connections, e.g. [5]; and a recurrent architecture, where the
asymmetry is introduced in the recurrent connections, as
shown in [6-8].
We are interested in seeing if the use of spike timing
information carries benefits, as compared to motion detection
architectures where the direction selectivity is based on the
neuronal firing rates. It is worth mentioning that, in most
hardware biologically inspired motion models, the speed is
encoded as an analog variable [9, 10]. However, real-time
direction selectivity requires fast responses which can be
encoded more easily through timing between individual
spikes rather than averaged spike rates.
978-1-4244-5309-2/10/$26.00 ©2010 IEEE
EXPERIMENTAL SETUP
Figure 1. Outline of the spiking multi-neuron chip used for implementing
the direction-selective architectures.
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B. Input Statistics
Inhomogeneous Poisson spike trains are used to model the
putative non direction-selective inputs from thalamic
geniculate neurons which drive the early visual cortical areas
(Figure 2). In this work, the putative geniculate neurons are
modeled as an input layer containing 18 neurons to the
neuronal network. The instantaneous firing rate of each
neuron in this layer is described by a Gaussian function over
time. The time difference between the mean of the Gaussian
functions of the neighboring neurons encodes the direction
and speed of motion. Following the Gaussian instantaneous
firing rate, a Poisson spike train is generated for each neuron.
An example is given in Figure 2 (on the right), where the
neuronal activity of the input layer encodes a leftward
moving stimulus with a mean speed of 10 ms/pixel (or
ms/neuron). Here we set the standard deviation of the
Gaussian function to be half of the mean speed, and the peak
instantaneous firing rate to be 1 kHz.
Figure 3. Feedforward architecture with mutual inhibition between pairs of
neurons in the two direction chains. Each neuron in the chain receives input
spikes from the input layer following a Gaussian tuning function of the
spatial location. The input connection profiles of neurons that are sensitive
to leftward movement are displaced by a spatial halfwidth.
Figure 2. Inhomogeneous Poisson spike trains used to model the nondirection selective feedforward inputs (on the left). On the right shows
example input spike trains to the direction-selective network. The spike
trains represent a leftward moving stimulus with a mean speed of 10
ms/pixel. Each dot corresponds to a spike. The standard deviation of the
Gaussian function is 5 ms/pixel, and the peak instantaneous firing rate is
equal to 1000 Hz.
III.
Figure 4. Response of feedforward network to a leftward stimulus. The top
panel plots the input spike trains from the 18 neurons in the input layer and
the bottom panel shows the responses of the 2 chains of 8 neurons; each
sensitive to either the leftward or rightward moving stimulus.
FEEDFORWARD MODEL
We first consider a simple feedforward network. It
consists of two chains; each with 8 neurons selective for
leftward and rightward motion, respectively. The feedforward synaptic weights from the input layer to each neuron
in the network follow a Gaussian tuning function of the
spatial location (Figure 3). We introduce asymmetry through
the spatial displacement of the feedforward input connection
profiles to the corresponding neurons in the two chains.
Furthermore, mutual inhibitory connections are introduced
between spatial corresponding neurons in the two chains.
IV.
RECURRENT MODEL
The basic structure of the recurrent network is the same as
that of the feedforward network, where two chains of neurons
mutually inhibit each other at corresponding spatial locations.
However, the asymmetry in the recurrent model is introduced
by the excitatory lateral connections, rather than the spatial
asymmetry of the input connection profiles [8]. That is, the
feedforward input connection profiles of the corresponding
neurons in both chains are the same, while directional lateral
connections to the nearest neighboring neuron are introduced
within each chain (Figure 5). The ratio of the lateral
excitatory synaptic weight to the input feedforward synaptic
weight dynamically varies from 1.1 to 1.6 and the ratio of the
lateral excitatory weight to the inhibitory weight varies from
2 to 8, depending on the speed of the stimulus.
We present the network with a leftward moving input
stimulus with a mean speed of 10 ms/pixel. As shown in
Figure 4, the neuronal responses of the rightward chain are
largely suppressed. This occurs because the neurons in the
leftward chain receive inputs earlier in time and are more
likely to spike first. Their spikes then inhibit the neurons
from the other chain. In this case, the spiking timing is used
in the competition between the two chains.
We measure the response of the network to input spike
trains representing stimuli moving at different velocities (see
Section IIB). First, the influence of the two types of recurrent
94
connections: the mutual inhibitory connections and the lateral
excitatory connections, on the direction selective performance
is illustrated with an example.
the red arrows are pointing to) despite their common input
stimulus. However, if the population instantaneous firing
activity is considered, in both chains the activities are still
similar as shown in the bottom panel of Figure 7.
Figure 5. Recurrent architecture proposed in Rao (2004) [8]. Each neuron
in the network has a Gaussian receptive field as a function of the spatial
location of the input layer. Neurons in the leftward and rightward chains
share the same tuning function.
Figure 7. Response of recurrent network with lateral excitatory
connections but without mutual inhibition. With the introduction of lateral
connections, the neurons (shown in the spike rasters) in the chain sensitive
to the stimulated direction spike earlier in time (contrast for example, the
time when the first spike of neuron 14 in the leftward array appears versus
that of neuron 5 in the rightward array), resulting in a weak directionselective response in the network.
We start off with a network without any mutual inhibition
or lateral excitation. As shown in Figure 6, the neuronal
activities of both chains (plotted either as raster plots or
population activities) look almost identical.
By adding the mutual inhibitory connections, these earlier
arriving spikes can effectively suppress the activity in the
rightward chain (Figure 8). Since the competition relies on
the timing of individual spikes instead of the firing rate, the
computation of the direction selectivity can be fast.
Figure 6. Response of the recurrent architecture with no lateral
connections and no mutual inhibition. The top panel shows the raster plot of
the activity of each neuron in the network (the neuron numbers are as shown
in Figure 5), and the bottom panel shows the population activity of each
chain calculated with a 10 ms time bin. Input spike trains represent leftward
motion with a mean speed of 10ms/pixel.
When the asymmetric lateral excitatory connections are
introduced into the network, not only do the neuronal
activities increase (Figure 7), but the network starts to display
weak direction selectivity. This is because in the preferred
chain, the predictive responses are generated by the neurons
through the lateral excitation. Therefore, neurons in the
leftward chain fire earlier in time compared to those in the
rightward chain. For example, neuron 14 spikes earlier than
neuron 6 as shown in the spike raster plot in Figure 7 (where
Figure 8. Response of the recurrent network with lateral connections and
mutual inhibition.
We then test the sensitivity range of this network to input
speeds by using inhomogeneous input spike trains of varying
speeds. The resulting output spikes from all neurons in the
network are used to predict the direction and speed of the
stimulus. We first estimate the direction of motion by
95
comparing the total neuronal activity generated within each
chain of the network. As shown in Figure 9, the direction can
be correctly predicted over almost 3 decades of speeds unless
the speed is very low (for example, 0.05 ms/pixel). The latter
corresponds to the case when the network activity is low and
the recurrent amplification is limited.
V.
CONCLUSION
In this paper, we explore the possible benefits of spikes in
the generation of motion-sensitive properties in a putative
spike-based cortical network. We find that with this spikebased recurrent network architecture, almost 3 decades of
motion speeds can be predicted. In the future, we will
compare the latency performance of a network that uses spike
rates over spike timing. We will also investigate how spatiotemporal correlations of individual spikes arriving on the
dendrite can generate the asymmetry needed for direction
selectivity [13].
ACKNOWLEDGMENT
The authors would like to thank M. Oster for help with
setting up the AER infrastructure. This work is partially
supported by ETH Research Grant TH-20/04-2.
REFERENCES
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Figure 9. Probability of correctly predicted direction of motion which is
computed from the output spikes. The speed of the input stimulus varies
from 0.05 to 25 ms/pixel, the standard deviation of the Gaussian function is
set to half of the speed, and the peak instantaneous firing rate is 10 kHz. The
results are averaged across 100 trials using leftward moving stimuli. Similar
results are obtained for the rightward moving stimuli.
[3]
We then extract the stimulus speed by using the timing
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Figure 10. Predicted speed computed from the output spikes. The speed of
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the Gaussian function is set to half of the speed, and the peak instantaneous
firing rate is 10 kHz. The result is averaged across 100 trials with leftward
moving stimuli. Similar results are obtained for the rightward moving
stimuli.
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