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) . 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  (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 . 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. ; 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. 93 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 . 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) . 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 . 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   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.  We then extract the stimulus speed by using the timing information in the output spike trains. 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