Elsevier

Neural Networks

Volume 14, Issues 6–7, 9 July 2001, Pages 715-725
Neural Networks

2001 Special issue
Spike-based strategies for rapid processing

https://doi.org/10.1016/S0893-6080(01)00083-1Get rights and content

Abstract

Most experimental and theoretical studies of brain function assume that neurons transmit information as a rate code, but recent studies on the speed of visual processing impose temporal constraints that appear incompatible with such a coding scheme. Other coding schemes that use the pattern of spikes across a population a neurons may be much more efficient. For example, since strongly activated neurons tend to fire first, one can use the order of firing as a code. We argue that Rank Order Coding is not only very efficient, but also easy to implement in biological hardware: neurons can be made sensitive to the order of activation of their inputs by including a feed-forward shunting inhibition mechanism that progressively desensitizes the neuronal population during a wave of afferent activity. In such a case, maximum activation will only be produced when the afferent inputs are activated in the order of their synaptic weights.

Introduction

Most models of neural systems implicitly assume that information is transmitted by neurons in the form of a firing rate code. For example, the vast majority of Artificial Neural Network and Connectionist models use an approach that can be summarized as follows: take a large number of neuron-like processing units, connect them together with variable weight connections that are the rough equivalent of synapses, and use a rule in which the activation level of each unit is some function of the weighed sum of all the inputs to each neuron. It is a strategy that seems obviously ‘biologically inspired’, but there is one feature of real biological neural networks that is missing from the vast majority of artificial systems. In nearly all artificial systems, each unit sends its activation level to all the targets as a continuous value, often a floating point number between 0 and 1 (sometimes between −1 and +1). In contrast, biological neurons send information in the form of a sequence of spikes. The notion that one can summarize a spike train as a single continuous variable is one that is very firmly entrenched, not just in artificial neural networks, but also throughout neuroscience. Indeed, it goes back to the very start of experimental neurophysiology in the 1920s when the first recordings of the electrical activity of sensory fibers by Adrian (1928) showed that firing rate increased with increasing stimulus intensity.

Even today, neurophysiologists often assume that all the useful information that can be learned about neural coding can be summarized in the form of a Post-Stimulus Time Histogram (PSTH) that plots firing rate as a function of time. Given this state of affairs, it is hardly surprising that few in the artificial neural network community have felt the need to look at alternative coding schemes. However, in the last few years, an increasing number of scientists has begun to take seriously the possibility that the use of spikes opens up a whole range of alternative coding options, some of which have profound implications for the nature of neural computation (Maass and Bishop, 1999, Rieke et al., 1996). One of the motivations behind such work has been the realization that there are situations where processing is too fast to be compatible with a conventional rate based code. We will review such evidence and argue that other alternative spike based coding schemes can be considerably more efficient. In particular, we will discuss the merits of a coding scheme that encodes information in the relative timing of spikes across a population of neurons, or more specifically, in the order in which neurons fire. We will argue that such coding schemes have a number of features that make them ideally suited for certain types of rapid processing tasks. These features include speed, robustness, and ease of implementation, and make such schemes particularly attractive for designing artificial processing systems.

Section snippets

The processing speed constraint

In 1989, Thorpe and Imbert argued that the existence of neurons in the primate brain that could respond selectively to complex visual stimuli such as faces, food and familiar 3D objects only 100–150 ms after stimulus onset imposes a major constraint on models of visual processing (Thorpe & Imbert, 1989). They argued that to reach such neurons, information about the stimulus would need to cross something like 10 layers of neurons on the way from the retinal photoreceptors. This means that each

Is rate coding fast enough?

Most neurophysiologists believe that a Poisson-like rate code is, to a first approximation, a reasonable description of the way that neurons transmit information. Describing the spike generation process as Poisson is clearly a simplification, because it ignores the fact that real neurons have refractory periods that prevent them from generating a large number of spiking events in a short period. Nevertheless, a Poisson model is a reasonable starting point. Gautrais and Thorpe (1998) looked at

Alternative coding schemes

Fortunately, rate coding is by no means the only option available. Over 30 years ago, a meeting on Neural Coding assessed the plausibility of a wide range of different coding schemes (Perkel & Bullock, 1968). Many of these alternative schemes are still perfectly viable. Furthermore, in recent years, a number of other coding schemes have been proposed, many of which make use of the fact that real neurons use spikes. Indeed, the fact that neurons use spikes to transmit information opens up a

The origin of temporal information

In the last section, we introduced a number of alternative coding strategies that make use of the temporal structure of the spikes produced by a population of neurons. We showed that if it was possible to determine the precise firing time of spikes on each channel, the total amount of information that can be transmitted can be very large. Alternatively, just using the rank order of spikes in different neurons can also be very effective. The question now is, where might such differences in spike

Rank order coding in the retina

The integrate and fire properties of retinal ganglion cells mean that, in response to a flashed stimulus, the neurons will tend to fire in an order that reflects the spatial characteristics of the image. The well known center-surround organization of receptive fields in the retina means that local contrast rather than the physical intensity of the stimulus will be most important for determining the responsiveness of retinal ganglion cells. Thus, one could in principle use the order of firing of

Decoding rank order

The rapid decrease in weighting that we use in the image reconstruction can in fact be used more generally as a decoding mechanism for rank based information. The idea is a simple one, and can be implemented in a feed-forward network that includes a population of inhibitory interneurons. Consider the situation in Fig. 6 in which a neuron N receives excitatory inputs from five input neurons in the previous layer, but that in addition, each of the input neurons also connects to a population of

Learning and rank order coding

A further advantage of the rank order coding scheme is that it is relatively straightforward to implement learning in such a network. As noted in the previous section, a target neuron can be made sensitive to the order of its inputs by using a desensitization mechanism such as shunting inhibition to progressively decrease the effectiveness of inputs arriving later on. In order to make a neuron sensitive to a particular temporal sequence of activation, it is sufficient to use a learning rule

Extensions to the basic model

Although the face-detection and face-identification models described in the previous section use an entirely feed-forward processing architecture, other work in our group has shown that other types of architecture can be incorporated into the same basic scheme. For example, in a recent study, we showed that horizontal connections between orientation selective maps can be used to implement contour integration even under conditions where each neuron only gets to fire one spike (Van Rullen and

Concluding comments

Rate coding has dominated almost all theoretical and experimental work on neural function for more than half a century. The idea that the output of a neuron can be distilled into a single number is certainly an appealing simplification, and one that has proved useful in a great deal of theoretical work. However, real neurons transmit information as spikes, and as soon as one tries to implement even the simplest rate coding model with real neurons that produce real spikes, things start to get

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