Neural Coding Of Visual Stimuli

National Institute Of Mental Health

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Abstract

Decoding the information carried in single neuronal responses requires knowing which response features carry information. To describe a neuronal response completely we must specify the arrival time of each spike. However, we are interested less in the spike train itself than in its role in transmitting information. Therefore, only those aspects of the response that carry unique information need be included. Previously we showed that all of the information carried by neuronal spike trains requires specifying only the spike count distribution (which is approximately truncated Gaussian), the variation in firing rate with a bandwidth of less than 30 Hz, the equivalent of measuring spike counts in 30 ms wide bins), and the interval histogram. If these features completely describe single neuronal responses, they contain all of the information available from those responses, no matter what representation of the response is chosen. The reason the spike count distribution (that is, knowing how many times each spike count occurs) is so important is that the temporal coding depends almost completely on the spike count. Intuitively this seems clear when we realize that the more spikes that are present, the richer the potential temporal code. Thus, the influence of variation in the number of spikes that occurs with successive presentations of a stimulus must be properly taken into account when estimates of neuronal coding are made. If the responses arise from a random process with a certain overall pattern in time, the responses must follow well-known statistical rules. We have shown that the order of spikes in responses follow the statistical properties codified by order statistics. One advantage of the order statistic representation is that it allows exact knowledge of the amount of information carried by neuronal responses if the spike count distribution and the average variation of firing rate can be measured. Using a straightforward reformulation of the basic formula of order statistics, we derived a decoder that decodes neuronal responses millisecond-by-millisecond as the response evolves . This algorithm can form the basis of an instant-by-instant neuronal controller. Decoding spike trains can be thought of as looking them up in a dictionary. Order statistics can be calculated for any distribution of spike counts, and experimental data can support a wide variety of models of the spike count distributions. Modeling the observed spike counts as a mixture of several (typically 1-3) Poisson lets us think of the spike trains as having arisen from a mixture of Poisson processes. The theory of Poisson processes can then be used to calculate order statistics much more efficiently than possible for an arbitrary distribution of spike counts, which substantially increases decoding speed. Given these accurate statistical models of neural responses, we studied what happens when they are applied to small populations (pairs) of neurons. Our measurements in two brain regions, primary motor cortex and inferior temporal cortex, show that all of the patterns of spikes including simultaneous spikes are related to the same measurements, i.e. the rate variation and the spike count distribution, plus the correlations of the spike counts taken over 100's of milliseconds. It appears that the patterns of spikes seen across neurons are directly related to the slow variations in firing rate. Thus, it appears that the same measurements that are decoding single neuronal responses are also adequate decoding the information carried in the population activity. Now we are studying how these statistical properties arise from the architecture of neuronal connections. We assume that each neuron, although a dynamical element, interacts with it neighbors according to the statistics of the signal and noise. In this mean field approach none of the connections are specified beyond specifying the number of neurons that are connected to each other. In doing this we find that the relations between the signals and noise are described almost exactly by this reduced 'mean-field' model. This shows that the basic statistics of neuronal firing do not necessarily depend on the specific patterns of connections within the neuronal networks.