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 (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 taken into account properlywhen 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. In new work we have used previously developed mathematical techniques to explore how the statistical methods we have used can give insight into development of biophysical models of neuronal information processing. One approach has been to learn what level of interactions among spikes are important, and how closely our Poisson based model describes data. To do this we have compared our model to another similar model by Kass and Ventura using Nakahara-Amari information geometry. This approach allows the evaluation of the differences between statistical models in a single framework. We have also been using a mean-field approach to approximate the activity of a small (~10000) population of neurons to determine whether simple descriptions of stochastic biophysically realistic networks match the properties of the data we typically collect. These two mathematical approaches have helped to confirm that our model matches our experimental data quite closely. In new work seeking to understand how information about visual images is remembered we have studied neuronal responses in the inferior temporal cortex area TE during a delayed stimulus matching task. We measured the correlations between trial-by-trial fluctuations in different task phases (sample, nonmatch, and match). The sample and match response fluctuations correlated more strongly than sample and nonmatch fluctuations, even though the interval between sample and nonmatch was shorter than the interval between sample and match (median variance explained: sample vs. match = 7.3%; sample vs. nonmatch = 1.9%). Such trial-by-trial correlation between sample and match responses is strong evidence for local storage of the short-term memory trace. There seems to be no way to explain these correlations if the TE neurons only encode the stimulus, because noise in encoding must be independent across different stimulus presentations, and thus can not preserve fluctuations across events. Here we propose that these correlations are a signature for iconic, short-term memory: these TE neurons hold the memory trace of the sample image in the strength of its synaptic inputs using a form of one-trial-learning. This population of neurons thus forms a matched filter (the best filter for detecting the presence of a known signal in white noise) for the sample image. The power in the responses of the population of TE neurons, but not in individual neurons, is higher for the match than for the nonmatch stimulus. This new theory is consistent with an idea we proposed in 1992 (Eskandar et al.), when we showed that responses of IT cortex neurons contained information about the sample and current images in a DMS task.
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