Temporal structure is an inherent property of various sensory inputs and motor outputs of the brain. For example, auditory stimuli are defined by the sound waveform. Temporal structure is also an important feature of certain visual stimuli, for example, the image on the retina of a fly during flight. In many cases, this temporal structure of the stimulus is being represented by a time-dependent neuronal activity that is locked to certain features of the stimulus. Here, we study the information capacity of the temporal code. In particular we are interested in the following questions. First, how does the information content of the code depend on the observation time of the cell's response, and what is the effect of temporal noise correlations on this information capacity? Second, what is the effect on the information content of reading the code with a finite temporal resolution for the neural response? We address these questions in the framework of a statistical model for the neuronal temporal response to a time-varying stimulus in a two-alternative forced-choice paradigm. We show that information content of the temporal response scales linearly with the overall time of the response, even in the presence of temporal noise correlations. More precisely, we find that positive temporal noise correlations have a scaling effect that decreases the information content. Nevertheless, the information content of the response continues to scale linearly with the observation time. We further show that finite temporal resolution is sufficient for obtaining most of the information from the cell's response. This finite timescale is related to the response properties of the cell.

Empirical studies seem to support conflicting hypotheses with regard to the nature of the neural code. While some studies highlight the role of a distributed population code, others emphasize the possibility of a “single-best-cell” readout. One particularly interesting example of single-best-cell readout is provided by the winner-takes-all (WTA) approach. According to the WTA, every cell is characterized by one particular preferred stimulus, to which it responds maximally. The WTA estimate for the stimulus is defined as the preferred stimulus of the cell with the strongest response. From a theoretical point of view, not much is known about the efficiency of single-best-cell readout mechanisms, in contrast to the considerable existing theoretical knowledge on the efficiency of distributed population codes. In this work, we provide a basic theoretical framework for investigating single-best-cell readout mechanisms. We study the accuracy of the WTA readout. In particular, we are interested in how the WTA accuracy scales with the number of cells in the population. Using this framework, we show that for large neuronal populations, the WTA accuracy is dominated by the tail of the single-cell-response distribution. Furthermore, we find that although the WTA accuracy does improve when larger populations are considered, this improvement is extremely weak compared to other types of population codes. More precisely, we show that while the accuracy of a linear readout scales linearly with the population size, the accuracy of the WTA readout scales logarithmically with the number of cells in the population.

In many cortical and subcortical areas, neurons are known to modulate their average firing rate in response to certain external stimulus features. It is widely believed that information about the stimulus features is coded by a weighted average of the neural responses. Recent theoretical studies have shown that the information capacity of such a coding scheme is very limited in the presence of the experimentally observed pairwise correlations. However, central to the analysis of these studies was the assumption of a homogeneous population of neurons. Experimental findings show a considerable measure of heterogeneity in the response properties of different neurons. In this study, we investigate the effect of neuronal heterogeneity on the information capacity of a correlated population of neurons. We show that information capacity of a heterogeneous network is not limited by the correlated noise, but scales linearly with the number of cells in the population. This information cannot be extracted by the population vector readout, whose accuracy is greatly suppressed by the correlated noise. On the other hand, we show that an optimal linear readout that takes into account the neuronal heterogeneity can extract most of this information. We study analytically the nature of the dependence of the optimal linear readout weights on the neuronal diversity. We show that simple online learning can generate readout weights with the appropriate dependence on the neuronal diversity, thereby yielding efficient readout.

Theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information. However, recent theoretical studies have investigated the effect of cross-correlations in the trial-to-trial fluctuations of the neuronal responses on the accuracy of the representation. Assuming that only the first-order statistics of the neuronal responses are tuned to the stimulus, these studies have shown that n the presence of correlations, similar to those observed experimentally in cortical ensembles of neurons, the amount of information in the population is limited, yielding nonzero error levels even in the limit of infinitely large populations of neurons. In this letter, we study correlated neuronal populations whose higher-order statistics, and in particular response variances, are also modulated by the stimulus. We ask two questions: Does the correlated noise limit the accuracy of the neuronal representation of the stimulus? and, How can a biological mechanism extract most of the information embedded in the higher-order statistics of the neuronal responses? Specifically, we address these questions in the context of a population of neurons coding an angular variable. We show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise. This information cannot be extracted by linear readout schemes, including the linear population vector. Instead, we propose a bilinear readout scheme that involves spatial decorrelation, quadratic nonlinearity, and population vector summation. We show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters, with an efficiency that grows linearly with the population size. This code can be implemented using biologically plausible neurons.