Nonlinear population codes

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 in 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.