Abstract
Over repeat presentations of the same stimulus, sensory neurons show variable responses. This “noise” is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population's ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem – neural tuning curves, etc. – held fixed. This work yields unifying insights into the role of noise correlations. These are summarized in the form of theorems, and illustrated with numerical examples involving neurons with diverse tuning curves. Our main contributions are as follows. (1) We generalize previous results to prove a sign rule (SR) — if noise correlations between pairs of neurons have opposite signs vs. their signal correlations, then coding performance will improve compared to the independent case. This holds for three different metrics of coding performance, and for arbitrary tuning curves and levels of heterogeneity. This generality is true for our other results as well. (2) As also pointed out in the literature, the SR does not provide a necessary condition for good coding. We show that a diverse set of correlation structures can improve coding. Many of these violate the SR, as do experimentally observed correlations. There is structure to this diversity: we prove that the optimal correlation structures must lie on boundaries of the possible set of noise correlations. (3) We provide a novel set of necessary and sufficient conditions, under which the coding performance (in the presence of noise) will be as good as it would be if there were no noise present at all.
Highlights
Neural populations typically show correlated variability over repeat presentation of the same stimulus [1,2,3,4]
In Section ‘‘The sign rule revisited’’, we will discuss our generalized version of the ‘‘sign rule’’, Theorem 1, namely that signal and noise correlations between pairs of neurons with opposite signs will always improve encoded information compared with the independent case
In Section ‘‘Optimal correlations lie on boundaries’’, we use the fact that all of our information quantities are convex functions of the noise correlation coefficients to conclude that the optimal noise correlation structure must lie on the boundary of the allowed set of correlation matrices, Theorem 2
Summary
Neural populations typically show correlated variability over repeat presentation of the same stimulus [1,2,3,4]. These are called noise correlations, to differentiate them from correlations that arise when neurons respond to similar features of a stimulus. Such signal correlations are measured by observing how pairs of mean (averaged over trials) neural responses co-vary as the stimulus is changed [3,5]. Similar results were obtained by [17], and these examples emphasize the need for general insights
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