Optimal Population Coding, Revisited

Abstract

Cortical circuits perform computations within few dozens of milliseconds with each neuron emitting only a few spikes. In this regime conclusions based on Fisher information, which is commonly used to assess the quality of population codes, are not always valid. Here we revisit the effect of tuning function width and correlation structure on neural population codes for angular variables using ideal observer analysis in both reconstruction and classification tasks employing Monte-Carlo simulations and analytical derivations. We show that the optimal tuning width of individual neurons and the optimal correlation structure of the population depend on the signal-to-noise ratio for both the reconstruction and the classification task. Strikingly, both ideal observers lead to very similar conclusions at low signal-to-noise ratio. In contrast, Fisher information favors severely suboptimal coding schemes in this regime. To further investigate the coding properties of Fisher-optimal codes, we compute the full neurometric functions of an ideal observer in the stimulus discrimination task, which allows us to evaluate population codes separately for fine and coarse discrimination. We find that codes with Fisher-optimal tuning width show strikingly bad performance for simple coarse discrimination tasks with a ëpedestal errorí, which is independent of population size. We show analytically that this is a necessary consequence of the fact that in such codes only few neurons are activated by each stimulus, irrespective of the population size. Further we show that the initial region of the neurometric function goes to zero with increasing population size. As a consequence, the overall error achieved by Fisher-optimal ensembles saturates for large populations. In summary, based on exact ideal observer analysis for both stimulus reconstruction and discrimination tasks we obtained (1) an accurate assessment of neural population codes at all signal-to-noise ratios and (2) analytical insights into the suboptimal behavior of Fisher-optimal population codes