An Information-Theoretic Framework For Optimizing Experimental Design To Distinguish Probabilistic Neural Codes

TL;DR

This paper introduces an information-theoretic framework to design experiments that effectively distinguish between likelihood and posterior neural coding hypotheses by maximizing the information gap, thus improving understanding of sensory uncertainty representation.

Contribution

It develops a method to optimize stimulus distributions for differentiating probabilistic neural codes using the information gap and KL divergence, guiding more effective experimental designs.

Findings

The information gap predicts decoder performance differences across tasks.

Maximizing the information gap enhances the ability to distinguish neural coding hypotheses.

Simulations confirm the framework's effectiveness in various task settings.

Abstract

The Bayesian brain hypothesis has been a leading theory in understanding perceptual decision-making under uncertainty. While extensive psychophysical evidence supports the notion of the brain performing Bayesian computations, how uncertainty information is encoded in sensory neural populations remains elusive. Specifically, two competing hypotheses propose that early sensory populations encode either the likelihood function (exemplified by probabilistic population codes) or the posterior distribution (exemplified by neural sampling codes) over the stimulus, with the key distinction lying in whether stimulus priors would modulate the neural responses. However, experimentally differentiating these two hypotheses has remained challenging, as it is unclear what task design would effectively distinguish the two. In this work, we present an information-theoretic framework for optimizing the task stimulus distribution that would maximally differentiate competing probabilistic neural codes. To quantify how distinguishable the two probabilistic coding hypotheses are under a given task design, we derive the information gap--the expected performance difference when likelihood versus posterior decoders are applied to neural populations--by evaluating the Kullback-Leibler divergence between the true posterior and a task-marginalized surrogate posterior. Through extensive simulations, we demonstrate that the information gap accurately predicts decoder performance differences across diverse task settings. Critically, maximizing the information gap yields stimulus distributions that optimally differentiate likelihood and posterior coding hypotheses. Our framework enables principled, theory-driven experimental designs with maximal discriminative power to differentiate probabilistic neural codes, advancing our understanding of how neural populations represent and process sensory uncertainty.