An Information-Theoretical Approach To Optimizing Task Design For Differentiating Probabilistic Neural Codes

Bayesian brain hypothesis has been among the leading theories in modeling perceptual decision-making under uncertainty. While many psychophysical studies have provided evidence in support of the brain performing Bayesian computation, how uncertainty information is encoded in sensory neural populations has remained 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 critical distinction being whether stimulus priors would modulate early sensory neural responses. However, differentiating the two probabilistic neural codes experimentally remains challenging, as it is unclear what task design would effectively distinguish the two hypotheses. In this work, we develop an information-theoretical approach to optimizing task stimulus distribution that would best differentiate competing probabilistic neural representations. Our method derives an information gap–––the expected performance difference between likelihood and posterior decoders applied to sensory population responses following a specific probabilistic neural code–––by measuring the KL divergence between true posterior distributions and surrogate posterior distributions utilizing Bayes-optimal estimators for a given task design. On simulated neural populations, we demonstrate that our information-gap measure accurately predicts decoder performance differences across a wide array of settings. Crucially, maximizing the information gap yields stimulus distributions that optimally differentiate likelihood and posterior coding hypotheses. Our framework enables principled, theory-driven experimental design for differentiating probabilistic neural codes, advancing our understanding of how neural populations represent and process sensory uncertainty.