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

TL;DR

This work presents an information-theoretic framework for optimizing the task stimulus distribution that would maximally differentiate competing probabilistic neural codes, and derives the information gap by evaluating the Kullback-Leibler divergence between the true posterior and a task-marginalized surrogate posterior.

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.

Figures (18)

• Figure 1: Two competing hypotheses on how sensory uncertainty information is encoded in early sensory neural populations. A) Likelihood coding hypothesis, exemplified by the probabilistic population code ma2006bayesian, proposes that early sensory populations encode the likelihood function over the stimulus, with posterior computation deferred to downstream areas. B) Posterior coding hypothesis, exemplified by the neural sampling code hoyer2002interpreting, posits that early sensory populations readily encode the posterior distribution over hidden world state by integrating prior knowledge conveyed via feedback connections from higher cortical areas.
• Figure 2: A decoding approach to differentiating probabilistic neural codes. A) An experimental paradigm consists of two contexts $c \in \{A,B\}$ with context-specific prior distributions $p^c(\theta)$. B) Information gap $\Delta^{\text{info}}$, the difference in likelihood (blue) and posterior (orange) decoder performances, can indicate whether the underlying neural population encodes the likelihood function (left) or the posterior distributions (right). C) Deep neural network-based decoders are used for decoding the likelihood function (top) or the posterior distribution (bottom) from population responses.
• Figure 3: Decoder performance difference on simulated populations converges to the theoretical prediction of information gap. A) On simulated neural populations encoding the likelihood function (left, blue) or the posterior distributions (right, orange) responding to high contrast stimuli, the difference between the likelihood and posterior decoder performances converges to the theoretical value of information gap (dashed lines) as the total number of trials increases (top, with fixed number of neurons $=500$), and as the total number of neurons in the population increases (bottom, with fixed number of trials $=30$k). (shaded areas denote the s.t.d. across 5 random seeds.) B) Same for medium contrast stimuli and C) for low contrast stimuli.
• Figure 4: Information gap accurately predicts decoder performance difference on simulated populations across diverse task settings. A) On simulated Poisson neural populations responding to high (left), medium (middle), and low (right) contrast stimuli, theoretical values of information gap (x-axis) accurately predicts the decoder performance difference on simulated neural populations (y-axis) across multiple task design parameters, for both the likelihood-coding and posterior-coding populations. (Each color marks one set of task parameters used for both types of simulated populations; Error bars denote the s.t.d. across 5 random seeds.) B) Same for simulated populations using a more complex, bio-realistic gain-modulated Poisson neural model goris2014partitioning.
• Figure 5: Information gap landscapes inform practical task designs that optimally differentiate probabilistic representations in neural populations. A) Information gap as a function of task parameters ($d$: separation between context priors, and $\sigma$: context prior standard deviations) for both the likelihood coding hypothesis (top) and the posterior coding hypothesis (bottom) when presented with high contrast stimuli. The asterisks identify strategic task designs that achieve the tradeoff where posterior-coding information gap approaches its maximum while likelihood-coding maintains sufficient discriminative signal. B) Same for medium contrast stimuli and C) for low contrast stimuli.