Efficient Sensory Encoding and Bayesian Inference with Heterogeneous Neural Populations

Abstract

The efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment. We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons, each characterized by a tuning curve. We parameterize the population with two continuous functions that control the density and amplitude of the tuning curves, assuming that the tuning widths vary inversely with the cell density. This parameterization allows us to solve, in closed form, for the information-maximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables. For the optimal population, the cell density is proportional to the prior, such that more cells with narrower tuning are allocated to encode higher-probability stimuli and that each cell transmits an equal portion of the stimulus probability mass. We also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. We examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder, the Bayesian population vector, that closely approximates a Bayesian least-squares estimator that has explicit access to the prior. Finally, we generalize these results to sigmoidal tuning curves, correlated neural variability, and a broader class of objective functions. These results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental, physiological, and perceptual data.

Theory of cortical function

“…1 are analogous to Bayesian inference, with the first term representing a negative log likelihood and the B C second term representing a prior probability. Following previous work on probabilistic population codes (4,21,40), the idea is that the neural responses encode an implicit representation of the posterior. Indeed, the values ofŷ can be interpreted as an implicit representation of a prior probability distribution, and the values of y can be interpreted as an implicit representation of the posterior (SI Appendix).…”

Origin of information-limiting noise correlations

“…Behavioral improvement achieved by perceptual learning and attention is typically accompanied by increased sensitivity in single neurons (i.e., tuning sharpening or amplification) (29,30) and reduced noise correlations (24,31,32), suggesting that these might by efficient strategies to increase information. Many previous theoretical studies have derived more general solutions for the optimal shape of tuning curves under the assumption of independent response variability (33)(34)(35)(36). Others have considered the effects of correlated variability on coding accuracy for a fixed set of tuning curves (3,4,6,37).…”

A Bayesian approach to person perception

“…Alternatively, it has been proposed that prior expectation might be encoded implicitly within the channel structure itself rather than through an explicit decoding stage (Fischer & Pena, 2011;Ganguli & Simoncelli, 2014). Take, for example, the perception of gaze direction, where there is a prior towards perceiving direct gaze (Mareschal et al, 2013b(Mareschal et al, , 2014.…”

“…While adaptation is generally considered to uncover the structure of the encoded representation of the stimulus dimensions under investigation, the Bayesian approach could be measuring either an expectation that is encoded within the channel structure (Fischer & Pena, 2011;Ganguli & Simoncelli, 2014) or one that becomes apparent not at the encoding but at a decoding stage (Zemel et al, 1998). A full investigation of the form of any biases measured should uncover more about the relationship between the underlying representation proposed via adaptation and that proposed by a Bayesian approach.…”