# Comp Neuro JC: “Implicit Encoding of Prior Probabilities in Optimal Neural Populations”

For Wednesday’s Computational & Theoretical Neuroscience Journal Club I presented a paper by Deep Ganguli and Eero Simoncelli on priors in optimal population coding,

The paper considers a population of neurons which encode a single, scalar stimulus variable, $s$. Given that each stimulus value $s$ has some probability $p(s)$ of occurring in the environment, what is the best possible population code?

The paper frames this question as a mathematical optimization problem, quantifying the notion of “best population” using Fisher Information
as a measure of the amount of information carried about a given stimulus in the population. Through the use of some careful assumptions and approximations, and by parameterizing the solutions through a very clever “warping” transform of a simple population, they’re able to obtain an optimization program that’s analytically solvable. The end result are predictions of a population’s density (neurons/stimulus, roughly) and gain (mean spike rate) as a function of the prior, $p(s)$ – an implicit encoding of the prior in the population. Comparisons of measured prior distributions of spatial frequency and orientation (in natural images) with predictions based on experimentally-recorded densities yield good matches.

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