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Implicit encoding of prior probabilities in optimal neural populations
Deep Ganguli · Eero Simoncelli

Wed Dec 08 12:00 AM -- 12:00 AM (PST) @

Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of cells and spikes in a neural population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information. This family includes lower bounds on mutual information and perceptual discriminability as special cases. In all cases, we find a closed form expression for the optimum, in which the density and gain of the cells in the population are power law functions of the stimulus prior. This also implies a power law relationship between the prior and perceptual discriminability. We show preliminary evidence that the theory successfully predicts the relationship between empirically measured stimulus priors, physiologically measured neural response properties (cell density, tuning widths, and firing rates), and psychophysically measured discrimination thresholds.

Author Information

Deep Ganguli (New York University)
Eero Simoncelli (FlatIron Institute / New York University)

Eero P. Simoncelli received the B.S. degree in Physics in 1984 from Harvard University, studied applied mathematics at Cambridge University for a year and a half, and then received the M.S. degree in 1988 and the Ph.D. degree in 1993, both in Electrical Engineering from the Massachusetts Institute of Technology. He was an Assistant Professor in the Computer and Information Science department at the University of Pennsylvania from 1993 until 1996. He moved to New York University in September of 1996, where he is currently a Professor in Neural Science, Mathematics, and Psychology. In August 2000, he became an Associate Investigator of the Howard Hughes Medical Institute, under their new program in Computational Biology. In Fall 2020, he resigned his HHMI appointment to become the scientific director of the Center for Computational Neuroscience at the Flatiron Institute, of the Simons Foundation. His research interests span a wide range of topics in the representation and analysis of visual images, in both machine and biological systems.

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