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Adam Brandenburger and Stefan Bucher's "Divisive Normalization is an Efficient Code for Multivariate Pareto-Distributed Environments," published in PNAS

October 12, 2022

Divisive normalization is a canonical computation in the brain, observed across neural systems, that is often considered to be an implementation of the efficient coding principle. We provide a theoretical result that makes the conditions under which divisive normalization is an efficient code analytically precise: We show that, in a low-noise regime, encoding an n-dimensional stimulus via divisive normalization is efficient if and only if its prevalence in the environment is described by a multivariate Pareto distribution. We generalize this multivariate analog of histogram equalization to allow for arbitrary metabolic costs of the representation, and show how different assumptions on costs are associated with different shapes of the distributions that divisive normalization efficiently encodes.

Adam Brandenburger is the J.P. Valles Professor of Business Economics and Strategy at NYU Stern.
Read the full paper here.