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Divisive normalization is an efficient code for multivariate Pareto-distributed environments.

Stefan F Bucher1,2,3, Adam M Brandenburger4,5,6

  • 1Department of Economics, New York University, New York, NY 10012.

Proceedings of the National Academy of Sciences of the United States of America
|September 26, 2022
PubMed
Summary
This summary is machine-generated.

Divisive normalization is an efficient neural code when stimuli follow a multivariate Pareto distribution. This finding, linking neural computation to environmental statistics, offers testable predictions for sensory systems.

Keywords:
Pareto distributiondivisive normalizationefficient codinghistogram equalizationnatural stimulus statistics

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Area of Science:

  • Computational neuroscience
  • Information theory
  • Systems neuroscience

Background:

  • Divisive normalization is a widespread neural computation.
  • It is theorized to implement efficient coding principles.
  • Efficient coding aims to minimize redundancy and maximize information transmission.

Purpose of the Study:

  • To analytically define the conditions under which divisive normalization is an efficient code.
  • To generalize this framework to include metabolic costs.
  • To connect theoretical findings with empirical observations of natural stimuli and neural responses.

Main Methods:

  • Theoretical analysis of encoding efficiency.
  • Derivation of conditions for optimal representation.
  • Generalization to include metabolic costs and arbitrary distributions.
  • Comparison with naturalistic stimulus statistics and empirical data.

Main Results:

  • Divisive normalization is efficient if and only if stimuli follow a multivariate Pareto distribution (in a low-noise regime).
  • Metabolic costs shape the efficiently encoded distributions.
  • The model aligns with naturalistic stimulus features like conditional variance dependence.
  • Empirical evidence supports the model's fit to natural image filter responses.

Conclusions:

  • Divisive normalization may have evolved to efficiently encode Pareto-distributed stimuli.
  • The theory provides a framework for understanding neural representations of natural environments.
  • Predictions are generated for tuning divisive normalization parameters across sensory domains.