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

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.