Learning in Neural Networks Based on a Generalized Fluctuation Theorem

TL;DR

This paper develops a theoretical framework for neural network learning based on a generalized fluctuation theorem, linking information maximization with environmental exploration and optimal encoding.

Contribution

It introduces a novel generalized fluctuation theorem tailored for neural-environment interactions, advancing understanding of information-based learning mechanisms.

Findings

Neural networks can efficiently explore environments using the proposed learning mechanism.

The theory demonstrates optimal information encoding in neural systems.

Analytical and numerical results support the effectiveness of the approach.

Abstract

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.