Neural network learning dynamics in a path integral framework

TL;DR

This paper introduces a path-integral formalism to analyze neural network dynamics under noise, providing a new way to understand pattern evolution and storage capacity.

Contribution

It develops a novel path-integral approach for neural network dynamics and offers a method to determine the network's storage capacity.

Findings

Provides a formalism for neural dynamics with noise

Derives an effective cost function for neural systems

Offers a perturbative method to assess storage capacity

Abstract

A path-integral formalism is proposed for studying the dynamical evolution in time of patterns in an artificial neural network in the presence of noise. An effective cost function is constructed which determines the unique global minimum of the neural network system. The perturbative method discussed also provides a way for determining the storage capacity of the network.