Fixed points of Hopfield type neural networks

TL;DR

This paper analytically investigates the fixed points of Hopfield neural networks with connection matrices derived from distorted patterns, linking the results to neural network behavior and the Ising model at zero temperature.

Contribution

It provides an analytical description of how the fixed points depend on pattern distortion in Hopfield networks, connecting neural dynamics to statistical physics models.

Findings

Fixed points depend analytically on pattern distortion parameter.

Connection to Ising model at T=0 offers physical interpretation.

Results enhance understanding of neural network stability and pattern retrieval.

Abstract

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the standard-vector. It is found that the dependence of the set of the fixed points on the value of the distortion parameter can be described analytically. The obtained results are interpreted in the terms of neural networks and the Ising model at T=0.