Highly Symmetric Neural Networks of Hopfield Type (exact results)

TL;DR

This paper analytically investigates the fixed points of highly symmetric Hopfield-type neural networks, focusing on how the connection matrix derived from symmetric patterns influences network stability and fixed points.

Contribution

It provides an exact analytical description of fixed points in Hopfield networks with symmetric patterns, enhancing understanding of their stability properties.

Findings

Analytic characterization of fixed points

Dependence of fixed points on external parameters

Insights into symmetry effects on network stability

Abstract

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter the analytic description of the fixed points set has been obtained.