Heteroclinic cycles in Hopfield networks

TL;DR

This paper investigates the existence of robust heteroclinic cycles in Hopfield networks, linking their dynamic patterns to the structure of synaptic couplings, providing insights into neural memory sequences.

Contribution

It establishes a direct connection between the structure of synaptic couplings and the presence of heteroclinic cycles in Hopfield networks, advancing understanding of neural dynamics.

Findings

Heteroclinic cycles are shown to be tightly linked to coupling structure.

The study characterizes conditions for the existence of robust heteroclinic cycles.

Results suggest implications for neural memory and sequence processing.

Abstract

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic pattern of the associated neural circuit. In this work we consider a class of network neuron models, known as Hopfield networks, with a learning rule which consists of transforming an information string to a coupling pattern. Within this class of models we study dynamic patterns, known as robust heteroclinic cycles, and establish a tight connection between their existence and the structure of the coupling.