Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model

TL;DR

This paper analyzes a neural network model explaining persistent neural activities, focusing on the retrieval properties of Hopfield and correlated attractors using statistical mechanics and dynamical replica theory.

Contribution

It provides a detailed theoretical and numerical analysis of the retrieval dynamics of Hopfield and correlated attractors in an associative memory model under finite and extensive loading.

Findings

Identification of characteristic temporal behaviors in attractor retrieval

Derivation of evolution equations using dynamical replica theory

Theoretical results confirmed by numerical simulations

Abstract

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including correlated attractors was reported in the cases of finite and infinite loading. In this paper, by means of a statistical mechanical method, we study the statics and dynamics of the model in both finite and extensive loading, mainly focusing on the retrieval properties of the Hopfield and correlated attractors. In the extensive loading case, we derive the evolution equations by the dynamical replica theory. We found several characteristic temporal behaviours, both in the finite and extensive loading cases. The theoretical results were confirmed by numerical simulations.