A replica approach to the state-dependent synapses neural network

TL;DR

This paper applies the replica method to analyze a neural network with state-dependent synapses, examining its storage capacity and comparing results with existing mean-field approaches.

Contribution

It introduces a replica-based analysis for a neural network with state-dependent synapses, providing new insights into its storage capacity and symmetry-breaking effects.

Findings

Replica-symmetric results for storage capacity

First-step replica-symmetry-breaking results

Comparison with mean-field equations

Abstract

The replica method is applied to a neural network model with state-dependent synapses built from those patterns having a correlation with the state of the system greater than a certain threshold. Replica-symmetric and first-step replica-symmetry-breaking results are presented for the storage capacity at zero temperature as a function of this threshold value. A comparison is made with existing results based upon mean-field equations obtained by using a statistical method.