Instability of frozen-in states in synchronous Hebbian neural networks

TL;DR

This paper investigates the stability of frozen-in states in synchronous Hebbian neural networks with binary units, showing that synaptic noise destabilizes these states and leads to retrieval or paramagnetic phases.

Contribution

It introduces a new method to analyze the dynamics over larger time scales and demonstrates the destabilizing effect of synaptic noise on frozen-in states.

Findings

Synaptic noise destabilizes frozen-in states.

Low stochastic noise can also destabilize frozen-in states.

The new analysis method allows longer-term dynamic tracking.

Abstract

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.