Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

TL;DR

This paper investigates the stationary states and dynamics of a recurrent neural network with symmetric sequence processing, revealing phase diagrams with various stable states and effects of noise and self-interactions.

Contribution

It introduces a detailed analysis of phase diagrams for a recurrent neural network model with symmetric sequence processing and self-interactions, expanding understanding of its stationary states.

Findings

Identified phases of retrieval, symmetric, and period-two cyclic states.

Showed that synaptic noise destabilizes frozen-in states.

Demonstrated that self-interactions influence the size of fixed-point and cyclic phases.

Abstract

The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilised by synaptic noise and well separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.