Parallel dynamics of the fully connected Blume-Emery-Griffiths neural network

TL;DR

This paper investigates the parallel dynamics of the fully connected Blume-Emery-Griffiths neural network at zero temperature, providing a recursive scheme for the evolution of order parameters and confirming results with simulations.

Contribution

It introduces a probabilistic recursive scheme to determine the complete time evolution of the network's order parameters, including feedback correlations.

Findings

Explicit analytic formulas for initial time steps of dynamics

Equilibrium fixed-point equations derived and validated

Analytic results confirmed by extensive simulations

Abstract

The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied at zero temperature for arbitrary using a probabilistic approach. A recursive scheme is found determining the complete time evolution of the order parameters, taking into account all feedback correlations. It is based upon the evolution of the distribution of the local field, the structure of which is determined in detail. As an illustrative example, explicit analytic formula are given for the first few time steps of the dynamics. Furthermore, equilibrium fixed-point equations are derived and compared with the thermodynamic approach. The analytic results find excellent confirmation in extensive numerical simulations.