Synchronous versus sequential updating in the three-state Ising neural network with variable dilution

TL;DR

This paper compares synchronous and sequential updating in a three-state Ising neural network with variable dilution, analyzing thermodynamic, retrieval, and dynamic properties to understand their differences and effects.

Contribution

It provides a comprehensive analysis of the effects of updating schemes and dilution on the network's properties using replica mean-field theory and generating function techniques.

Findings

Capacity-temperature phase diagrams vary with dilution and activity.

Self-coupling influences network performance.

Differences between synchronous and sequential updating are characterized.

Abstract

The three-state Ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate Hamiltonians. The thermodynamic and retrieval properties are examined using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution, and the information content is calculated. The results are compared with those for sequential updating. The effect of self-coupling is established. Also the dynamics is studied using the generating function technique for both synchronous and sequential updating. Typical flow diagrams for the overlap order parameter are presented. The differences with the signal-to-noise approach are outlined.