Thermodynamics of fully connected Blume-Emery-Griffiths neural networks

TL;DR

This paper analyzes the thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths neural networks with ternary patterns, deriving phase diagrams and comparing with diluted models to understand their stability and capacity.

Contribution

It provides a detailed thermodynamic analysis of fully connected BEG neural networks, including phase diagrams and stability of phases, which was not previously comprehensively studied.

Findings

The retrieval phase is the largest among three-state neuron models.

The stability of the quadrupolar phase depends on temperature and pattern activity.

Comparison with diluted models highlights differences in phase behavior.

Abstract

The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks, storing ternary patterns, are studied using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the pattern activity. It is found that the retrieval phase is the largest in comparison with other three-state neuron models. Furthermore, the meaning and stability of the so-called quadrupolar phase is discussed as a function of both the temperature and the pattern activity. Where appropriate, the results are compared with the diluted version of the model.