The Ashkin-Teller neural network near saturation

TL;DR

This paper investigates the thermodynamic and retrieval behaviors of the Ashkin-Teller neural network, a complex model extending the Hopfield network, analyzing phase diagrams and symmetry breaking in the mean-field approximation.

Contribution

It introduces a detailed analysis of the Ashkin-Teller neural network's properties, including phase diagrams and symmetry considerations, as a novel extension of classical neural network models.

Findings

Derived temperature-capacity phase diagrams for various coupling strengths

Identified unique features of the Ashkin-Teller model compared to Hopfield networks

Discussed implications of replica-symmetry breaking in the model

Abstract

The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns temperature-capacity phase diagrams are derived for different values of the two-neuron and four-neuron coupling strengths. This model can be considered as a particular non-trivial generalisation of the Hopfield model and exhibits a number of interesting new features. Some aspects of replica-symmetry breaking are discussed.