Statics and dynamics of an Ashkin-Teller neural network with low loading

TL;DR

This paper investigates an Ashkin-Teller neural network with two neuron types under low loading, analyzing its thermodynamic and dynamic properties, and demonstrating improved retrieval over Hopfield models for linked patterns.

Contribution

It introduces a detailed analysis of an Ashkin-Teller neural network with dual neuron types, focusing on low loading conditions and pattern dependence.

Findings

Linked patterns enhance retrieval performance.

The model exhibits stable Mattis states.

Flow equations describe the network's dynamic behavior.

Abstract

An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the two types of neurons, with different degrees of (in)dependence is studied. In particular, thermodynamic properties including the existence and stability of Mattis states are discussed. Furthermore, the dynamic behaviour is examined by deriving flow equations for the macroscopic overlap. It is found that for linked patterns the model shows better retrieval properties than a corresponding Hopfield model.