Time evolution of the extremely diluted Blume-Emery-Griffiths neural network

TL;DR

This paper investigates the dynamic behavior of an extremely diluted Blume-Emery-Griffiths neural network, revealing phase diagrams and the impact of saddle-point solutions on network convergence, with comparisons to similar three-state models.

Contribution

It provides a detailed analysis of the time evolution and phase structure of the model, highlighting the role of fluctuation overlaps and comparing performance with other three-state networks.

Findings

Identification of distinct phases including pattern and fluctuation retrieval

Saddle-point solutions slow down network convergence

Performance comparison with other three-state networks

Abstract

The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases. It is shown that saddle-point solutions associated with fluctuation overlaps slow down considerably the flow of the network states towards the retrieval fixed points. A comparison of the performance with other three-state networks is also presented.