The number of metastable states in the generalized random orthogonal model

TL;DR

This paper investigates the count of metastable states in a generalized orthogonal neural network model, comparing it with the Hopfield model to understand the impact of orthonormality constraints.

Contribution

It provides analytical calculations and numerical verification of metastable states in the generalized orthogonal model, highlighting differences due to pattern orthonormality.

Findings

Number of metastable states calculated and verified for small systems.

Comparison shows effects of orthonormality on metastable state count.

Finite size effects are considered in the analysis.

Abstract

We calculate the number of metastable states in the generalized random orthogonal model. The results obtained are verified by exact numerical enumeration for small systems sizes but taking into account finite size effects. These results are compared with those for Hopfield model in order to examine the effect of strict orthonormality of neural network patterns on the number of metastable states.