On rates of convergence for the overlap in the Hopfield model

TL;DR

This paper uses Stein's method to analyze the convergence rates of the overlap parameters' distribution in the Hopfield model with many neurons and patterns, establishing a central limit theorem for almost all pattern realizations.

Contribution

It provides explicit convergence rates for the CLT of overlap parameters in the Hopfield model, a novel application of Stein's method in this context.

Findings

Established rates of convergence for the overlap's CLT.

Proved the CLT holds for almost all pattern realizations.

Applicable to models with increasing pattern numbers.

Abstract

We consider the Hopfield model with $n$ neurons and an increasing number $p=p(n)$ of randomly chosen patterns and use Stein's method to obtain rates of convergence for the central limit theorem of overlap parameters, which holds for every fixed choice of the overlap parameter for almost all realisations of the random patterns.