Universality in bipartite mean field spin glasses

TL;DR

This paper proves that the free energy of bipartite mean field spin glasses is universal across different noise distributions, using advanced spin glass techniques, and applies this to show convergence in the Hopfield Model.

Contribution

It establishes universality in bipartite mean field spin glasses and demonstrates convergence of the Hopfield Model's free energy to its expected value.

Findings

Universality of free energy with respect to noise distribution.

Convergence of Hopfield Model free energy in the sup norm.

Application of Guerra's interpolation and cavity methods.

Abstract

In this work we give a proof of universality with respect to the choice of the statistical distribution of the quenched noise, for mean field bipartite spin glasses. We use mainly techniques of spin glasses theory, as Guerra's interpolation and the cavity approach. As a direct conseguence of our results, we have a proof of convergence in the sup norm of the free energy of the Hopfield Model to its expectation value.