Statistical mechanics of neural networks: The Hopfield model and the Kac-Hopfield model

Abstract

We survey the statistical mechanics approach to the analysis of neural networks of the Hopfield type. We consider both models on complete graphs (mean-field), random graphs (dilute model), and on regular lattices (Kac-model). We try to explain the main ideas and techniques, as well as the results obtained by them, without however going into too much technical detail. We also give a short history of the main developments in the mathematical analysis of these models over the last 20 years