Statistical Mechanics of Neural Networks: the Hopfield Model and the Kac-Hopfield Model

A. Bovier, V. Gayrard

1997, v.3, Issue 4, 393-422


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.

Keywords: Hopfield model,mean field theory,Kac-models,neural networks,Gibbs measures,large deviations,replica symmetry


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