WIAS Preprint No. 353, (1997)

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


Authors

  • Bovier, Anton
  • Gayrard, Véronique

2010 Mathematics Subject Classification

  • 82B44 82C32 60K35

Keywords

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

DOI

10.20347/WIAS.PREPRINT.353

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.

Appeared in

  • Markov Proc. Related Fields, 3 (1997), pp. 393-423

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