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Hopfield model with planted patterns: A teacher-student self-supervised learning model

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  • Alemanno, Francesco
  • Camanzi, Luca
  • Manzan, Gianluca
  • Tantari, Daniele

Abstract

While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student self-supervised learning problem with Boltzmann machines in terms of a suitable generalization of the Hopfield model with structured patterns, where the spin variables are the machine weights and patterns correspond to the training set's examples. We analyze the learning performance by studying the phase diagram in terms of the training set size, the dataset noise and the inference temperature (i.e. the weight regularization). With a small but informative dataset the machine can learn by memorization. With a noisy dataset, an extensive number of examples above a critical threshold is needed. In this regime the memory storage limits become an opportunity for the occurrence of a learning regime in which the system can generalize.

Suggested Citation

  • Alemanno, Francesco & Camanzi, Luca & Manzan, Gianluca & Tantari, Daniele, 2023. "Hopfield model with planted patterns: A teacher-student self-supervised learning model," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004228
    DOI: 10.1016/j.amc.2023.128253
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    References listed on IDEAS

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    1. Adriano Barra & Andrea Galluzzi & Francesco Guerra & Andrea Pizzoferrato & Daniele Tantari, 2014. "Mean field bipartite spin models treated with mechanical techniques," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(3), pages 1-13, March.
    2. De Marzo, Giordano & Iannelli, Giulio, 2023. "Effect of spatial correlations on Hopfield Neural Network and Dense Associative Memories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    3. Agliari, Elena & Leonelli, Francesca Elisa & Marullo, Chiara, 2022. "Storing, learning and retrieving biased patterns," Applied Mathematics and Computation, Elsevier, vol. 415(C).
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    Cited by:

    1. Centonze, Martino Salomone & Kanter, Ido & Barra, Adriano, 2024. "Statistical mechanics of learning via reverberation in bidirectional associative memories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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