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A spectral approach to Hebbian-like neural networks

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  • Agliari, Elena
  • Fachechi, Alberto
  • Luongo, Domenico

Abstract

We consider the Hopfield neural network as a model of associative memory and we define its neuronal interaction matrix J as a function of a set of K×M binary vectors {ξμ,A}μ=1,...,KA=1,...,M representing a sample of the reality that we want to retrieve. In particular, any item ξμ,A is meant as a corrupted version of an unknown ground pattern ζμ, that is the target of our retrieval process. We consider and compare two definitions for J, referred to as supervised and unsupervised, according to whether the class μ, each example belongs to, is unveiled or not, also, these definitions recover the paradigmatic Hebb's rule under suitable limits. The spectral properties of the resulting matrices are studied and used to inspect the retrieval capabilities of the related models as a function of their control parameters.

Suggested Citation

  • Agliari, Elena & Fachechi, Alberto & Luongo, Domenico, 2024. "A spectral approach to Hebbian-like neural networks," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001619
    DOI: 10.1016/j.amc.2024.128689
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    References listed on IDEAS

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    1. Zhu, Lei & Xu, Wei-wei, 2016. "The inverse eigenvalue problem of structured matrices from the design of Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1-7.
    2. Galluccio, Stefano & Bouchaud, Jean-Philippe & Potters, Marc, 1998. "Rational decisions, random matrices and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 259(3), pages 449-456.
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