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Random features Hopfield networks generalize retrieval to previously unseen examples

Author

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  • Kalaj, Silvio
  • Lauditi, Clarissa
  • Perugini, Gabriele
  • Lucibello, Carlo
  • Malatesta, Enrico M.
  • Negri, Matteo

Abstract

It has been recently shown that a feature-learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we reveal that the network also develops attractors corresponding to previously unseen examples generated as mixtures from the same set of features. We explain this surprising behavior in terms of spurious states of the learned features: increasing the number of stored examples beyond the feature-learning transition, the model also learns to mix the features to represent both stored and previously unseen examples. We support this claim by computing the phase diagram of the model and matching the numerical results with the spinodal lines of mixed spurious states.

Suggested Citation

  • Kalaj, Silvio & Lauditi, Clarissa & Perugini, Gabriele & Lucibello, Carlo & Malatesta, Enrico M. & Negri, Matteo, 2025. "Random features Hopfield networks generalize retrieval to previously unseen examples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 678(C).
    • Handle: RePEc:eee:phsmap:v:678:y:2025:i:c:s0378437125005989
    DOI: 10.1016/j.physa.2025.130946
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    References listed on IDEAS

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    1. Agliari, Elena & Albanese, Linda & Alemanno, Francesco & Alessandrelli, Andrea & Barra, Adriano & Giannotti, Fosca & Lotito, Daniele & Pedreschi, Dino, 2023. "Dense Hebbian neural networks: A replica symmetric picture of supervised learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    2. Giulio Biroli & Tony Bonnaire & Valentin Bortoli & Marc Mézard, 2024. "Dynamical regimes of diffusion models," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    3. Agliari, Elena & Albanese, Linda & Alemanno, Francesco & Alessandrelli, Andrea & Barra, Adriano & Giannotti, Fosca & Lotito, Daniele & Pedreschi, Dino, 2023. "Dense Hebbian neural networks: A replica symmetric picture of unsupervised learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
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    1. Agliari, Elena & Fachechi, Alberto & Duarte Mourão, Paulo, 2026. "The beneficial role of noises for disentanglement tasks in modular Hebbian networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).

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