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Thermodynamics of Forgetting in a Bounded Hopfield Network — arXiv:2611.08258

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.08258
License (as archived): CC0-1.0
Archived: 2026-11-06T14:55:26.896Z
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Thermodynamics of Forgetting in a Bounded Hopfield Network — arXiv:2611.08258 — arXiv (en), https://arxiv.org/abs/2611.08258 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b4e7553ae901 (Metraipolis archive dc_b4e7553ae901, sha256 dbd9a178a5d80efc09cd5a2d1068f3171f1e7494bc7367d3f4926db571634db2)

BibTeX

@misc{dcb4e7553ae901,
  title = {Thermodynamics of Forgetting in a Bounded Hopfield Network — arXiv:2611.08258},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.08258},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b4e7553ae901; sha256 dbd9a178a5d80efc09cd5a2d1068f3171f1e7494bc7367d3f4926db571634db2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.08258. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A memory that keeps learning must also forget. The Hopfield network does not: beyond a critical number of stored patterns it falls into a state of total confusion and retrieves none of them. Parisi showed in 1986 that bounding the synaptic strength cures this pathology, since the clipping of the couplings gradually erases the oldest memories and leaves room for the new ones. In this paper we provide a thermodynamic description of the resulting network, known as the Hopfield-Parisi model. Starting from the learning rule, we show that the network is equivalent to a Hopfield model whose patterns are weighted according to their age, superimposed on a Sherrington-Kirkpatrick spin glass, both governed by the synaptic bound: a larger bound makes the memory longer, but also noisier. The theory of nonlinear networks developed in the eighties already provides, through the heuristic replica method, the equations that govern this model at any temperature, but to the best of our knowledge they have been solved only at zero temperature. We rederive them at the replica symmetric level through Guerra's interpolation and solve them at finite temperature, obtaining the phase diagram of the model together with its memory horizon, namely the largest age at which a pattern can still be retrieved. The solution shows that forgetting acts on the signal alone, the noise being the same for patterns of every age, and that the horizon is maximal at an intermediate bound which is essentially insensitive to temperature. Monte Carlo simulations of networks trained with the original learning rule support these predictions.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.dis-nn, nuovi lavori del giorno).
Categorie arXiv: Disordered Systems and Neural Networks (cond-mat.dis-nn).
Pagina del lavoro: https://arxiv.org/abs/2611.08258 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-06T14:36:20.987Z dalla pagina https://arxiv.org/list/cond-mat.dis-nn/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).