High storage capacity in the Hopfield model with auto-interactions - stability analysis

Jacopo Rocchi, David Saad, Daniele Tantari

Research output: Contribution to journalArticlepeer-review


Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that they exhibit instabilities for small perturbations and are therefore of limited value as
associative memories. Moreover, a large deviations approach also shows that errors introduced to the original patterns induce additional errors and increased corruption with respect to the stored patterns.
Original languageEnglish
Article number465001
Number of pages9
JournalJournal of Physics A: Mathematical and Theoretical
Publication statusPublished - 23 Oct 2017

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://iopscience.iop.org/article/10.1088/1751-8121/aa8fd7/meta.

Funding: The Leverhulme Trust grant RPG-2013-48, National Group of Mathematical Physics (GNFM-Indam)


  • Hopfield model
  • associative memory
  • stability
  • statistical physics


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