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

Abstract

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.

Publication DOI: https://doi.org/10.1088/1751-8121/aa8fd7
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
College of Engineering & Physical Sciences
Additional Information: 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)
Uncontrolled Keywords: Hopfield model,associative memory,stability,statistical physics
Publication ISSN: 1751-8121
Full Text Link: http://iopscien ... 121/aa8fd7/meta
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PURE Output Type: Article
Published Date: 2017-10-23
Accepted Date: 2017-09-29
Authors: Rocchi, Jacopo
Saad, David (ORCID Profile 0000-0001-9821-2623)
Tantari, Daniele

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