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Random interactions in higher order neural networksRecurrent networks of polynomial threshold elements with random symmetric interactions are studied. Precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability. In particular, it is shown that there is a critical range of margins of stability (depending on the degree of polynomial interaction) such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network, while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network. The random energy model is also briefly examined and links with higher order neural networks and higher order spin glass models made explicit.
Document ID
19930048796
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Baldi, Pierre
(JPL Pasadena, CA, United States)
Venkatesh, Santosh S.
(Pennsylvania Univ. Philadelphia, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1993
Publication Information
Publication: IEEE Transactions on Information Theory
Volume: 39
Issue: 1
ISSN: 0018-9448
Subject Category
Cybernetics
Accession Number
93A32793
Funding Number(s)
CONTRACT_GRANT: NSF EET-87-09198
CONTRACT_GRANT: NSF DMS-88-00322
CONTRACT_GRANT: AF-AFOSR-89-0523
Distribution Limits
Public
Copyright
Other

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