RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 1999, Volume 118, Number 1, Pages 133–158 (Mi tmf691)  

This article is cited in 6 scientific papers (total in 6 papers)

High-symmetry Hopfield-type neural networks

L. B. Litinskii

Institute for High Pressure Physics, Russian Academy of Sciences

Abstract: We study the set of fixed points of a Hopfield-type neural network with a connection matrix constructed from a high-symmetry set of memorized patterns using the Hebb rule. The memorized patterns depending on an external parameter are interpreted as distorted copies of a vector standard to be learned by the network. The dependence of the fixed-point set of the network on the distortion parameter is described analytically. The investigation results are interpreted in terms of neural networks and the Ising model.

DOI: https://doi.org/10.4213/tmf691

Full text: PDF file (364 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1999, 118:1, 107–127

Bibliographic databases:

Received: 04.06.1998

Citation: L. B. Litinskii, “High-symmetry Hopfield-type neural networks”, TMF, 118:1 (1999), 133–158; Theoret. and Math. Phys., 118:1 (1999), 107–127

Citation in format AMSBIB
\Bibitem{Lit99}
\by L.~B.~Litinskii
\paper High-symmetry Hopfield-type neural networks
\jour TMF
\yr 1999
\vol 118
\issue 1
\pages 133--158
\mathnet{http://mi.mathnet.ru/tmf691}
\crossref{https://doi.org/10.4213/tmf691}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702824}
\zmath{https://zbmath.org/?q=an:0942.82023}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 1
\pages 107--127
\crossref{https://doi.org/10.1007/BF02557200}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079262300010}


Linking options:
  • http://mi.mathnet.ru/eng/tmf691
  • https://doi.org/10.4213/tmf691
  • http://mi.mathnet.ru/eng/tmf/v118/i1/p133

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Phys. Usp., 44:4 (2001), 424–427  mathnet  crossref  crossref  isi
    2. Litinskii L.B., “Generalization in the Hopfield model”, International Joint Conference on Neural Networks, 2001, 65–70  isi
    3. L. B. Litinskii, “Hopfield Model with a Dynamic Threshold”, Theoret. and Math. Phys., 130:1 (2002), 136–151  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Litinskii, LB, “Rigorous results for the Hopfield-type neural networks”, Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment, 502:2–3 (2003), 537  crossref  adsnasa  isi  scopus  scopus  scopus
    5. Litinskii L., “Minimization of Quadratic Binary Functional with Additive Connection Matrix”, Artificial Neural Networks - ICANN 2009, Lecture Notes in Computer Science, 5768, 2009, 161–170  crossref  isi  scopus  scopus  scopus
    6. Karandashev Ya.M., Kryzhanovsky B.V., Litinskii L.B., “Strong instability of the minima spectrum of a quadratic binary functional”, Doklady Mathematics, 83:1 (2011), 116–120  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:245
    Full text:136
    References:49
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020