The TAP approach to intensive and extensive connectivity systems

Yoshiyuki Kabashima, David Saad

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.
Original languageEnglish
Title of host publicationAdvanced mean field methods: Theory and practice
EditorsManfred Opper, David Saad
Place of PublicationCambridge, US
PublisherMIT
Pages51-65
Number of pages15
ISBN (Print)0262150549
Publication statusPublished - Feb 2001

Publication series

NameNeural Information Processing
PublisherMassachusetts Institute of Technology Press (MIT Press)

Bibliographical note

Copyright of the Massachusetts Institute of Technology Press (MIT Press) Partially available on Google Books

Keywords

  • Thouless-Anderson-Palmer
  • Sherrington-Kirkpatrick
  • general intensively connected systems
  • Hopfield associative memory model

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  • Research Output

    Advanced mean field methods: theory and practice

    Opper, M. (ed.) & Saad, D. (ed.), Feb 2001, Cambridge, Massachusetts (US): MIT. 287 p. (Neural Information Processing)

    Research output: Book/ReportBook

  • Cite this

    Kabashima, Y., & Saad, D. (2001). The TAP approach to intensive and extensive connectivity systems. In M. Opper, & D. Saad (Eds.), Advanced mean field methods: Theory and practice (pp. 51-65). (Neural Information Processing). MIT.