The TAP approach to intensive and extensive connectivity systems

Kabashima, Yoshiyuki and Saad, David (2001). The TAP approach to intensive and extensive connectivity systems. IN: Advanced mean field methods: Theory and practice. Opper, Manfred and Saad, David (eds) Neural Information Processing . Cambridge, US: MIT.

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.

Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Non-linearity and complexity research group
Additional Information: Copyright of the Massachusetts Institute of Technology Press (MIT Press) Partially available on Google Books
Uncontrolled Keywords: Thouless-Anderson-Palmer,Sherrington-Kirkpatrick,general intensively connected systems,Hopfield associative memory model
Published Date: 2001-02
Authors: Kabashima, Yoshiyuki
Saad, David

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