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Boltzmann Machines : High-Order Interactions and Synchronous Learning

  • Robert Azencott
Part of the Lecture Notes in Statistics book series (LNS, volume 74)

Abstract

A now classical innovative paper [H.S.A.] by Hinton-Sejnowski-Ackley intro­duced a class of formal neural networks, the Boltzmann machines, governed by asynchronous stochastic dynamics, quadratic energy functions, and pairwise interac­tions defined by synaptic weights. One of the exciting aspects of [H.S.A.] was the derivation of a locally implementable learning rule linked to a scheme of decreasing (artificial) temperatures, in the spirit of simulated annealing.

Keywords

Learning Rule Gibbs Distribution Stochastic Network Boltzmann Machine Random Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [A]
    R. Azencott - - Markov fields and low-level vision tasks, Proc. Int. Cong. App. Math. ICIAM, Paris (1987).Google Scholar
  2. R. Azencott Gibbs fields, simulated annealing, and low-level vision tasks, Proc. Cong. Pattern Recognition, AFCET-INRIA, Antibes (1987).Google Scholar
  3. R. Azencott Synchronous Boltzmann machines : learning rules,Proc. Congress “Neural networks”, Les Arcs (1989), Springer-Verlag, NATO series (1990), vol. 68, Editors : Fogelman-Herault.Google Scholar
  4. R. AzencottParameter estimation for synchronous Markov fields (to appear).Google Scholar
  5. [Bo]
    P. Bourlard- Multilayer perceptions and learning, Proc. Congress “Neural networks”, Les Arcs (1989), to appear in Springer-Verlag, NATO series (1990).Google Scholar
  6. [G.G.]
    D. and S. Geman - Gibbs fields, simulated annealing, and Bayesian reconstruction of images, IEEE, PAMI (1984).Google Scholar
  7. [H.S.A.]
    G. Hinton, T. Sejnowski, D.H. Ackley - Boltzmann machines: constraint satisfaction networks that learn, Technical Report, Carnegie Mellon University (1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Robert Azencott
    • 1
    • 2
  1. 1.École Normale Supérieure (DIAM) and Université Paris-SudFrance
  2. 2.CNRS labs: [LMENS] and [Stat. App. Univ. Paris-Sud]Paris Cedex 05France

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