On the Hopfield neural networks and mean field theory

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Other Title
  • ホップフィールドニューラルネットワークと平均場理論について

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Description

Recantly,it has been expected that the mean field theory network(MFT)model can be used to solve combinatorial optimization problems.This model,which is obtained by applying the mean field approximation to the Boltzmann machines,is discrete-time recurrent neural networks with symmetric weights.And it has been reported that the MFT model can obtain experimentally the promising result. However,the theoretical analysis of the MFT model has not yet been done sufficiently.In this paper,we analyze mathematically the relationship between the MFT model and the continuous Hopfield model by using theory of dynamical systems.We prove that the set of the asymptotically stable fixed points of the asynchronous MFT model is equal to the set of the asymptotically stable equilibria of the Hopfield model.The refore,it is shown that the asynchronous MFT model is equivalent to the Hopfield model on the nature of the fixed points(equilibria).

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Details 詳細情報について

  • CRID
    1573387452283897728
  • NII Article ID
    110003233335
  • NII Book ID
    AN10091178
  • Text Lang
    ja
  • Data Source
    • CiNii Articles

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