Mean Field Theory and Self-Consistent Monte Carlo Method for Self-Organization of Formal Neuron Model : Cross-Disciplinary Physics

概要

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An Ising spin system with strong self-fields and two types of long-range antiferromagnetic interactions is investigated by a mean field theory and a self-consistent Monte Carlo (SCMC) method. Spin averages of the Ising spin system correspond to output responses of neurons for self-organization of a formal neuron model with a sigmoidal output function. Since the strong self-fields and the long-range antiferromagnetic interactions give a variety of spin averages, it is difficult to know an appropriate distribution of spin averages beforehand. An iterative procedure for mean field equations often falls into an oscillation between two sets of interative variables and fails to converge, depending on parameters and the initial distribution of spin averages. On the other hand, SCMC method is able to give spin averages independent of parameters and of initial conditions even if the iterative procedure fails to converge. SCMC method is effective and practical in finding a variety of distributions of spin averages.
社団法人日本物理学会の論文
2000-06-15