Information Geometry of Mean Field Theory

Toshiyuki TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.5   pp.709-715
Publication Date: 1996/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Neural Networks
neural networks,  mean field theory,  simulated annealing,  information geometry,  optimization problem.,  

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The mean field theory has been recognized as offering an efficient computational framework in solving discrete optimization problems by neural networks. This paper gives a formulation based on the information geometry to the mean field theory, and makes clear from the information-theoretic point of view the meaning of the mean field theory as a method of approximating a given probability distribution. The geometrical interpretation of the phase transition observed in the mean field annealing is shown on the basis of this formulation. The discussion of the standard mean field theory is extended to introduce a more general computational framework, which we call the generalized mean field theory.