Takashi Shinzato and Yoshiyuki Kabashima 2008 J. Phys. A: Math. Theor. 41 324013 doi:10.1088/1751-8113/41/32/324013
Takashi Shinzato and Yoshiyuki Kabashima
Show affiliationsIn this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes are developed based on the replica method and the Thouless–Anderson–Palmer (TAP) approach by utilizing an integral formula concerning random rectangular matrices. The validity and relevance of the developed methodologies are shown for one known result and two example problems. A message-passing algorithm to perform the TAP scheme is also presented.
07.05.Mh Neural networks, fuzzy logic, artificial intelligence
Issue 32 (15 August 2008)
Received 25 December 2007, in final form 27 February 2008
Published 30 July 2008
Takashi Shinzato and Yoshiyuki Kabashima 2008 J. Phys. A: Math. Theor. 41 324013
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