Perceptron capacity revisited: classification ability for correlated patterns
Disordered Systems and Neural Networks
2016-12-15 v1 Statistical Mechanics
Abstract
In 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 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.
Cite
@article{arxiv.0712.4050,
title = {Perceptron capacity revisited: classification ability for correlated patterns},
author = {Takashi Shinzato and Yoshiyuki Kabashima},
journal= {arXiv preprint arXiv:0712.4050},
year = {2016}
}