Storage capacity of a constructive learning algorithm
Abstract
Upper and lower bounds for the typical storage capacity of a constructive algorithm, the Tilinglike Learning Algorithm for the Parity Machine [M. Biehl and M. Opper, Phys. Rev. A {\bf 44} 6888 (1991)], are determined in the asymptotic limit of large training set sizes. The properties of a perceptron with threshold, learning a training set of patterns having a biased distribution of targets, needed as an intermediate step in the capacity calculation, are determined analytically. The lower bound for the capacity, determined with a cavity method, is proportional to the number of hidden units. The upper bound, obtained with the hypothesis of replica symmetry, is close to the one predicted by Mitchinson and Durbin [Biol. Cyber. {\bf 60} 345 (1989)].
Keywords
Cite
@article{arxiv.cond-mat/9909248,
title = {Storage capacity of a constructive learning algorithm},
author = {Arnaud Buhot and Mirta B. Gordon},
journal= {arXiv preprint arXiv:cond-mat/9909248},
year = {2009}
}
Comments
13 pages, 1 figure