Storage capacity of a constructive learning algorithm

Details Storage capacity of a constructive learning algorithm Storage capacity of a constructive learning algorithm

1999-09-16

arxiv.org/abs/cond-mat/9909248v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages, 1 figure

Scientific paper

10.1088/0305-4470/33/9/301

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)].

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