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Storage capacity of a constructive learning algorithm

Arnaud Buhot·Mirta B. Gordon
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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)].

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Arnaud Buhot, Mirta B. Gordon. 1999-09-16. Storage capacity of a constructive learning algorithm. https://doi.org/10.1088/0305-4470%2F33%2F9%2F301

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