A polynomial training algorithm for calculating perceptrons of optimal stability

Details A polynomial training algorithm for calculating perceptrons of optimal stability A polynomial training algorithm for calculating perceptrons of optimal stability

1994-07-29

arxiv.org/abs/cond-mat/9407116v3

Journal of Physics A 28(8), p. 2173-2181, 1995

Physics

Condensed Matter

11 pages, Latex, 4 EPS figures

Scientific paper

10.1088/0305-4470/28/8/011

Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast algorithm for searching optimally stable solutions of the perceptron learning problem. For random unbiased and biased patterns it is shown that the algorithm is able to find optimal solutions, if any exist, in at worst O(N^4) floating point operations. Even beyond the critical storage capacity alpha_c the algorithm is able to find locally stable solutions (with negative stability) at the same speed. There are no divergent time scales in the learning process. A full proof of convergence cannot yet be given, only major constituents of a proof are shown.

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