A polynomial training algorithm for calculating perceptrons of optimal stability

TL;DR

Recomi is a polynomial-time algorithm that efficiently finds optimally stable perceptron solutions, including in challenging regimes beyond the critical capacity, with proven convergence properties.

Contribution

Introduces Recomi, a polynomially fast algorithm for finding stable perceptron solutions, extending applicability beyond the critical storage capacity.

Findings

Finds optimal perceptron solutions in O(N^4) operations

Successfully locates locally stable solutions beyond critical capacity

No divergent time scales observed in learning process

Abstract

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.