Local minima of a quadratic binary functional with a quasi-hebbian connection matrix

Abstract

The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight. For such matrices statistical physics methods allow one to derive an equation describing local minima of the functional. A model where only one weight differs from other ones is discussed in details. In this case the equation can be solved analytically. Obtained results are confirmed by computer simulations. © 2010 Springer-Verlag Berlin Heidelberg.