Local Minima of a Quadratic Binary Functional with Quasi-Hebbian Connection Matrix

Details Local Minima of a Quadratic Binary Functional with Quasi-Hebbian Connection Matrix Local Minima of a Quadratic Binary Functional with Quasi-Hebbian Connection Matrix

2010-05-24

arxiv.org/abs/1005.4285v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 8 figures

Scientific paper

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 above-mention equation can be solved analytically. Obtained results are confirmed by computer simulations.

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