Introduction to the theory of neural computation
Introduction to the theory of neural computation
Collective phenomena in neural networks
Models of neural networks
Properties of the hopfield model with weighted patterns
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
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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.