Abstract
A comprehensive theoretical framework is proposed for the learning of a class of gradient-type neural networks with an additive Gaussian white noise process. The study is based on stochastic sensitivity analysis techniques, and formal expressions are obtained for the stochastic learning laws in terms of the functional derivative sensitivity coefficients. The present method efficiently processes the learning information inherent in the stochastic correlation between the signal and corresponding noise processes without the need for actually computing equations of the back-propagation type. New stochastic implementations of the Hebbian and competitive learning laws are derived to elucidate this theoretical development.
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