Information-theoretic Aspects of Neural Stochastic Resonance
Joseph C. Park
Department of Ocean Engineering,
Florida Atlantic University,
Boca Raton, FL, USA
P. S. Neelakanta
Department of Electrical Engineering,
Florida Atlantic University,
Boca Raton, FL, USA
Abstract
Information flow through a neural network learning to recognize state-transition statistics produced from a nonlinear, bistable detector under conditions of stochastic resonance (SR) is investigated. The information flow dynamics are examined in terms of an information-theoretic cost-function defined by the relative informational entropy associated with an ensemble of training sets averaged over the temporal evolution of training cycles. The network architecture consists of a multilayer perceptron evolving under the guidance of the backpropagation algorithm. For the purpose of emulating SR, a Schmitt-trigger logic is utilized as the nonlinear detector, and generates state-transitions exhibiting SR in response to a sine-wave signal superimposed with gaussian noise. The output statistics of the Schmitt trigger are used to train the multilayer perceptron towards recognizing the extent of SR present in the detector state-transition dynamics. It is demonstrated that information flow dynamics under conditions of SR are inherently more informatic (or less negentropic) than cases wherein the state-transition statistics are dominated by nonSR conditions, that is, under higher or lower signal-to-threshold ratios. Some details concerning SR in relation to biological neurons are also discussed.
