Neural Networks and Chaos: Construction, Evaluation of Chaotic Networks, and Prediction of Chaos with Multilayer Feedforward Networks

摘要

Many research works deal with chaotic neural networks for various fields ofapplication. Unfortunately, up to now these networks are usually claimed to bechaotic without any mathematical proof. The purpose of this paper is toestablish, based on a rigorous theoretical framework, an equivalence betweenchaotic iterations according to Devaney and a particular class of neuralnetworks. On the one hand we show how to build such a network, on the otherhand we provide a method to check if a neural network is a chaotic one.Finally, the ability of classical feedforward multilayer perceptrons to learnsets of data obtained from a dynamical system is regarded. Various Booleanfunctions are iterated on finite states. Iterations of some of them are provento be chaotic as it is defined by Devaney. In that context, importantdifferences occur in the training process, establishing with various neuralnetworks that chaotic behaviors are far more difficult to learn.