Chaos in Back Propagation Neural Networks and its Control

Abstract

It is interesting to determine the states of the neural network (NN) when it falls into chaos. This is because chaos has been found in biological brain. This paper investigates the several chaotic behaviors of supervised neural networks using Lyapunov exponent (LE), Hurst Exponent (HE), fractal dimension (FD) and bifurcation diagram. The update rule for NN trained with back propagation (BP) algorithm contains the function of the form exhibiting chaos in the output of the network at increased learxn (i1n-gx ,r)a twe.h Tichhe i sH rEe sipso cnosmibpleu tfeodr from the time series taken from the output of a NN. One can comment on the classification of the network from the values of HEs. We have examined the chaotic dynamics of NNs for two-bit parity, cancer, and diabetes classification problems. It is found that the distribution network output is absorbed at the increase of size of the network. As a result chaosness is margiially reduced.