UNIVERSAL APPROXIMATION USING FEEDFORWARD NEURAL NETWORKS - A SURVEY OF SOME EXISTING METHODS, AND SOME NEW RESULTS

In this paper, we present a review of some recent works on approximati on by feedforward neural networks. A particular emphasis is placed on the computational aspects of the problem, i.e. we discuss the possibil ity of realizing a feedforward neural network which achieves a prescri bed degree of accuracy of approximation, and the determination of the number of hidden layer neurons required to achieve this accuracy. Furt hermore, a unifying framework is introduced to understand existing app roaches to investigate the universal approximation problem using feedf orward neural networks. Some new results are also presented. Finally, two training algorithms are introduced which can determine the weights of feedforward neural networks, with sigmoidal activation neurons, to any degree of prescribed accuracy. These training algorithms are desi gned so that they do not suffer from the problems of local minima whic h commonly affect neural network learning algorithms. (C) 1998 Elsevie r Science Ltd. All rights reserved.