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 approximation by feedforward neural networks. A particular emphasis is placed on the computational aspects of the problem, i.e. we discuss the possibility of realizing a feedforward neural network which achieves a prescribed degree of accuracy of approximation, and the determination of the number of hidden layer neurons required to achieve this accuracy. Furthermore, a unifying framework is introduced to understand existing approaches to investigate the universal approximation problem using feedforward 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 designed so that they do not suffer from the problems of local minima which commonly affect neural network learning algorithms.