NEURAL SUBNET DESIGN BY DIRECT POLYNOMIAL MAPPING

In a recent paper by two of the authors, it was shown that multilayer perceptron neural networks can be used to form products of any number of inputs, thereby constructively proving universal approximation. In this letter we extend this result, describing a new method for the analysis and synthesis of single-input, single-output neural subnetworks. Given training samples of a function to be approximated, a feedforward neural network is designed which implements a polynomial approximation of the function with arbitrary accuracy. For comparison, example subnets are designed by classical back-propagation training and by mapping. The examples illustrate that (1) our mapped subnets avoid local minima which back-propagation-trained subnets get trapped in and that (2) the mapping approach is much faster.