Neural subnet design by direct polynomial mapping

In a recent paper by M. Chen and M. Maury (1990), it was shown that multilayer perceptron neural networks can be used to form products of any number of inputs, thereby constructively proving universal approximation. This result is extended, and a method for the analysis and synthesis of single-input, single-output neural subnetworks is described. 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 backpropagation training and by mapping. The examples illustrate that the mapped subnets avoid local minima which backpropagation-trained subnets get trapped in and that the mapping approach is much faster