A constructive method for multivariate function approximation by multilayer perceptrons

Abstract

Mathematical theorems establish the existence of feedforward multilayered neural networks, based on neurons with sigmoidal transfer functions, that approximate arbitrarily well any continuous multivariate function. However, these theorems do not provide any hint on how to find the network parameters in practice. It is shown how to construct a perceptron with two hidden layers for multivariate function approximation. Such a network can perform function approximation in the same manner as networks based on Gaussian potential functions, by linear combination of local functions.