Approximation properties of a multilayered feedforward artificial neural network

We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can be achieved. We also discuss the problem of approximation of a compact subset of a Euclidean space with such networks with a classical sigmoidal response function.Dedicated to Dr. C.A. Micchelli on the occasion of his fiftieth birthday, December 1992Research supported in part by AFOSR Grant No. 226 113 and by the AvH Foundation.