Neural-network approximation of functions of several variables

Abstract

The main result of the work is as follows: in the Chebyshev-Hermite weighted integral metric, it is possible to approximate any function of sufficiently general form by a neural network. The approximating net consists of two layers, where the first uses any predefined sigmoid function of activation and the second uses a linear-threshold function. The Chebyshev-Hermite weight is chosen because it allows one to imitate the distribution of receptors, for example, in the eye of a human or some mammal. © 2010 Springer Science+Business Media, Inc.