Approximation Capability to Compact Sets of Functions and Operators by Feedforward Neural Networks

This paper is concerned with the approximation capability of feedforward neural networks to a compact set of functions. We follow a general approach that covers all the existing results and gives some new results in this respect. To elaborate, we have proved the following: If a family of feedforward neural networks is dense in H, a complete linear metric space of functions, then given a compact set V subH and an error bound epsiv, one can fix the quantity of the hidden neurons and the weights between the input and hidden layers, such that in order to approximate any function f isinV with accuracy epsiv, one only has to further choose suitable weights between the hidden and output layers. We also apply our theorem to the problem of system identification, or approximation to an operator, by neural networks.