Geometrie rates of approximation by neural networks

Abstract

Model complexity of feedforward neural networks is studied in terms of rates of variable-basis approximation. Sets of functions, for which the errors in approximation by neural networks with n hidden units converge to zero geometrically fast with increasing number n, are described. However, the geometric speed of convergence depends on parameters, which are specific for each function to be approximated. The results are illustrated by examples of estimates of such parameters for functions in infinite-dimensional Hulbert spaces. © Springer-Verlag Berlin Heidelberg 2008.