Approximation capability of interpolation neural networks

It is well-known that single hidden layer feed-forward neural networks (SLFNs) with at most n hidden neurons can learn n distinct samples with zero error, and the weights connecting the input neurons and the hidden neurons and the hidden node thresholds can be chosen randomly. Namely, for n distinct samples, there exist SLFNs with n hidden neurons that interpolate them. These networks are called exact or integrable functions) not all exact interpolation networks have good approximation effect. This paper, by using a functional approach, rigorously proves that for given distinct samples there exists an SLFN which not only exactly interpolates samples but also near best approximates the target function. Crown Copyright & 2010 Published by Elsevier B.V. All rights reserved.