Neural network approximation and estimation of functions

Approximation and estimation bounds were obtained by Barron (see Proc. of the 7th Yale workshop on adaptive and learning systems, 1992, IEEE Transactions on Information Theory, vol.39, pp.930-944, 1993 and Machine Learning, vol.14, p.113-143, 1994) for function estimation by single hidden-layer neural nets. This paper highlights the extension of his results to the two hidden-layer case. The bounds derived for the two hidden-layer case depend on the number of nodes T/sub 1/ and T/sub 2/ in each hidden-layer, and also on the sample size N. It is seen from our bounds that in some cases, an exponentially large number of nodes, and hence parameters, is not required.