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Universal approximation in p-mean by neural networks

✍ Scribed by Robert M. Burton; Herold G. Dehling

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 112 KB
Volume: 11
Category: Article
ISSN: 0893-6080
DOI: 10.1016/s0893-6080(98)00009-4

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✦ Synopsis

A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by

where a j , v j , w ji ʦ R. In this paper we study the approximation of arbitrary functions f: R d → R by a neural net in an L p (m) norm for some finite measure m on R d . We prove that under natural moment conditions, a neural net with non-polynomial function can approximate any given function.

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