Transcription of Multilayer Feedforward Networks are Universal Approximators
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Neural Networks , Vol. 2, pp. 35Y-366, 198Y Printed in the USA. All nghts reserved. OX!%hOXO189 $ + .oo Copyright ( 8 lY8Y Pcrgamon Press plc ORIGINAL CONTRIBUTION Multilayer Feedforward Networks are Universal Approximators KURTHORNIK Technische Universittit Wien MAXWELL~TINCHCOMBE AND HALBERTWHITE University of California, San Diego (Received 16 September 19X8; revised und acrepled 9 March 1989) Abstract-This paper rigorously establishes thut standard rnultiluyer Feedforward Networks with as f&v us one hidden layer using arbitrary squashing functions ure capable of upproximating uny Bore1 measurable function from one finite dimensional space to another to any desired degree of uccuracy, provided sujficirntly muny hidden units are available. In this sense, Multilayer Feedforward Networks are u class of universul rlpproximators. Keywords- Feedforward Networks , Universal approximation, Mapping Networks , Network representation capability, Stone-Weierstrass Theorem.)
Kolmogorov’s (1957) superposition theorem or its more recent improvements (e.g.. Lorentz, 1976) in support of their capabilities. However, these results require a different unknown transformation (g in Lorentz’s notation) for each continuous function to be represented, while specifying an exact upper limit
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