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On the approximate realization of continuous mappings by neural networks

โœ Scribed by Ken-Ichi Funahashi

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
733 KB
Volume
2
Category
Article
ISSN
0893-6080

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โœฆ Synopsis

In this paper, we prove that any continuous mapping can be approximately realized by Rumelhart-Hinton-Williams' multilayer neural networks with at least one hidden layer whose output functions are sigmoid functions. The starting point of the proof for the one hidden layer case is an integral formula recently proposed by Irie-Miyake and from this, the general case (for any number of hidden layers) can be proved by induction. The two hidden layers case is proved also by using the Kolmogorov-Arnold-Sprecher theorem and this proof also gives non-trivial realizations.

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