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Constructive function-approximation by three-layer artificial neural networks

✍ Scribed by Shin Suzuki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
493 KB
Volume
11
Category
Article
ISSN
0893-6080

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✦ Synopsis

Constructive theorems of three-layer artificial neural networks with (1) trigonometric, (2) piecewise linear, and (3) sigmoidal hidden-layer units are proved in this paper. These networks approximate 2p-periodic pth-order Lebesgue-integrable functions (L p 2p ) on R m to R n for p Υ† 1 with L p 2p ΒΉ norm. (In the case of (1), the networks also approximate 2p-periodic continuous functions (C 2p ) with C 2p -norm.) These theorems provide explicit equational representations of these approximating networks, specifications for their numbers of hidden-layer units, and explicit formulations of their approximation-error estimations. The function-approximating networks and the estimations of their approximation errors can practically and easily be calculated from the results. The theorems can easily be applied to the approximation of a nonperiodic function defined in a bounded set on R m to R n .

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