Estimates of the Number of Hidden Units and Variation with Respect to Half-Spaces

We estimate variation with respect to half-spaces in terms of “flows through hyperplanes”. Our estimate is derived from an integral representation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequently we obtain condition...

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Published in:Neural networks 1997-08, Vol.10 (6), p.1061-1068
Main Authors: Kůrková, Věra, Kainen, Paul C., Kreinovich, Vladik
Format: Article
Language:English
Subjects:
Applied sciences
Approximation of functions
Artificial intelligence
Computer science
control theory
systems
Connectionism. Neural networks
Exact sciences and technology
One-hidden-layer sigmoidal networks – Estimates of the number of hidden units – Variation with respect to half-spaces – Integral representation
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description We estimate variation with respect to half-spaces in terms of “flows through hyperplanes”. Our estimate is derived from an integral representation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequently we obtain conditions which guarantee approximation error rate of order O 1/ n by one-hidden-layer networks with n sigmoidal perceptrons. © 1997 Elsevier Science Ltd.
doi_str_mv 10.1016/S0893-6080(97)00028-2
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source ScienceDirect Freedom Collection 2022-2024
subjects Applied sciences
Approximation of functions
Artificial intelligence
Computer science
control theory
systems
Connectionism. Neural networks
Exact sciences and technology
One-hidden-layer sigmoidal networks – Estimates of the number of hidden units – Variation with respect to half-spaces – Integral representation
title Estimates of the Number of Hidden Units and Variation with Respect to Half-Spaces
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