Constructive approximations for neural networks by sigmoidal functions

Constructive approximations for neural networks by sigmoidal functions

A constructive algorithm for uniformly approximating real continuous mappings by linear combinations of bounded sigmoidal functions is given. G. Cybenko (1989) has demonstrated the existence of uniform approximations to any continuous f provided that sigma is continuous; the proof is nonconstructive...

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Veröffentlicht in:Proceedings of the IEEE 1990-10, Vol.78 (10), p.1586-1589
1. Verfasser: Jones, L.K.
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Frequency
Mathematics
Neural networks
Neurons
Pursuit algorithms
Visualization
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description A constructive algorithm for uniformly approximating real continuous mappings by linear combinations of bounded sigmoidal functions is given. G. Cybenko (1989) has demonstrated the existence of uniform approximations to any continuous f provided that sigma is continuous; the proof is nonconstructive, relying on the Hahn-Branch theorem and the dual characterization of C(I/sup n/). Cybenko's result is extended to include any bounded sigmoidal (even nonmeasurable ones). The approximating functions are explicitly constructed. The number of terms in the linear combination is minimal for first-order terms.< >
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subjects Frequency
Mathematics
Neural networks
Neurons
Pursuit algorithms
Visualization
title Constructive approximations for neural networks by sigmoidal functions
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