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Constructive approximations for neural networks by sigmoidal functions

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1 Author(s)
Jones, L.K. ; Dept. of Math., Lowell Univ., MA, USA

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 σ is continuous; the proof is nonconstructive, relying on the Hahn-Branch theorem and the dual characterization of C(In ). 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

Published in:

Proceedings of the IEEE  (Volume:78 ,  Issue: 10 )

Date of Publication:

Oct 1990

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