DocumentCode
324565
Title
The general approximation theorem
Author
Gorban, A.N. ; Wunsch, Donald C., II
Author_Institution
Comput. Center, Acad. of Sci., Krasnoyarsk, Russia
Volume
2
fYear
1998
fDate
4-9 May 1998
Firstpage
1271
Abstract
A general approximation theorem is proved. It uniformly envelopes both the classical Stone theorem and approximation of functions of several variables by means of superpositions and linear combinations of functions of one variable. This theorem is interpreted as a statement on universal approximating possibilities (“approximating omnipotence”) of arbitrary nonlinearity. For the neural networks, our result states that the function of neuron activation must be nonlinear, and nothing else
Keywords
approximation theory; function approximation; mathematics computing; neural nets; Stone theorem; function approximation; general approximation theorem; neural networks; neuron activation function; Algebra; Books; Computational intelligence; Laboratories; Neural networks; Neurons; Piecewise linear approximation; Piecewise linear techniques; Polynomials; Region 8;
fLanguage
English
Publisher
ieee
Conference_Titel
Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence. The 1998 IEEE International Joint Conference on
Conference_Location
Anchorage, AK
ISSN
1098-7576
Print_ISBN
0-7803-4859-1
Type
conf
DOI
10.1109/IJCNN.1998.685957
Filename
685957
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