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
D. C. Wunsch and A. N. Gorban, "The General Approximation Theorem," Proceedings of the 1998 IEEE International Joint Conference on Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence, vol. 2, pp. 1271-1274, Institute of Electrical and Electronics Engineers (IEEE), Jan 1998.
The definitive version is available at https://doi.org/10.1109/IJCNN.1998.685957
IEEE World Congress on Computational Intelligence (WCCI'98) (1998: May 4-9, Anchorage, AK)
Electrical and Computer Engineering
Keywords and Phrases
Stone Theorem; Approximation Theory; Function Approximation; General Approximation Theorem; Mathematics Computing; Neural Nets; Neural Networks; Neuron Activation Function
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Article - Conference proceedings
© 1998 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
01 Jan 1998