The General Approximation Theorem
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.
A. N. Gorban and D. C. Wunsch, "The General Approximation Theorem," Neural Netrowks Proceedings, 1998. IEEE World Congress on Computational Intelligence. IEEE / INNS International Joint Conference on Neural Networks '98, vol. 2, pp. 1271-1274, Institute of Electrical and Electronics Engineers (IEEE), Jan 1998.
The definitive version is available at http://dx.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
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