Title :
The general approximation theorem
Author :
Gorban, A.N. ; Wunsch, Donald C., II
Author_Institution :
Comput. Center, Acad. of Sci., Krasnoyarsk, Russia
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;
Conference_Titel :
Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence. The 1998 IEEE International Joint Conference on
Conference_Location :
Anchorage, AK
Print_ISBN :
0-7803-4859-1
DOI :
10.1109/IJCNN.1998.685957
