Multilayer feedforward networks with a nonpolynomial activation function can approximate any function

Adams, 1975

Bachman, 1972

Chui, 1992, Approximation by ridge functions and neural networks with one hidden layer, Journal of Approximation Theory, 70, 131, 10.1016/0021-9045(92)90081-X

Cybenko, 1989, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals, and Systems, 2, 303, 10.1007/BF02551274

Dahmen, 1987, Some remarks on ridge functions, Approximation Theory and its Applications, 3, 2

Friedman, 1963

Funahashi, 1989, On the approximate realization of continuous mappings by neural networks, Neural Networks, 2, 183, 10.1016/0893-6080(89)90003-8

Gallant, 1988, There exists a neural network that does not make avoidable mistakes, I, 657

Hecht-Nielsen, 1989, Theory of the back propagation neural network, I, 593

Hinton, 1989, Connectionist learning procedure, Artificial Intelligence, 40, 185, 10.1016/0004-3702(89)90049-0

Hornik, 1991, Approximation capabilities of multilayer feedforward networks, Neural Networks, 4, 251, 10.1016/0893-6080(91)90009-T

Hornik, 1989, Multilayer feedforward networks are universal approximators, Neural Networks, 2, 359, 10.1016/0893-6080(89)90020-8

Irie, 1988, Capabilities of three layer perceptrons, I, 641

Lapedes, 1988, How neural networks work

LeCun, 1987, Models connexionistes de l'apprentissage

Lin, V. Ya., & Pinkus, A. (in press). Fundamentality of ridge functions. Journal of Approximation Theory.

Schwartz, 1947, Théorie générale des fonctions moyenne-périodiques, Annals of Mathematics, 48, 857, 10.2307/1969386

Stinchcombe, 1990, Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights, 10.1109/IJCNN.1990.137817

Vostrecov, 1961, Approximation of continuous functions by superposition of plane waves, Doklady Akademia Nauk SSSR (Soviet Math. Dokl.), 140, 2