01225807

j

01225807 Gorban', A.N. A generalized approximation theorem and computational capabilities of neural networks. Sib. Zh. Vychisl. Mat. 1, No.1, 12-24 (1998). 1998 Rossijskaya Akademiya Nauk, Sibirskoe Otdelenie, Novosibirsk; Izdatel'stvo SO RAN, Novosibirsk RU artificial neural networks generalized Stone theorem adaptive connection approximation by superposition of function

http://www.sscc.ru/SibJNM/cont98.html

Author's summary: ``Computational capabilities of artificial neural networks are studied. In this connection, the classical problem arises on representating a function of several variables by means of superpositions and sums of functions of a single variable, and a new vertion of this problem appers (using only one arbitrarily chosen nonlinear function of a single variable). It has been shown that it is possible to obtain an arbitrarily exact approximation of any continuous function of several variables using the operations of summation and multiplication by a number, superposition of functions, linear functions, and one arbitrary continuous nonlinear function of a single variable. For polynomials, an algebraic version of the theorem is proven. For neural networks, the results obtained mean that the only requirement for the activation function of a neuron is nonlinearity''. S.A.Malyugin (Novosibirsk)