Approximation by superpositions of a sigmoidal function
نویسندگان
چکیده
منابع مشابه
Approximation by Superpositions of a Sigmoidal Function*
Abstr,,ct. In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of sing...
متن کاملApproximation by superpositions of a sigmoidal function
We generalize a result of Gao and Xu [4] concerning the approximation of functions of bounded variation by linear combinations of a fixed sigmoidal function to the class of functions of bounded φ-variation (Theorem 2.7). Also, in the case of one variable, [1: Proposition 1] is improved. Our proofs are similar to that of [4].
متن کاملApproximation by Superpositions of a Sigmoidal Function*
Abstr,,ct. In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of sing...
متن کاملApproximation by Superpositions of a Sigmoidal Function*
Abstr,,ct. In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of sing...
متن کاملUniversal approximation bounds for superpositions of a sigmoidal function
Approximation properties of a class of artificial neural networks are established. It is shown that feedforward networks with one layer of sigmoidal nonlinearities achieve inte grated squared error of order O(l/n), where n is the number of nodes. The function appruximated is assumed to have a bound on the first moment of the magnitude distribution of the Fourier transform. The nonlinear parame...
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ژورنال
عنوان ژورنال: Mathematics of Control, Signals, and Systems
سال: 1992
ISSN: 0932-4194,1435-568X
DOI: 10.1007/bf02134016