Opuscula Mathematica

Opuscula Math.
, no. 1
 (), 59-72
Opuscula Mathematica

Approximation properties of some two-layer feedforward neural networks

Abstract. In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\), where \(n\) is the number of function values used.
Keywords: neural networks, approximation of functions, sigmoidal function.
Mathematics Subject Classification: 41A35, 41A63, 41A25, 92B20.
Cite this article as:
Michał A. Nowak, Approximation properties of some two-layer feedforward neural networks, Opuscula Math. 27, no. 1 (2007), 59-72
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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