Opuscula Math. 27, no. 1 (2007), 59-72

Opuscula Mathematica

Approximation properties of some two-layer feedforward neural networks

Michał A. Nowak

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.

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  • Michał A. Nowak
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
  • Received: 2004-05-17.
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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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