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

Michał A. Nowak, Approximation properties of some two-layer feedforward neural networks, Opuscula Math. 27, no. 1 (2007), 59-72

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