Error Bounds for Approximation with Neural Networks |
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Authors: | Martin Burger Andreas Neubauer |
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Affiliation: | Institute for Industrial Mathematics, Johannes-Kepler University, A-4040, Linz, Austriaf1 |
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Abstract: | In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisfies an integral representation. We give error bounds not only in Hilbert spaces but also in general Sobolev spaces Wm, r(Ω). Finally, we apply our results to a class of perceptrons and present a sufficient smoothness condition on f guaranteeing the integral representation. |
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Keywords: | neural networks error bounds nonlinear function approximation |
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