Error bounds for approximation with neural networks

被引：43

作者：

Burger, M ^{[1
]}

Neubauer, A ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, Inst Ind Math, A-4040 Linz, Austria

来源：

JOURNAL OF APPROXIMATION THEORY | 2001年 / 112卷 / 02期

基金：

奥地利科学基金会;

关键词：

neural networks; error bounds; nonlinear function approximation;

D O I：

10.1006/jath.2001.3613

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 W-m,W-r(Omega). Finally, we apply our results to a class of perceptrons and present a sufficient smoothness condition on f guaranteeing the integral representation, (C) 2001 Academic Press.

引用

页码：235 / 250

页数：16

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