The Ridge Function Representation of Polynomials and an Application to Neural Networks

被引：7

作者：

Xie, Ting Fan ^{[1
]}

Cao, Fei Long ^{[1
]}

机构：

[1] China Jiliang Univ, Dept Informat & Math Sci, Hangzhou 310018, Zhejiang, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Ridge function; neural network; polynomial; approximation; UNIVERSAL APPROXIMATION; ERROR-BOUNDS;

D O I：

10.1007/s10114-011-9407-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.

引用

页码：2169 / 2176

页数：8

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