New study on neural networks: The essential order of approximation

被引：39

作者：

Wang, Jianjun ^{[1
,2
]}

Xu, Zongben ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Inst Informat & Syst Sci, Xian 710049, Shaanxi, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

NEURAL NETWORKS | 2010年 / 23卷 / 05期

基金：

中国博士后科学基金;

关键词：

The essential order of approximation; Nearly exponential type neural networks; Modulus of smoothness; MULTILAYER FEEDFORWARD NETWORKS; UNIVERSAL APPROXIMATION; HIDDEN LAYER; BOUNDS; SMOOTH;

D O I：

10.1016/j.neunet.2010.01.004

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

For the nearly exponential type of feedforward neural networks (neFNNs), the essential order of their approximation is revealed. It is proven that for any continuous function defined on a compact set of R-d, there exist three layers of neFNNs with the fixed number of hidden neurons that attain the essential order. Under certain assumption on the neFNNs, the ideal upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also proclaim the implicit relationship between the precision (speed) and the number of hidden neurons of the neFNNs. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：618 / 624

页数：7

共 32 条

[1]

[Anonymous], 1994, SCI CHINA A

[2] Approximations of functions by a multilayer perceptron: a new approach [J].

Attali, JG ;

Pages, G .

NEURAL NETWORKS, 1997, 10 (06) :1069-1081

[3] UNIVERSAL APPROXIMATION BOUNDS FOR SUPERPOSITIONS OF A SIGMOIDAL FUNCTION [J].

BARRON, AR .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1993, 39 (03) :930-945

[4]

Cao Fei-Long, 2001, Chinese Journal of Computers, V24, P903

[5] APPROXIMATION OF A FUNCTION AND ITS DERIVATIVE WITH A NEURAL NETWORK [J].

CARDALIAGUET, P ;

EUVRARD, G .

NEURAL NETWORKS, 1992, 5 (02) :207-220

[6] UNIVERSAL APPROXIMATION TO NONLINEAR OPERATORS BY NEURAL NETWORKS WITH ARBITRARY ACTIVATION FUNCTIONS AND ITS APPLICATION TO DYNAMICAL-SYSTEMS [J].

CHEN, TP ;

CHEN, H .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 1995, 6 (04) :911-917

[7] APPROXIMATION BY RIDGE FUNCTIONS AND NEURAL NETWORKS WITH ONE HIDDEN LAYER [J].

CHUI, CK ;

LI, X .

JOURNAL OF APPROXIMATION THEORY, 1992, 70 (02) :131-141

[8]

CHUI CK, 1993, MULTIVARIATE APPROXI, P7

[9]

Cybenko G., 1989, Mathematics of Control, Signals, and Systems, V2, P303, DOI 10.1007/BF02551274

[10]

Ditzian Z., 1987, Springer Series in Computational Mathematics

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