Approximation bounds by neural networks in LωP

Jianjun Wang; Zongben Xu; Weijun Xu

doi:10.1007/978-3-540-28647-9_1

Approximation bounds by neural networks in L_ω^P

Jianjun Wang
, Zongben Xu
, Weijun Xu

数学与统计学院

Xi'an Jiaotong University

科研成果: 书/报告/会议事项章节 › 章节 › 同行评审

5 引用（Scopus）

摘要

We consider approximation of multidimensional functions by feedforward neural networks with one hidden layer of Sigmoidal units and a linear output. Under the Orthogonal polynomials basis and certain assumptions of activation functions in the neural network, the upper bounds on the degree of approximation are obtained in the class of functions considered in this paper. The order of approximation O(n^-r/d), d being dimension, n the number of hidden neurons, and r the natural number.

源语言	英语
主期刊名	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
编辑	Fuliang Yin, Chengan Guo, Jun Wang
出版商	Springer Verlag
页	1-6
页数	6
ISBN（印刷版）	3540228411, 9783540228417
DOI	https://doi.org/10.1007/978-3-540-28647-9_1
出版状态	已出版 - 2004

出版系列

姓名	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
卷	3173
ISSN（印刷版）	0302-9743
ISSN（电子版）	1611-3349

访问文件

10.1007/978-3-540-28647-9_1

其它文件与链接

链接到 Scopus 的出版物

引用此

Wang, J., Xu, Z., & Xu, W. (2004). Approximation bounds by neural networks in L_ω^P. 在 F. Yin, C. Guo, & J. Wang (编辑), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (页码 1-6). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 卷 3173). Springer Verlag. https://doi.org/10.1007/978-3-540-28647-9_1

Wang, Jianjun ; Xu, Zongben ; Xu, Weijun. / Approximation bounds by neural networks in L_ω^P. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 编辑 / Fuliang Yin ; Chengan Guo ; Jun Wang. Springer Verlag, 2004. 页码 1-6 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Approximation bounds by neural networks in LωP",

abstract = "We consider approximation of multidimensional functions by feedforward neural networks with one hidden layer of Sigmoidal units and a linear output. Under the Orthogonal polynomials basis and certain assumptions of activation functions in the neural network, the upper bounds on the degree of approximation are obtained in the class of functions considered in this paper. The order of approximation O(n-r/d), d being dimension, n the number of hidden neurons, and r the natural number.",

author = "Jianjun Wang and Zongben Xu and Weijun Xu",

year = "2004",

doi = "10.1007/978-3-540-28647-9\_1",

language = "英语",

isbn = "3540228411",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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editor = "Fuliang Yin and Chengan Guo and Jun Wang",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Wang, J, Xu, Z & Xu, W 2004, Approximation bounds by neural networks in L_ω^P. 在 F Yin, C Guo & J Wang (编辑), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 卷 3173, Springer Verlag, 页码 1-6. https://doi.org/10.1007/978-3-540-28647-9_1

Approximation bounds by neural networks in L_ω^P. / Wang, Jianjun; Xu, Zongben; Xu, Weijun.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 编辑 / Fuliang Yin; Chengan Guo; Jun Wang. Springer Verlag, 2004. 页码 1-6 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 卷 3173).

科研成果: 书/报告/会议事项章节 › 章节 › 同行评审

TY - CHAP

T1 - Approximation bounds by neural networks in LωP

AU - Wang, Jianjun

AU - Xu, Zongben

AU - Xu, Weijun

PY - 2004

Y1 - 2004

N2 - We consider approximation of multidimensional functions by feedforward neural networks with one hidden layer of Sigmoidal units and a linear output. Under the Orthogonal polynomials basis and certain assumptions of activation functions in the neural network, the upper bounds on the degree of approximation are obtained in the class of functions considered in this paper. The order of approximation O(n-r/d), d being dimension, n the number of hidden neurons, and r the natural number.

AB - We consider approximation of multidimensional functions by feedforward neural networks with one hidden layer of Sigmoidal units and a linear output. Under the Orthogonal polynomials basis and certain assumptions of activation functions in the neural network, the upper bounds on the degree of approximation are obtained in the class of functions considered in this paper. The order of approximation O(n-r/d), d being dimension, n the number of hidden neurons, and r the natural number.

UR - https://www.scopus.com/pages/publications/84941165858

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DO - 10.1007/978-3-540-28647-9_1

M3 - 章节

AN - SCOPUS:84941165858

SN - 3540228411

SN - 9783540228417

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 6

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Yin, Fuliang

A2 - Guo, Chengan

A2 - Wang, Jun

PB - Springer Verlag

ER -

Wang J, Xu Z, Xu W. Approximation bounds by neural networks in L_ω^P. 在 Yin F, Guo C, Wang J, 编辑, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. 页码 1-6. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-28647-9_1

Approximation bounds by neural networks in LωP

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Approximation bounds by neural networks in L_ω^P