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

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

5 Scopus citations

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.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Fuliang Yin, Chengan Guo, Jun Wang
Publisher	Springer Verlag
Pages	1-6
Number of pages	6
ISBN (Print)	3540228411, 9783540228417
DOIs	https://doi.org/10.1007/978-3-540-28647-9_1
State	Published - 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3173
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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

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Wang, J., Xu, Z., & Xu, W. (2004). Approximation bounds by neural networks in L_ω^P. In F. Yin, C. Guo, & J. Wang (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 1-6). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 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). editor / Fuliang Yin ; Chengan Guo ; Jun Wang. Springer Verlag, 2004. pp. 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",

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

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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. in F Yin, C Guo & J Wang (eds), 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), vol. 3173, Springer Verlag, pp. 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). ed. / Fuliang Yin; Chengan Guo; Jun Wang. Springer Verlag, 2004. p. 1-6 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3173).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Approximation bounds by neural networks in LωP

AU - Wang, Jianjun

AU - Xu, Zongben

AU - Xu, Weijun

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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.

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SN - 3540228411

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

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

A2 - Yin, Fuliang

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PB - Springer Verlag

ER -

Wang J, Xu Z, Xu W. Approximation bounds by neural networks in L_ω^P. In Yin F, Guo C, Wang J, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 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 L_ω^P

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