The Estimate for Approximation Error of Neural Network with Two Weights

The Estimate for Approximation Error of Neural Network with Two Weights

The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset o...

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Bibliographic Details
Main Authors: Fanzi Zeng, Yuting Tang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2013/935312
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spelling doaj-ca5036987554432dae0637eef723a0f52020-11-24T21:32:21ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/935312935312The Estimate for Approximation Error of Neural Network with Two WeightsFanzi Zeng0Yuting Tang1Key Laboratory for Embedded and Network Computing of Hunan Province, Hunan University, Changsha 410082, ChinaKey Laboratory for Embedded and Network Computing of Hunan Province, Hunan University, Changsha 410082, ChinaThe neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of Rm to Rn and any continuous function, which has limit at infinite place, from limitless close subset of Rm to Rn. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.http://dx.doi.org/10.1155/2013/935312
collection DOAJ
language English
format Article
sources DOAJ
author Fanzi Zeng
Yuting Tang
spellingShingle Fanzi Zeng
Yuting Tang
The Estimate for Approximation Error of Neural Network with Two Weights
The Scientific World Journal
author_facet Fanzi Zeng
Yuting Tang
author_sort Fanzi Zeng
title The Estimate for Approximation Error of Neural Network with Two Weights
title_short The Estimate for Approximation Error of Neural Network with Two Weights
title_full The Estimate for Approximation Error of Neural Network with Two Weights
title_fullStr The Estimate for Approximation Error of Neural Network with Two Weights
title_full_unstemmed The Estimate for Approximation Error of Neural Network with Two Weights
title_sort estimate for approximation error of neural network with two weights
publisher Hindawi Limited
series The Scientific World Journal
issn 1537-744X
publishDate 2013-01-01
description The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of Rm to Rn and any continuous function, which has limit at infinite place, from limitless close subset of Rm to Rn. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.
url http://dx.doi.org/10.1155/2013/935312
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AT yutingtang theestimateforapproximationerrorofneuralnetworkwithtwoweights
AT fanzizeng estimateforapproximationerrorofneuralnetworkwithtwoweights
AT yutingtang estimateforapproximationerrorofneuralnetworkwithtwoweights
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