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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/935312 |
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| _version_ | 1832551490982510592 |
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| author | Fanzi Zeng Yuting Tang |
| author_facet | Fanzi Zeng Yuting Tang |
| author_sort | Fanzi Zeng |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ca5036987554432dae0637eef723a0f5 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-ca5036987554432dae0637eef723a0f52025-02-03T06:01:20ZengWileyThe 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 |
| spellingShingle | Fanzi Zeng Yuting Tang The Estimate for Approximation Error of Neural Network with Two Weights The Scientific World Journal |
| title | 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_short | The Estimate for Approximation Error of Neural Network with Two Weights |
| title_sort | estimate for approximation error of neural network with two weights |
| url | http://dx.doi.org/10.1155/2013/935312 |
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