Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling
Deep learning with specific network topologies has been successfully applied in many fields. However, what is primarily called into question by people is its lack of theoretical foundation investigations, especially for structured neural networks. This paper theoretically studies the multichannel de...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8208424 |
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| _version_ | 1849698188896763904 |
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| author | Xinling Liu Jingyao Hou |
| author_facet | Xinling Liu Jingyao Hou |
| author_sort | Xinling Liu |
| collection | DOAJ |
| description | Deep learning with specific network topologies has been successfully applied in many fields. However, what is primarily called into question by people is its lack of theoretical foundation investigations, especially for structured neural networks. This paper theoretically studies the multichannel deep convolutional neural networks equipped with the downsampling operator, which is frequently used in applications. The results show that the proposed networks have outstanding approximation and generalization ability of functions from ridge class and Sobolev space. Not only does it answer an open and crucial question of why multichannel deep convolutional neural networks are universal in learning theory, but it also reveals the convergence rates. |
| format | Article |
| id | doaj-art-9ed5b2f4f4e847729a846d83724976ce |
| institution | DOAJ |
| issn | 1687-0042 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9ed5b2f4f4e847729a846d83724976ce2025-08-20T03:18:58ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/8208424Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with DownsamplingXinling Liu0Jingyao Hou1Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan ProvinceKey Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan ProvinceDeep learning with specific network topologies has been successfully applied in many fields. However, what is primarily called into question by people is its lack of theoretical foundation investigations, especially for structured neural networks. This paper theoretically studies the multichannel deep convolutional neural networks equipped with the downsampling operator, which is frequently used in applications. The results show that the proposed networks have outstanding approximation and generalization ability of functions from ridge class and Sobolev space. Not only does it answer an open and crucial question of why multichannel deep convolutional neural networks are universal in learning theory, but it also reveals the convergence rates.http://dx.doi.org/10.1155/2023/8208424 |
| spellingShingle | Xinling Liu Jingyao Hou Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling Journal of Applied Mathematics |
| title | Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling |
| title_full | Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling |
| title_fullStr | Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling |
| title_full_unstemmed | Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling |
| title_short | Error Bounds for Approximations Using Multichannel Deep Convolutional Neural Networks with Downsampling |
| title_sort | error bounds for approximations using multichannel deep convolutional neural networks with downsampling |
| url | http://dx.doi.org/10.1155/2023/8208424 |
| work_keys_str_mv | AT xinlingliu errorboundsforapproximationsusingmultichanneldeepconvolutionalneuralnetworkswithdownsampling AT jingyaohou errorboundsforapproximationsusingmultichanneldeepconvolutionalneuralnetworkswithdownsampling |