Fredholm integral equations for function approximation and the training of neural networks
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911957261484032 |
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| author | Gelß, Patrick Issagali, Aizhan Kornhuber, Ralf |
| author_facet | Gelß, Patrick Issagali, Aizhan Kornhuber, Ralf |
| contents | We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05262 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fredholm integral equations for function approximation and the training of neural networks Gelß, Patrick Issagali, Aizhan Kornhuber, Ralf Numerical Analysis We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods. |
| title | Fredholm integral equations for function approximation and the training of neural networks |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2303.05262 |