Controllability of continuous networks and a kernel-based learning approximation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910366062084096 |
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| author | Herty, Michael Segala, Chiara Visconti, Giuseppe |
| author_facet | Herty, Michael Segala, Chiara Visconti, Giuseppe |
| contents | Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field description allows also the recast of the training processes as a controllability problem for the solution to the mean-field dynamics. We show theoretical results on the controllability of the linear microscopic and mean-field dynamics through the Hilbert Uniqueness Method and propose a computational approach based on kernel learning methods to solve numerically, and efficiently, the training problem. Further aspects of the structural properties of the mean-field equation will be reviewed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Controllability of continuous networks and a kernel-based learning approximation Herty, Michael Segala, Chiara Visconti, Giuseppe Optimization and Control 49J15, 49J20, 35Q49, 92B20, 90C31 Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field description allows also the recast of the training processes as a controllability problem for the solution to the mean-field dynamics. We show theoretical results on the controllability of the linear microscopic and mean-field dynamics through the Hilbert Uniqueness Method and propose a computational approach based on kernel learning methods to solve numerically, and efficiently, the training problem. Further aspects of the structural properties of the mean-field equation will be reviewed. |
| title | Controllability of continuous networks and a kernel-based learning approximation |
| topic | Optimization and Control 49J15, 49J20, 35Q49, 92B20, 90C31 |
| url | https://arxiv.org/abs/2403.08690 |