Approximation and Gradient Descent Training with Neural Networks
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914802628034560 |
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| author | Welper, G. |
| author_facet | Welper, G. |
| contents | It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training error, these two theories are not immediately compatible. Recent work uses the smoothness that is required for approximation results to extend a neural tangent kernel (NTK) optimization argument to an under-parametrized regime and show direct approximation bounds for networks trained by gradient flow. Since gradient flow is only an idealization of a practical method, this paper establishes analogous results for networks trained by gradient descent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation and Gradient Descent Training with Neural Networks Welper, G. Machine Learning 41A46, 65K10, 68T07 It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training error, these two theories are not immediately compatible. Recent work uses the smoothness that is required for approximation results to extend a neural tangent kernel (NTK) optimization argument to an under-parametrized regime and show direct approximation bounds for networks trained by gradient flow. Since gradient flow is only an idealization of a practical method, this paper establishes analogous results for networks trained by gradient descent. |
| title | Approximation and Gradient Descent Training with Neural Networks |
| topic | Machine Learning 41A46, 65K10, 68T07 |
| url | https://arxiv.org/abs/2405.11696 |