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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.01842 |
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| _version_ | 1866914363273641984 |
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| author | Guillin, Arnaud Nectoux, Boris Stos, Paul |
| author_facet | Guillin, Arnaud Nectoux, Boris Stos, Paul |
| contents | We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and their mean-field limit, for quadratic loss and ridge regularization. As a key ingredient, we establish T p transportation inequalities (p $\in$ {1, 2}) for the law of the SGD parameters, with explicit constants independent of the iteration index. We then prove uniform-in-time concentration of the empirical parameter measure around its mean-field limit in the Wasserstein distance W 1 , and we translate these bounds into prediction-error estimates against a fixed test function $Φ$. We also derive analogous concentration bounds in the sliced-Wasserstein distance SW 1 , leading to dimension-free rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01842 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time concentration in two-layer neural networks via transportation inequalities Guillin, Arnaud Nectoux, Boris Stos, Paul Neural and Evolutionary Computing Probability We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and their mean-field limit, for quadratic loss and ridge regularization. As a key ingredient, we establish T p transportation inequalities (p $\in$ {1, 2}) for the law of the SGD parameters, with explicit constants independent of the iteration index. We then prove uniform-in-time concentration of the empirical parameter measure around its mean-field limit in the Wasserstein distance W 1 , and we translate these bounds into prediction-error estimates against a fixed test function $Φ$. We also derive analogous concentration bounds in the sliced-Wasserstein distance SW 1 , leading to dimension-free rates. |
| title | Uniform-in-time concentration in two-layer neural networks via transportation inequalities |
| topic | Neural and Evolutionary Computing Probability |
| url | https://arxiv.org/abs/2603.01842 |