Generalization error bounds for two-layer neural networks with Lipschitz loss function
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913013141864448 |
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| author | Nguwi, Jiang Yu Privault, Nicolas |
| author_facet | Nguwi, Jiang Yu Privault, Nicolas |
| contents | We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its associated empirical measure, together with moment bounds for the associated stochastic gradient method. In the case of independent test data, we obtain a dimension-free rate of order $O(n^{-1/2} )$ on the $n$-sample generalization error, whereas without independence assumption, we derive a bound of order $O(n^{-1 / ( d_{\rm in}+d_{\rm out} )} )$, where $d_{\rm in}$, $d_{\rm out}$ denote input and output dimensions. Our bounds and their coefficients can be explicitly computed prior to the training of the model, and are confirmed by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06281 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalization error bounds for two-layer neural networks with Lipschitz loss function Nguwi, Jiang Yu Privault, Nicolas Machine Learning Probability 62M45, 68T07 We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its associated empirical measure, together with moment bounds for the associated stochastic gradient method. In the case of independent test data, we obtain a dimension-free rate of order $O(n^{-1/2} )$ on the $n$-sample generalization error, whereas without independence assumption, we derive a bound of order $O(n^{-1 / ( d_{\rm in}+d_{\rm out} )} )$, where $d_{\rm in}$, $d_{\rm out}$ denote input and output dimensions. Our bounds and their coefficients can be explicitly computed prior to the training of the model, and are confirmed by numerical simulations. |
| title | Generalization error bounds for two-layer neural networks with Lipschitz loss function |
| topic | Machine Learning Probability 62M45, 68T07 |
| url | https://arxiv.org/abs/2604.06281 |