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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/2603.19524 |
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| _version_ | 1866915876398170112 |
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| author | de Oliveira, Arthur C. B. Wang, Ruigang Manchester, Ian R. Sontag, Eduardo D. |
| author_facet | de Oliveira, Arthur C. B. Wang, Ruigang Manchester, Ian R. Sontag, Eduardo D. |
| contents | This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose, among all functions that (approximately) interpolate a given data set, one with a minimal Lipschitz constant. The paper establishes rigorous generalization bounds over practically relevant classes of approximators, including deep neural networks. It also presents a neural network implementation based on Lipschitz-bounded network layers and an augmented Lagrangian method. The results are illustrated for a problem of learning the dynamics of an input-to-state stable system with certified bounds on simulation error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19524 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on Lipschitz-Minimal Interpolation: Generalization Bounds and Neural Network Implementation de Oliveira, Arthur C. B. Wang, Ruigang Manchester, Ian R. Sontag, Eduardo D. Systems and Control This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose, among all functions that (approximately) interpolate a given data set, one with a minimal Lipschitz constant. The paper establishes rigorous generalization bounds over practically relevant classes of approximators, including deep neural networks. It also presents a neural network implementation based on Lipschitz-bounded network layers and an augmented Lagrangian method. The results are illustrated for a problem of learning the dynamics of an input-to-state stable system with certified bounds on simulation error. |
| title | Remarks on Lipschitz-Minimal Interpolation: Generalization Bounds and Neural Network Implementation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.19524 |