Remarks on Lipschitz-Minimal Interpolation: Generalization Bounds and Neural Network Implementation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915876398170112 |
|---|---|
| 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 |