Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909032953937920 |
|---|---|
| author | Pacifico, Feliciano Giuseppe Fanelli, Duccio Buffoni, Lorenzo Chicchi, Lorenzo Febbe, Diego Marino, Raffaele |
| author_facet | Pacifico, Feliciano Giuseppe Fanelli, Duccio Buffoni, Lorenzo Chicchi, Lorenzo Febbe, Diego Marino, Raffaele |
| contents | We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality Pacifico, Feliciano Giuseppe Fanelli, Duccio Buffoni, Lorenzo Chicchi, Lorenzo Febbe, Diego Marino, Raffaele Disordered Systems and Neural Networks Machine Learning We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models. |
| title | Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality |
| topic | Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2605.10613 |