A Bregman Proximal Viewpoint on Neural Operators
We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal space. This novel viewpoint is general enough to recover classical neural operators as well as a new variant, coined Bregman neural operators, which includes the inverse activation operator and features the same expressivity of standard neural operators. Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models.
Authors
- Saverio Salzo (ORCID: https://orcid.org/0000-0003-0494-9101)
- Marc Sebban (ORCID: https://orcid.org/0000-0001-6851-169X)
- Massimiliano Pontil (ORCID: https://orcid.org/0000-0001-9415-098X)
- Amaury Habrard (ORCID: https://orcid.org/0000-0003-3038-9347)
- Rémi Emonet (ORCID: https://orcid.org/0000-0002-1870-1329)
Institutions
- Institut Universitaire de France (FR)
- Italian Institute of Technology (IT)
- Laboratoire Hubert Curien (FR)
- Centre Inria de Lyon (FR)
- MALICE: Apprentissage automatique avec intégration des connaissances en ingénierie de surface : théorie et algorithmes (FR)
- Université Jean Monnet (FR)
- Sapienza University of Rome (IT)
- Université Jean Monnet (FR)
Publication Details
- Journal
- HAL (Le Centre pour la Communication Scientifique Directe)
- Published
- 2026-10-14
- DOI
- https://doi.org/10.48550/arxiv.2610.20120
- Primary Topic
- Model Reduction and Neural Networks
- Type
- preprint