| Title: |
A Bregman Proximal Viewpoint on Neural Operators |
| Authors: |
Mezidi, Abdel-Rahim; Patracone, Jordan; Salzo, Saverio; Habrard, Amaury; Pontil, Massimiliano; Emonet, Rémi; Sebban, Marc |
| Contributors: |
Apprentissage automatique avec intégration des connaissances en ingénierie de surface : théorie et algorithmes (MALICE); Laboratoire Hubert Curien (LabHC); Institut d'Optique Graduate School (IOGS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-Institut d'Optique Graduate School (IOGS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Lyon; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Institut d'Optique Graduate School (IOGS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); Dipartimento di Ingegneria informatica automatica e gestionale Roma (DIAG UNIROMA); Università degli Studi di Roma "La Sapienza" = Sapienza University Rome (UNIROMA); Université Jean Monnet - Saint-Étienne (UJM); Institut universitaire de France (IUF); Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.); Italian Institute of Technology = Istituto Italiano di Tecnologia Genova (IIT) |
| Source: |
International Conference on Machine Learning ; https://inria.hal.science/hal-04584456 ; International Conference on Machine Learning, Jul 2025, Vancouver, Canada |
| Publisher Information: |
CCSD |
| Publication Year: |
2025 |
| Collection: |
Université Jean Monnet – Saint-Etienne: HAL |
| Subject Terms: |
bregman distance; deep learning; neural operators; [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] |
| Subject Geographic: |
Vancouver |
| Time: |
Vancouver, Canada |
| Description: |
International audience ; 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. |
| Document Type: |
conference object |
| Language: |
English |
| Availability: |
https://inria.hal.science/hal-04584456; https://inria.hal.science/hal-04584456v3/document; https://inria.hal.science/hal-04584456v3/file/A_Proximal_Viewpoint_on_Neural_Operators-17.pdf |
| Rights: |
http://creativecommons.org/licenses/by-nc-sa/ ; info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.AD26EC0E |
| Database: |
BASE |