arXiv：cs.LG· Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo, Amaury Habrard, Massimiliano Pontil, Remi Emonet, Marc Sebban·· 3 小时前
Bregman 近端视角下的神经算子：Bregman 神经算子与 Fourier 神经算子的新变体
A Bregman Proximal Viewpoint on Neural Operators
AI 导读
研究者提出用 Bregman 正则化优化问题的极小值视角来理解神经算子层，将激活算子解释为从对偶空间到原空间的 Bregman 近端算子。该框架可涵盖经典神经算子，并衍生出包含逆激活算子的新变体 Bregman 神经算子，其表达能力与标准神经算子相同。数值实验表明，Bregman 变体的 Fourier 神经算子在训练更深、更准确的模型上具有额外优势。
正文
Abstract: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.
| Comments: | Accepted at ICML 2025 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.20120 [cs.LG] |
| (or arXiv:2610.20120v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20120 arXiv-issued DOI via DataCite (pending registration) |
|
| Journal reference: | Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:43965-43989, 2025 |
Submission history
From: Abdel-Rahim Mezidi [view email]
[v1]
Wed, 14 Oct 2026 12:44:41 UTC (1,344 KB)
来源：arXiv：cs.LG · arxiv.org