A Bregman Proximal Viewpoint on Neural Operators
cs.LG
Submitted: 2026-10-14
Updated: 2026-10-14
Comments: Accepted at ICML 2025
Journal ref: Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:43965-43989, 2025
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
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.
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