A Bregman Proximal Viewpoint on Neural Operators

Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo, Amaury Habrard, Massimiliano Pontil, Rémi Emonet, Marc Sebban

Keywords: neural operators, proximal optimization, bregman divergence, fourier neural operator

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 activatio 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.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 11181