Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.20120

A Bregman Proximal Viewpoint on Neural Operators

Abdel-Rahim Mezidi·Jordan Patracone·Saverio Salzo·Amaury Habrard·Massimiliano Pontil·Remi Emonet·Marc Sebban
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo, Amaury Habrard, Massimiliano Pontil, Remi Emonet, Marc Sebban. 2026-10-14. A Bregman Proximal Viewpoint on Neural Operators. https://arxiv.org/abs/2610.20120

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generation of data on discontinuous manifolds via continuous stochastic non-invertible networks

The generation of discontinuous distributions is a difficult task for most known frameworks such as generative autoencoders and generative adversarial networks. Generative non-invertible models are unable to accurately generate such distributions, require long training and often are subject to mode collapse. Variational autoencoders (VAEs), which are based on the idea of keeping the latent space to be Gaussian for the sake of a simple sampling, allow an accurate reconstruction, while they experience significant limitations at generation task. In this work, instead of trying to keep the latent space to be Gaussian, we use a pre-trained contrastive encoder to obtain a clustered latent space. Then, for each cluster, representing a unimodal submanifold, we train a dedicated low complexity network to generate this submanifold from the Gaussian distribution. The proposed framework is based on the information-theoretic formulation of mutual information maximization between the input data and latent space representation. We derive a link between the cost functions and the information-theoretic formulation. We apply our approach to synthetic 2D distributions to demonstrate both reconstruction and generation of discontinuous distributions using continuous stochastic networks.

cs.LG↗
arXiv2026

Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides calibrated prediction intervals. Unlike the existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. When the raw forecast intervals are approximately calibrated, we prove that BCI is near optimal for its surrogate model predictive control problem. We find empirically that BCI avoids uninformative intervals with infinite lengths under our main experimental configuration and generates substantially shorter prediction intervals when the raw forecast intervals are poorly calibrated.

cs.LG↗
arXiv2026

GLL: A Differentiable Graph Learning Layer for Neural Networks

Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.

cs.LG↗