arXiv AI

Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learning

arXiv AI

Jun 30

Representation Learning for Equivariant Inference with Guarantees

arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.

By Daniel Ordo\~nez-Apraez, Vladimir Kosti\'c, Alek Fr\"ohlich, Vivien Brandt, Karim Lounici, Massimiliano Pontil

robotics

arXiv AI

Aug 11

Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields

arXiv:2608. 09071v1 Announce Type: cross Abstract: Forward uncertainty propagation in complex physical systems can induce structured covariance across field-valued outputs.

By Yupei Nie, Lei Wang, Jiasen Liu

arXiv Machine Learning

Jun 5

Equivariant Neural Belief Propagation

arXiv:2606. 06344v1 Announce Type: new Abstract: Probabilistic inference over spatially embedded variables requires beliefs that respect $SE(3)$ symmetry, yet existing equivariant networks produce only scalars and vectors -- not the rank-2 precision tensors needed for anisotropic uncertainty, and single-component messages collapse multi-modal energy landscapes to physically meaningless averages.

By Zehua Cheng, Wei Dai, Jiahao Sun

agents diffusion robotics multimodal

arXiv Machine Learning

Sep 1

Rotational Equivariance in Machine Learning: A Comprehensive Tutorial

arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...

By Peter Lippmann, Fred A. Hamprecht

computer-vision

arXiv Machine Learning

Sep 21

Triply-Scalable Equivariant Gaussian Process Modeling

arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.

By Tim Steinert, David Ginsbourger

arXiv AI

Jun 3

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers

arXiv:2605. 18106v3 Announce Type: replace-cross Abstract: A striking geometric disparity has long persisted in the practice of deep learning.

By Tim Tsz-Kit Lau, Weijie Su

llms rag

arXiv AI

Jun 17

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.

By Oriol Vendrell-Gallart, Nima Negarandeh, Ramin Bostanabad

rag benchmarks

arXiv Machine Learning

Jul 16

Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning

arXiv:2605. 07914v2 Announce Type: replace Abstract: Sharpness-aware and gradient-alignment methods have been shown to improve generalization, however each family of methods targets a single geometric property of the loss landscape, while ignoring the other.

By Aristotelis Ballas, Christos Diou

benchmarks safety

arXiv Statistics ML

Sep 10

DFNN: A Deep Fr\'echet Neural Network Framework for Learning Metric-Space-Valued Responses

arXiv:2510.17072v2 Announce Type: replace Abstract: Regression with non-Euclidean responses---e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions---has b...

By Kyum Kim, Yaqing Chen, Paromita Dubey

benchmarks

arXiv Machine Learning

Jul 21

Singular Bayesian Neural Networks

arXiv:2602. 00387v4 Announce Type: replace-cross Abstract: Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors.

By Mame Diarra Toure, David A. Stephens

llms benchmarks safety

arXiv Machine Learning

Jul 22

Contraction-Gauge Preconditioning for Quantized Matrix Multiplication

arXiv:2607. 18745v1 Announce Type: new Abstract: We study low-precision computation of C=AB with both factors quantized.

By Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara, Keita Teranishi, Sudip Seal

efficiency

arXiv Machine Learning

Aug 3

Moment kernels: a simple and scalable approach for equivariance to rotations and reflections in deep convolutional networks

arXiv:2505. 21736v2 Announce Type: replace-cross Abstract: Translation equivariance is a central reason convolutional neural networks have been successful in computer vision.

By Siqi Fang, Zachary Schlamowitz, Andrew Bennecke, Daniel J. Tward

computer-vision

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