Preprint
Aug 2026
Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learning
A framework for E(3)-equivariant UQ is introduced, modeling the full predictive distribution where both mean and covariance preserve rotational symmetry, and a Log-Euclidean Equivariant Scoring Objective (LE-ESO) is formulated, a robust surrogate loss based on the Multivariate Laplace distribution providing robustness to heavy-tailed errors and stable optimization.
Ruihan Liu, Yunting Ji, Jianbo Yu et al.
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