Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules
Symmetry determines which physical responses of molecules and crystals are allowed and underlies many models used throughout the physical sciences. Yet several widely used machine-learned models learn symmetry only approximately from data, raising the question of whether approximate symmetry is sufficient for scientific prediction. Using the Orb-v3 force field, we show that it is often not: the relaxed space group of a crystal depends on the orientation of the input for $47\%$ of a $150$-crystal subsample, and relaxation lowers the space group for half of all $399$ crystals studied. To characterize, quantify, and correct such failures, we introduce a tensor algebra, $\star_G$, defined by ...
| Authors | Paulina Hoyos, Shashanka Ubaru, Dongsung Huh et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 12 October 2026 |
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