Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery
Computer Science > Machine Learning arXiv:2605.20440 (cs) [Submitted on 19 May 2026] Title:Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery Authors:Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. The framework provides capabilities that equivariant neural networks (ENNs) structurally cannot: a closed-form per-irreducible-representation decomposition of every prediction, and data-driven discovery of the symmetry group that best fits a dataset. On full QM9 (130{,}831 molecules), $\star_G$-SVD with ridge regression provides closed form predictions at $\sim50-90\times$ fewer parameters than parameter-matched MLPs.
- ▪Computer Science > Machine Learning arXiv:2605.20440 (cs) [Submitted on 19 May 2026] Title:Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery Authors:Paulina Hoyos, Shashanka Ubaru, Dongsung Huh,
- ▪The framework provides capabilities that equivariant neural networks (ENNs) structurally cannot: a closed-form per-irreducible-representation decomposition of every prediction, and data-driven discovery of the symmetry group that best fits
- ▪On full QM9 (130{,}831 molecules), $\star_G$-SVD with ridge regression provides closed form predictions at $\sim50-90\times$ fewer parameters than parameter-matched MLPs.
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Computer Science > Machine Learning arXiv:2605.20440 (cs) [Submitted on 19 May 2026] Title:Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery Authors:Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. Clarkson, Misha Kilmer, Haim Avron, Lior Horesh View a PDF of the paper titled Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery, by Paulina Hoyos and 7 other authors View PDF HTML (experimental) Abstract:We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint.
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