arXiv AI July 3, 2026 By Chenxing Liang, Yuchao Lin, Andrii Kryvenko, Wendi Yu, Chuan Li, Jianwen Xie, Xiaofeng Qian, Shuiwang Ji

Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$-Equivariant Networks

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arXiv:2607. 01408v1 Announce Type: cross Abstract: $\mathrm{E}(3)$-equivariant networks are promising for 3D atomistic system modeling, yet their scalability is limited by the $O(L^6)$ complexity of the Clebsch-Gordan Tensor Product (CGTP).

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arXiv Machine Learning

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A Cartesian-3j Framework for Machine Learning Interatomic Potentials

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arXiv Machine Learning

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Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames

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arXiv Machine Learning

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Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

arXiv:2607. 10664v1 Announce Type: cross Abstract: In this paper, we provide a systematic investigation of SO(2) theory to machine learning interatomic potentials (MLIPs) and identify the limitations of conventional SO(2) Linear architectures relative to SO(3) Clebsch-Gordan Tensor Products (CGTP).

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arXiv Machine Learning

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arXiv:2606. 29584v1 Announce Type: cross Abstract: $\mathrm{Cl}(3,0)$ interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly.

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arXiv Machine Learning

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When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws

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