Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials
2026-07-12 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied different ways to use mathematical symmetry theories, specifically SO(2) and SO(3), to improve machine learning models that predict how atoms interact. They found that older SO(2) methods have shortcomings compared to newer SO(3) based approaches. To address this, they created new building blocks for these models, including a method to directly handle complex interactions between atoms and an improved attention mechanism to better make predictions. They tested their improved models on several datasets and achieved the best performance reported so far on the Matbench Discovery benchmark.
SO(2) theorySO(3) Clebsch-Gordan Tensor ProductsWigner D-matricesmachine learning interatomic potentialsmany-body expansionequivariant multiplicationsattention mechanismsAtomic Cluster ExpansionMatbench Discoveryextrapolation performance
Authors
Zemin Xu, Wenbo Xie, P. Hu
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). Building on these insights, we propose direct Cartesian construction and recursive Clebsch-Gordan construction of Wigner D-matrices and introduce two novel interaction building blocks. First, we propose the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications. Second, we introduce Radial Rotary Complex Attention(RRA), which enhances extrapolation performance and surpasses existing attention vector formulations. We also introduce several improvements to the Atomic Cluster Expansion module. Building on these advances, we train our models on OMat24, sAlex, and MPTrj, and introduce TECE-OAM-RRA-1.0, which achieve state-of-the-art (SOTA) performance on the Matbench Discovery.