Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

Zemin Xu Wenbo Xie P. Hu

Jul 2026 · arXiv.org · Vol abs/2607.10664 · 1 citation · 47 references

Computer Science Mathematics Physics

TL;DR

This paper proposes 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 and introduces Radial Rotary Complex Attention (RRA), which enhances extrapolation performance and surpasses existing attention vector formulations.

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.

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