mlsanityData to 14 Oct 2026

Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

arXiv 2607.10664 ↗First posted 12 Jul 2026stat.ML cond-mat.mtrl-sci cs.LGcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 33 of its 47 references that are in the map. First posted on arXiv 12 Jul 2026.

Builds on

33 of 47 references.

References · 33

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  12. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
21 more
  1. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 117
  2. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 101
  3. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  4. 2026Attention Residualscited by 65
  5. 2024Open Materials 2024 (OMat24) Inorganic Materials Dataset and Modelscited by 52
  6. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  7. 2025An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networkscited by 22
  8. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 19
  9. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  10. 2025E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Productscited by 12
  11. 2026Pushing the limits of unconstrained machine-learned interatomic potentialscited by 11
  12. 2026EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformerscited by 11
  13. 2024High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spacescited by 6
  14. 2025Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Framescited by 6
  15. 2025Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Spacecited by 6
  16. 2026Asymptotically Fast Clebsch-Gordan Tensor Products with Vector Spherical Harmonicscited by 4
  17. 2025A Cartesian-3j Framework for Machine Learning Interatomic Potentialscited by 3
  18. 2026E2Former-V2: On-the-Fly Equivariant Attention with Linear Activation Memorycited by 3
  19. 2026Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentialscited by 3
  20. 2026Better without U: Impact of Selective Hubbard U Correction on Foundational MLIPscited by 2
  21. 2026Integral Formulas for Vector Signal Tensor Productscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Neural-Network Solutions to Real-Space Charge Density and Generalizationcited by 0
  2. 2026A strategic roadmap for an atomistic machine-learning ecosystemcited by 0