Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials
Zemin Xu, Wenbo Xie, P. Hu
stat.ML, cond-mat.mtrl-sci, cs.LG, physics.chem-ph
Submitted: 2026-07-12
Code: https://github.com/xvzemin/tace
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: 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
Terminology
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.
Sources
- Deep Networks with Stochastic Depth
- E2Former-V2: On-the-Fly Equivariant Attention with Linear Activation Memory
- Pushing the limits of unconstrained machine-learned interatomic potentials
- Dyna-Mat: End-to-end benchmarking of foundation machine learning interatomic potentials in finite-temperature ensembles
- Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials
- DPA4: Pushing the Accuracy-Cost Frontier of Interatomic Potentials with EMFA SO(2) Convolution
- Integral Formulas for Vector Signal Tensor Products
- Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fields
- Orb-v3: atomistic simulation at scale
- EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers
- Muon is Scalable for LLM Training
- Decoupled Weight Decay Regularization
- Attention Residuals
- Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
- E3x: $\mathrm{E}(3)$-Equivariant Deep Learning Made Easy
- SOAP: Improving and Stabilizing Shampoo using Adam
- UMA: A Family of Universal Models for Atoms
- A Cartesian-3j Framework for Machine Learning Interatomic Potentials
- Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space
- Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Related papers
- Behavior of prediction performance metrics with rare events
- Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
- A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
- One Permutation Is All You Need: Fast, Deterministic Feature Importance and Model Stress-Testing
- Online Conformal Prediction for Non-Exchangeable Panel Data
- Deep Time-Series Forecasting in 10 Years: A Survey