arXiv subjects

Zemin Xu

Publications and source records attributed to Zemin Xu.

4 recordsLinked to original sources

arXiv2026

Complete O(3) Interactions from Wigner-6j Recoupling to Local O(2) Frames

Equivariant atomistic models commonly use either Clebsch Gordan tensor product(CGTP) or edge aligned SO(2) operationsCGTP support general O(3) representations but become expensive at high angular degree, while existing local SO(2) frame methods are designed for SO(3) or the natural-parity subset of O(3). They therefore do not provide a complete local representation when polar tensors and pseudotensors occur at the same time. In this work, we introduce a generalized Wigner-6j convolution for non-collinear magnetism, electric fields, and magnetic fields, providing a general convolution scheme under O(3) that can incorporate arbitrary node-wise equivariant features. We further develop a complete O(3) convolution framework based on local O(2) frames, reducing the computational complexity of CGTPs from O(L6) to O(L3). We establish the correspondence between global O(3) irreducible representations (irreps) and local O(2) irreps and use this correspondence to construct a closed operator system comprising O2Linear, O2TensorProduct, and O2Gate.

physics.chem-ph↗

arXiv2026

Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

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.

stat.ML↗

arXiv2026

Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space

Equivariant atomistic machine learning models have largely been built on spherical-tensor representations, where explicit angular-momentum coupling introduces substantial complexity and systematic extensions beyond energies and forces remain challenging, often requires problem-specific architectural choices. Here we introduce the Tensor Atomic Cluster Expansion (TACE), which unifies scalar and tensorial modeling in Cartesian and space by decomposing local environments into irreducible Cartesian tensors (ICT) constructing a controlled many-body hierarchy with atomic cluster expansion (ACE). In addition to performing ACE in the frequency domain, we propose an efficient Clebsch-Gordan-free alternative in the spatial domain. TACE provides universal invariant (e.g., fidelity tags and charges) and equivariant (e.g., external electric fields and non-collinear magnetic moments) embeddings and predicted tensorial observables are handled on equal footing and enabling explicit control at inference. We demonstrate the accuracy, stability, and efficiency across finite molecules and extended materials, including in-domain and out-of-domain benchmarks, spectra, Hessian, external-field responses, charged systems, and multi-fidelity/head training. We further show its robustness on nonequilibrium/reactive datasets and controlled scaling when extending to large foundation model datasets.

stat.ML↗

arXiv2025

A Cartesian-3j Framework for Machine Learning Interatomic Potentials

Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by introduce the \texttt{Cartesian-3j} symbol and Cartesian Generalized Clebsch-Gordan Coefficients, which serve as direct analogues of the \texttt{Wigner-3j} symbol and Generalized Clebsch-Gordan coefficients defined for ST coupling. We extend the \texttt{e3nn} library to support ICT product, and use this framework to build Cartesian counterparts of \texttt{MACE}, \texttt{NequIP}, and \texttt{Allegro}, allowing the first controlled comparison where architectures are held fixed and only the tensor basis is changed. Our experiments show that irreducible Cartesian models can achieve accuracy comparable to spherical counterparts, but direct Cartesianization incurs unfavorable compute and memory scaling, motivating dedicated Cartesian architectural choices. Leveraging ICTs and our framework, we introduce \texttt{TACE-v1-OAM-M} and demonstrate that it achieves competitive performance on Matbench Discovery compared to state-of-the-art ST models.

physics.chem-ph↗