mlsanityData to 14 Oct 2026

Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations

arXiv 2507.01131 ↗First posted 1 Jul 2025cs.LG physics.comp-phcited by 1

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Abstract (arXiv)

rmSO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of rmSO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L6) to O(L4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (hrefhttps://github.com/divelab/AIRS/tree/main/OpenMol/TDNhttps://github.com/divelab/AIRS/).

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 37 of its 47 references that are in the map. First posted on arXiv 1 Jul 2025.

Builds on

37 of 47 references.

References · 37

  1. 2021E(n) Equivariant Graph Neural Networkscited by 965
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  4. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  5. 2020Directional Message Passing for Molecular Graphscited by 561
  6. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  8. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  9. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  10. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 305
  11. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
  12. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
25 more
  1. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 256
  2. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 255
  3. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  4. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
  5. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 182
  6. 2021Spherical Message Passing for 3D Graph Networkscited by 168
  7. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
  8. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 117
  9. 2022The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalystscited by 95
  10. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 84
  11. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  12. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
  13. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  14. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  15. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  16. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  17. 2020An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storagecited by 45
  18. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 43
  19. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  20. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 39
  21. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  22. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 19
  23. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 15
  24. 2023Connectivity Optimized Nested Graph Networks for Crystal Structurescited by 11
  25. 2024Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Predictioncited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026E2Former-V2: On-the-Fly Equivariant Attention with Linear Activation Memorycited by 3