mlsanityData to 7 Oct 2026

Spatial Attention Kinetic Networks with E(n)-Equivariance

arXiv 2301.08893 ↗First posted 21 Jan 2023cs.LG physics.app-phcited by 11

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Abstract (arXiv)

Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex potential energy surfaces to guiding the sampling of complex dynamical systems or forecasting their time evolution. Current state-of-the-art methods employ spherical harmonics to encode higher-order interactions among particles, which are computationally expensive. In this paper, we propose a simple alternative functional form that uses neurally parametrized linear combinations of edge vectors to achieve equivariance while still universally approximating node environments. Incorporating this insight, we design spatial attention kinetic networks with E(n)-equivariance, or SAKE, which are competitive in many-body system modeling tasks while being significantly faster.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 37 of its 53 references that are in the map. First posted on arXiv 21 Jan 2023.

Builds on

37 of 53 references.

References · 37

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  11. 2021E(n) Equivariant Graph Neural Networkscited by 951
  12. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
25 more
  1. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  2. 2020Benchmarking Graph Neural Networkscited by 672
  3. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  4. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  5. 2020Directional Message Passing for Molecular Graphscited by 556
  6. 2020Principal Neighbourhood Aggregation for Graph Netscited by 477
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  8. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  9. 2018Neural Relational Inference for Interacting Systemscited by 339
  10. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  11. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  12. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  13. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  14. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  15. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  16. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  17. 2021E(n) Equivariant Normalizing Flowscited by 165
  18. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  19. 2017Continuously Differentiable Exponential Linear Unitscited by 73
  20. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  21. 2020Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscited by 66
  22. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
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  24. 2021Directional Message Passing on Molecular Graphs via Synthetic Coordinatescited by 24
  25. 2017Continuous-Time Flows for Efficient Inference and Density Estimationcited by 21

Built on by

Cited by year

Citing papers per year: 2023: 3; 2024: 7; 2025: 1.

11 papers.

  1. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  2. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 37
  3. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  4. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  5. 2024Non-convolutional Graph Neural Networkscited by 11
  6. 2024GeoMFormer: A General Architecture for Geometric Molecular Representation Learningcited by 6
  7. 2025Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Framescited by 5
  8. 2023EspalomaCharge: Machine learning-enabled ultra-fast partial charge assignmentcited by 4
  9. 2024On the design space between molecular mechanics and machine learning force fieldscited by 3
  10. 2024Relaxing Continuous Constraints of Equivariant Graph Neural Networks for Physical Dynamics Learningcited by 1
  11. 2024Molecular Dynamics and Machine Learning Unlock Possibilities in Beauty Design -- A Perspectivecited by 1