mlsanityData to 7 Oct 2026

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data

arXiv 2002.12880 ↗First posted 25 Feb 2020stat.ML cs.LGcited by 248

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Abstract (arXiv)

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.

Key facts. Cited by 248 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 50; 2022: 53; 2023: 47; 2024: 37; 2025: 32; 2026: 29.

248 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  3. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  4. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  5. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  6. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  7. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  8. 2022Graph neural networks for materials science and chemistrycited by 181
  9. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  10. 2021E(n) Equivariant Normalizing Flowscited by 165
  11. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  12. 2021CKConv: Continuous Kernel Convolution For Sequential Datacited by 117
38 more
  1. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  2. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  3. 2021Generative Models as Distributions of Functionscited by 89
  4. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  5. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  6. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
  7. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  8. 2022PAC-Bayes Compression Bounds So Tight That They Can Explain Generalizationcited by 75
  9. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  10. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  11. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  12. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  13. 2021FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizescited by 66
  14. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  15. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  16. 2021Exploring Complementary Strengths of Invariant and Equivariant Representations for Few-Shot Learningcited by 56
  17. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  18. 2023Clifford Group Equivariant Neural Networkscited by 54
  19. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  20. 2022The Lie Derivative for Measuring Learned Equivariancecited by 51
  21. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  22. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  23. 2021Learning Partial Equivariances from Datacited by 44
  24. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  25. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  26. 2022S4ND: Modeling Images and Videos as Multidimensional Signals Using State Spacescited by 41
  27. 2022How Much Data Are Augmentations Worth? An Investigation into Scaling Laws, Invariance, and Implicit Regularizationcited by 40
  28. 2023Generative Adversarial Symmetry Discoverycited by 40
  29. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  30. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  31. 2022Energy-Motivated Equivariant Pretraining for 3D Molecular Graphscited by 37
  32. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  33. 2021Equivariant neural networks for inverse problemscited by 29
  34. 2023Latent Space Symmetry Discoverycited by 29
  35. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  36. 2021Commutative Lie Group VAE for Disentanglement Learningcited by 27
  37. 2023E(2)-Equivariant Vision Transformercited by 27
  38. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27

50 most cited of 248 All 248 (JSON)