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3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data

arXiv 1807.02547 ↗First posted 6 Jul 2018cs.LG stat.MLcited by 348

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Abstract (arXiv)

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R^3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

Key facts. Cited by 348 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jul 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 62; 2022: 78; 2023: 63; 2024: 57; 2025: 45; 2026: 43.

348 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  3. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  4. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  5. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  6. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  7. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  8. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  9. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  10. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  11. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  12. 2022Pure Transformers are Powerful Graph Learnerscited by 188
38 more
  1. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  2. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  3. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
  4. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  5. 2022e3nn: Euclidean Neural Networkscited by 171
  6. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  7. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  8. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  9. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  10. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  11. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  12. 2022Clifford Neural Layers for PDE Modelingcited by 91
  13. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  14. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  15. 2022PiFold: Toward effective and efficient protein inverse foldingcited by 82
  16. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  17. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  18. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  19. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  20. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  21. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  22. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  23. 2023Clifford Group Equivariant Neural Networkscited by 54
  24. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  25. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  26. 2022Transformation-Equivariant 3D Object Detection for Autonomous Drivingcited by 52
  27. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  28. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  29. 2021Learning Partial Equivariances from Datacited by 44
  30. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  31. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  32. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  33. 2022Structure-based drug design with geometric deep learningcited by 40
  34. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  35. 20233D molecule generation by denoising voxel gridscited by 38
  36. 2023Geometric Clifford Algebra Networkscited by 37
  37. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  38. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35

50 most cited of 348 All 348 (JSON)