mlsanityData to 7 Oct 2026

Implicit Convolutional Kernels for Steerable CNNs

arXiv 2212.06096 ↗First posted 12 Dec 2022cs.LG cs.AI cs.CVcited by 9

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Abstract (arXiv)

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group G, such as reflections and rotations. They rely on standard convolutions with G-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group G, implementing a kernel basis does not generalize to other symmetry transformations, complicating the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize G-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group G for which a G-equivariant MLP can be built. We prove the effectiveness of our method on multiple tasks, including N-body simulations, point cloud classification and molecular property prediction.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 43 of its 55 references that are in the map. First posted on arXiv 12 Dec 2022.

Builds on

43 of 55 references.

References · 43

  1. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  4. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  5. 2016Group Equivariant Convolutional Networkscited by 1,154
  6. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  7. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  11. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  12. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
31 more
  1. 2019General E(2)-Equivariant Steerable CNNscited by 441
  2. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  3. 2022Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Frameworkcited by 376
  4. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  5. 2018Neural Relational Inference for Interacting Systemscited by 339
  6. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  7. 2016Steerable CNNscited by 298
  8. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  9. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  10. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  11. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  12. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  13. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  14. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  15. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  16. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  17. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  18. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  19. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  20. 2021CKConv: Continuous Kernel Convolution For Sequential Datacited by 117
  21. 2019B-Spline CNNs on Lie Groupscited by 97
  22. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
  23. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  24. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  25. 2021FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizescited by 66
  26. 2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
  27. 2020Universal Equivariant Multilayer Perceptronscited by 49
  28. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  29. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  30. 2022Equivariant Networks for Crystal Structurescited by 24
  31. 2021Nonlinearities in Steerable SO(2)-Equivariant CNNscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 2.

9 papers.

  1. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  2. 2024SE(3)-Hyena Operator for Scalable Equivariant Learningcited by 6
  3. 2025Geometric Hyena Networks for Large-scale Equivariant Learningcited by 4
  4. 2025AdS-GNN -- a Conformally Equivariant Graph Neural Networkcited by 2
  5. 2024Efficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier-Bessel basescited by 0
  6. 2025A Steerable Deep Network for Model-Free Diffusion MRI Registrationcited by 0
  7. 2025Conditional Clifford-Steerable CNNs for PDE Modelingcited by 0
  8. 2026Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Groupcited by 0
  9. 2026Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysiscited by 0