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Steerable CNNs

arXiv 1612.08498 ↗First posted 27 Dec 2016cs.LG stat.MLcited by 298

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Abstract (arXiv)

It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and flexible class of equivariant convolutional networks. We show that steerable CNNs achieve state of the art results on the CIFAR image classification benchmark. The mathematical theory of steerable representations reveals a type system in which any steerable representation is a composition of elementary feature types, each one associated with a particular kind of symmetry. We show how the parameter cost of a steerable filter bank depends on the types of the input and output features, and show how to use this knowledge to construct CNNs that utilize parameters effectively.

Key facts. Cited by 298 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Dec 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 51; 2022: 55; 2023: 71; 2024: 42; 2025: 50; 2026: 29.

298 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  3. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  4. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  5. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  6. 2021E(n) Equivariant Normalizing Flowscited by 165
  7. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  8. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  9. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  10. 2022Clifford Neural Layers for PDE Modelingcited by 91
  11. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  12. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
38 more
  1. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  2. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  3. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  4. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  5. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  6. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  7. 2022Equivariant Transporter Networkcited by 44
  8. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  9. 2023TacticAI: an AI assistant for football tacticscited by 43
  10. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  11. 2021Autobahn: Automorphism-based Graph Neural Netscited by 39
  12. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  13. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  14. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  15. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 35
  16. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  17. 2021Revisiting Consistency Regularization for Semi-Supervised Learningcited by 34
  18. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  19. 2024Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3Dcited by 32
  20. 2022A case for using rotation invariant features in state of the art feature matcherscited by 27
  21. 2023E(2)-Equivariant Vision Transformercited by 27
  22. 2022Self-Supervised Equivariant Learning for Oriented Keypoint Detectioncited by 26
  23. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  24. 2021Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representationscited by 24
  25. 2021Multi-Agent MDP Homomorphic Networkscited by 24
  26. 2021Roto-translated Local Coordinate Frames For Interacting Dynamical Systemscited by 24
  27. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  28. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  29. 2023Learning Rotation-Equivariant Features for Visual Correspondencecited by 23
  30. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  31. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  32. 2021Enabling equivariance for arbitrary Lie groupscited by 22
  33. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  34. 2022SEIL: Simulation-augmented Equivariant Imitation Learningcited by 22
  35. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  36. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
  37. 2021Multiresolution Equivariant Graph Variational Autoencodercited by 20
  38. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20

50 most cited of 298 All 298 (JSON)