mlsanityData to 7 Oct 2026

Group Equivariant Convolutional Networks

arXiv 1602.07576 ↗First posted 24 Feb 2016cs.LG stat.MLcited by 1,154

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Cited by 28 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.

Key facts. Cited by 1,154 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Feb 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 175; 2022: 216; 2023: 226; 2024: 162; 2025: 183; 2026: 192.

1,154 papers.

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  1. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  2. 2021Perceiver: General Perception with Iterative Attentioncited by 1,089
  3. 2021E(n) Equivariant Graph Neural Networkscited by 951
  4. 2023Large Language Modelscited by 774
  5. 2021CLIPort: What and Where Pathways for Robotic Manipulationcited by 617
  6. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  7. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  8. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  9. 2021NeRV: Neural Representations for Videoscited by 255
  10. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  11. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 225
  12. 2021ReDet: A Rotation-equivariant Detector for Aerial Object Detectioncited by 202
38 more
  1. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  2. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  3. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
  4. 2021DC3: A learning method for optimization with hard constraintscited by 181
  5. 2022Graph neural networks for materials science and chemistrycited by 181
  6. 2021E(n) Equivariant Normalizing Flowscited by 165
  7. 2021No-Reference Image Quality Assessment via Transformers, Relative Ranking, and Self-Consistencycited by 165
  8. 2021Equivariant Subgraph Aggregation Networkscited by 154
  9. 2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 143
  10. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  11. 2021Geometric Deep Learning on Molecular Representationscited by 113
  12. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  13. 2021Generalized Shape Metrics on Neural Representationscited by 109
  14. 2022Equivariance with Learned Canonicalization Functionscited by 106
  15. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  16. 2024An analytic theory of creativity in convolutional diffusion modelscited by 103
  17. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  18. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 97
  19. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  20. 2021Trustworthy AI: A Computational Perspectivecited by 93
  21. 2022Clifford Neural Layers for PDE Modelingcited by 91
  22. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  23. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  24. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 85
  25. 2021ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reductioncited by 84
  26. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  27. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  28. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  29. 2024Robust agents learn causal world modelscited by 81
  30. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  31. 2021Input Similarity from the Neural Network Perspectivecited by 78
  32. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  33. 2021Is Attention Better Than Matrix Decomposition?cited by 75
  34. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  35. 2022PAC-Bayes Compression Bounds So Tight That They Can Explain Generalizationcited by 75
  36. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  37. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 74
  38. 2023Permutation Equivariant Neural Functionalscited by 69

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