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Attentive Group Equivariant Convolutional Networks

arXiv 2002.03830 ↗First posted 7 Feb 2020cs.CV cs.LG stat.MLcited by 62

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Abstract (arXiv)

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we present attentive group equivariant convolutions, a generalization of the group convolution, in which attention is applied during the course of convolution to accentuate meaningful symmetry combinations and suppress non-plausible, misleading ones. We indicate that prior work on visual attention can be described as special cases of our proposed framework and show empirically that our attentive group equivariant convolutional networks consistently outperform conventional group convolutional networks on benchmark image datasets. Simultaneously, we provide interpretability to the learned concepts through the visualization of equivariant attention maps.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 16; 2022: 9; 2023: 18; 2024: 9; 2025: 7; 2026: 3.

62 papers.

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  1. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  2. 2021Is Attention Better Than Matrix Decomposition?cited by 75
  3. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  4. 2023GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformerscited by 75
  5. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  6. 2023Geometric Algebra Transformercited by 46
  7. 2021Learning Partial Equivariances from Datacited by 44
  8. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  9. 2022Attention Mechanism in Neural Networks: Where it Comes and Where it Goescited by 29
  10. 2023E(2)-Equivariant Vision Transformercited by 27
  11. 2021Enabling equivariance for arbitrary Lie groupscited by 22
  12. 2022Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networkscited by 18
38 more
  1. 2021Equivariant Networks for Pixelized Spherescited by 16
  2. 2023Making Vision Transformers Truly Shift-Equivariantcited by 16
  3. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  4. 2021Group Equivariant Subsamplingcited by 15
  5. 2021Addressing the Topological Defects of Disentanglement via Distributed Operatorscited by 14
  6. 2023Alias-Free Convnets: Fractional Shift Invariance via Polynomial Activationscited by 11
  7. 2022Learning with Capsules: A Surveycited by 10
  8. 2023VTAE: Variational Transformer Autoencoder with Manifolds Learningcited by 10
  9. 2023Investigating how ReLU-networks encode symmetriescited by 8
  10. 2024Steerable Transformers for Volumetric Datacited by 8
  11. 2025Flopping for FLOPs: Leveraging equivariance for computational efficiencycited by 8
  12. 2022Improving the Sample-Complexity of Deep Classification Networks with Invariant Integrationcited by 7
  13. 2023FRED: Towards a Full Rotation-Equivariance in Aerial Image Object Detectioncited by 7
  14. 2024Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networkscited by 7
  15. 2025GradMetaNet: An Equivariant Architecture for Learning on Gradientscited by 7
  16. 2021Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transformscited by 6
  17. 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
  18. 2025Diffusion Generative Modeling on Lie Group Representationscited by 6
  19. 2021Exploiting Learned Symmetries in Group Equivariant Convolutionscited by 5
  20. 2022A Graph and Attentive Multi-Path Convolutional Network for Traffic Predictioncited by 5
  21. 2023Steerable Equivariant Representation Learningcited by 5
  22. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 5
  23. 2023Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolutioncited by 4
  24. 2023Using and Abusing Equivariancecited by 4
  25. 2023Self-Supervised Detection of Perfect and Partial Input-Dependent Symmetriescited by 4
  26. 2025Measuring the Impact of Rotation Equivariance on Aerial Object Detectioncited by 4
  27. 2021Autoequivariant Network Search via Group Decompositioncited by 3
  28. 2023Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictorscited by 3
  29. 2024ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3Dcited by 3
  30. 2025Quick ViTs: Speeding up Vision Transformers through Equivariancecited by 3
  31. 20216DCNN with roto-translational convolution filters for volumetric data processingcited by 2
  32. 2023Deep Neural Networks with Efficient Guaranteed Invariancescited by 2
  33. 2024Building Hybrid B-Spline And Neural Network Operatorscited by 2
  34. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  35. 2026RoVE: Rotary Value Embeddings Attention for Relative Position-dependent Value Pathwayscited by 2
  36. 2021Salient Positions based Attention Network for Image Classificationcited by 1
  37. 2022Towards the Human Global Context: Does the Vision-Language Model Really Judge Like a Human Being?cited by 1
  38. 2022Equivariant Light Field Convolution and Transformercited by 1

50 most cited of 62 All 62 (JSON)