mlsanityData to 7 Oct 2026

Using and Abusing Equivariance

arXiv 2308.11316 ↗First posted 22 Aug 2023cs.CVcited by 4

Not on the map. Why?

Abstract (arXiv)

In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on network performance. We show that a change in the input dimension of a network as small as a single pixel can be enough for commonly used architectures to become approximately equivariant, rather than exactly. We investigate the impact of networks not being exactly equivariant and find that approximately equivariant networks generalise significantly worse to unseen symmetries compared to their exactly equivariant counterparts. However, when the symmetries in the training data are not identical to the symmetries of the network, we find that approximately equivariant networks are able to relax their own equivariant constraints, causing them to match or outperform exactly equivariant networks on common benchmark datasets.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 29 of its 42 references that are in the map. First posted on arXiv 22 Aug 2023.

Builds on

29 of 42 references.

References · 29

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 11,979
  4. 2015Spatial Transformer Networkscited by 1,423
  5. 2016Group Equivariant Convolutional Networkscited by 1,154
  6. 2015An Introduction to Convolutional Neural Networkscited by 510
  7. 2018Rotation Equivariant CNNs for Digital Pathologycited by 420
  8. 2019Making Convolutional Networks Shift-Invariant Againcited by 390
  9. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  10. 2021ReDet: A Rotation-equivariant Detector for Aerial Object Detectioncited by 202
  11. 2020On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Locationcited by 141
  12. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
17 more
  1. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  2. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  3. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  4. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  5. 2020Attentive Group Equivariant Convolutional Networkscited by 62
  6. 2020Truly shift-invariant convolutional neural networkscited by 53
  7. 2018Learning Invariances using the Marginal Likelihoodcited by 51
  8. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  9. 2022How Much Data Are Augmentations Worth? An Investigation into Scaling Laws, Invariance, and Implicit Regularizationcited by 40
  10. 2019Equivariant Transformer Networkscited by 35
  11. 2020Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysiscited by 32
  12. 2022RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Networkcited by 20
  13. 2022Learning Invariant Weights in Neural Networkscited by 16
  14. 2021Group Equivariant Subsamplingcited by 15
  15. 2021Global Pooling, More than Meets the Eye: Position Information is Encoded Channel-Wise in CNNscited by 12
  16. 2021Rotation Equivariant Deforestation Segmentation and Driver Classificationcited by 7
  17. 2022Pooling Revisited: Your Receptive Field is Suboptimalcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 0; 2025: 1; 2026: 1.

4 papers.

  1. 2023Steerers: A framework for rotation equivariant keypoint descriptorscited by 21
  2. 2025Measuring the Impact of Rotation Equivariance on Aerial Object Detectioncited by 4
  3. 2023SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networkscited by 1
  4. 2026REDI-Match: Rotation-Equivariant Distillation for Efficient and Robust Dense Matchingcited by 0