mlsanityData to 7 Oct 2026

Polar Transformer Networks

arXiv 1709.01889 ↗First posted 6 Sep 2017cs.CVcited by 81

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Abstract (arXiv)

Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classifier. PTN achieves state-of-the-art on rotated MNIST and the newly introduced SIM2MNIST dataset, an MNIST variation obtained by adding clutter and perturbing digits with translation, rotation and scaling. The ideas of PTN are extensible to 3D which we demonstrate through the Cylindrical Transformer Network.

Key facts. Cited by 81 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Sep 2017.

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Citing papers per year: 2021: 22; 2022: 18; 2023: 15; 2024: 9; 2025: 9; 2026: 8.

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  1. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  2. 2022Equivariance with Learned Canonicalization Functionscited by 106
  3. 2021Model-Based Domain Generalizationcited by 103
  4. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  5. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  6. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  7. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  8. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  9. 2022Accurate 3-DoF Camera Geo-Localization via Ground-to-Satellite Image Matchingcited by 44
  10. 2022Expansion and Shrinkage of Localization for Weakly-Supervised Semantic Segmentationcited by 37
  11. 2021Deep Learning for UAV-based Object Detection and Tracking: A Surveycited by 33
  12. 2022RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 29
38 more
  1. 2021Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutionscited by 26
  2. 2022VN-Transformer: Rotation-Equivariant Attention for Vector Neuronscited by 26
  3. 2021RoI Tanh-polar Transformer Network for Face Parsing in the Wildcited by 23
  4. 2022RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Networkcited by 20
  5. 2021Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scalescited by 17
  6. 2022Learning Invariant Weights in Neural Networkscited by 16
  7. 2023A General Framework for Equivariant Neural Networks on Reductive Lie Groupscited by 16
  8. 2024LieRE: Lie Rotational Positional Encodingscited by 16
  9. 2021Addressing the Topological Defects of Disentanglement via Distributed Operatorscited by 14
  10. 2023A Dual-Stream Neural Network Explains the Functional Segregation of Dorsal and Ventral Visual Pathways in Human Brainscited by 12
  11. 2024RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentationcited by 12
  12. 2021Rotation Equivariant Feature Image Pyramid Network for Object Detection in Optical Remote Sensing Imagerycited by 11
  13. 2021VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifoldscited by 11
  14. 2021Training or Architecture? How to Incorporate Invariance in Neural Networkscited by 9
  15. 2021Homography Decomposition Networks for Planar Object Trackingcited by 9
  16. 2021Learning Canonical 3D Object Representation for Fine-Grained Recognitioncited by 7
  17. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  18. 2022Improving the Sample-Complexity of Deep Classification Networks with Invariant Integrationcited by 7
  19. 2023Foveation in the Era of Deep Learningcited by 7
  20. 2024Tilt your Head: Activating the Hidden Spatial-Invariance of Classifierscited by 7
  21. 2025GAGrasp: Geometric Algebra Diffusion for Dexterous Graspingcited by 7
  22. 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
  23. 2023DeDA: Deep Directed Accumulatorcited by 5
  24. 2025A Regularization-Guided Equivariant Approach for Image Restorationcited by 5
  25. 2025Rotation Equivariant Arbitrary-scale Image Super-Resolutioncited by 5
  26. 2021Towards high-accuracy deep learning inference of compressible turbulent flows over aerofoilscited by 4
  27. 2022Human Eyes Inspired Recurrent Neural Networks are More Robust Against Adversarial Noisescited by 4
  28. 2022PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNscited by 4
  29. 2023Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolutioncited by 4
  30. 2023Explaining V1 Properties with a Biologically Constrained Deep Learning Architecturecited by 4
  31. 2024Pioneering SE(2)-Equivariant Trajectory Planning for Automated Drivingcited by 4
  32. 2024Learning Color Equivariant Representationscited by 4
  33. 2021Autoequivariant Network Search via Group Decompositioncited by 3
  34. 2025Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoderscited by 3
  35. 2025Geometrically Constrained and Token-Based Probabilistic Spatial Transformerscited by 3
  36. 2021Oriental Language Recognition (OLR) 2020: Summary and Analysiscited by 2
  37. 2022A Simple Strategy to Provable Invariance via Orbit Mappingcited by 2
  38. 2023Deep Neural Networks with Efficient Guaranteed Invariancescited by 2

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