mlsanityData to 14 Oct 2026

Scale-Equivariant Steerable Networks

arXiv 1910.11093 ↗First posted 14 Oct 2019cs.CV cs.LG stat.MLcited by 110

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Abstract (arXiv)

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various tasks due to the changing distances between the objects and the camera. First, we introduce the general theory for building scale-equivariant convolutional networks with steerable filters. We develop scale-convolution and generalize other common blocks to be scale-equivariant. We demonstrate the computational efficiency and numerical stability of the proposed method. We compare the proposed models to the previously developed methods for scale equivariance and local scale invariance. We demonstrate state-of-the-art results on MNIST-scale dataset and on STL-10 dataset in the supervised learning setting.

Key facts. Cited by 110 papers in the map (data through 14 Oct 2026). First posted on arXiv 14 Oct 2019.

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Citing papers per year: 2021: 29; 2022: 23; 2023: 30; 2024: 12; 2025: 7; 2026: 9.

110 papers.

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  1. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  2. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 89
  3. 2024Neural Operators with Localized Integral and Differential Kernelscited by 62
  4. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  5. 2021Self-Supervised Learning Disentangled Group Representation as Featurecited by 47
  6. 2021Learning Partial Equivariances from Datacited by 45
  7. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  8. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 41
  9. 2021DISCO: accurate Discrete Scale Convolutionscited by 36
  10. 2022Robust (Controlled) Table-to-Text Generation with Structure-Aware Equivariance Learningcited by 32
  11. 2022LieGG: Studying Learned Lie Group Generatorscited by 31
  12. 2021Equivariant neural networks for inverse problemscited by 29
38 more
  1. 2022Sample Efficiency of Data Augmentation Consistency Regularizationcited by 28
  2. 2021Commutative Lie Group VAE for Disentanglement Learningcited by 27
  3. 2021Resolution learning in deep convolutional networks using scale-space theorycited by 26
  4. 2022Self-Supervised Equivariant Learning for Oriented Keypoint Detectioncited by 26
  5. 2024Clifford-Steerable Convolutional Neural Networkscited by 25
  6. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  7. 2021Enabling equivariance for arbitrary Lie groupscited by 22
  8. 2022Maximum Class Separation as Inductive Bias in One Matrixcited by 21
  9. 2021Dilated convolution with learnable spacingscited by 20
  10. 2021PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNscited by 19
  11. 20223D Equivariant Graph Implicit Functionscited by 18
  12. 2023Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNNcited by 18
  13. 2021Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scalescited by 17
  14. 2024Graph Neural PDE Solvers with Conservation and Similarity-Equivariancecited by 17
  15. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  16. 2022Learning Instance-Specific Augmentations by Capturing Local Invariancescited by 15
  17. 2023Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariancecited by 14
  18. 2023On genuine invariance learning without weight-tyingcited by 14
  19. 2022M"obius Convolutions for Spherical CNNscited by 13
  20. 2022Reflection and Rotation Symmetry Detection via Equivariant Learningcited by 13
  21. 2022Scale Equivariant U-Netcited by 13
  22. 2022Equivariant Mesh Attention Networkscited by 12
  23. 2023Lie Group Decompositions for Equivariant Neural Networkscited by 12
  24. 2025Probing Equivariance and Symmetry Breaking in Convolutional Networkscited by 12
  25. 2022Siamese Object Tracking for Unmanned Aerial Vehicle: A Review and Comprehensive Analysiscited by 11
  26. 2023Scale-Equivariant UNet for Histopathology Image Segmentationcited by 11
  27. 2021Truly shift-equivariant convolutional neural networks with adaptive polyphase upsamplingcited by 10
  28. 2023SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRIcited by 10
  29. 2022In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?cited by 9
  30. 2022Robust Perception through Equivariancecited by 9
  31. 2023ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learningcited by 9
  32. 2023Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fieldscited by 8
  33. 2023Riesz networks: scale invariant neural networks in a single forward passcited by 8
  34. 2023As large as it gets: Learning infinitely large Filters via Neural Implicit Functions in the Fourier Domaincited by 8
  35. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  36. 2022Improving the Sample-Complexity of Deep Classification Networks with Invariant Integrationcited by 7
  37. 2023On the Implicit Bias of Linear Equivariant Steerable Networkscited by 7
  38. 2023Color Equivariant Convolutional Networkscited by 7

50 most cited of 110 All 110 (JSON)