mlsanityData to 7 Oct 2026

DISCO: accurate Discrete Scale Convolutions

arXiv 2106.02733 ↗First posted 4 Jun 2021cs.CVcited by 35

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Abstract (arXiv)

Scale is often seen as a given, disturbing factor in many vision tasks. When doing so it is one of the factors why we need more data during learning. In recent work scale equivariance was added to convolutional neural networks. It was shown to be effective for a range of tasks. We aim for accurate scale-equivariant convolutional neural networks (SE-CNNs) applicable for problems where high granularity of scale and small kernel sizes are required. Current SE-CNNs rely on weight sharing and kernel rescaling, the latter of which is accurate for integer scales only. To reach accurate scale equivariance, we derive general constraints under which scale-convolution remains equivariant to discrete rescaling. We find the exact solution for all cases where it exists, and compute the approximation for the rest. The discrete scale-convolution pays off, as demonstrated in a new state-of-the-art classification on MNIST-scale and on STL-10 in the supervised learning setting. With the same SE scheme, we also improve the computational effort of a scale-equivariant Siamese tracker on OTB-13.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Builds on 41 of its 60 references that are in the map. First posted on arXiv 4 Jun 2021.

Builds on

41 of 60 references.

References · 41

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networkscited by 9,617
  3. 2016Feature Pyramid Networks for Object Detectioncited by 5,021
  4. 2016Wide Residual Networkscited by 3,057
  5. 2017Improved Regularization of Convolutional Neural Networks with Cutoutcited by 1,623
  6. 2016Group Equivariant Convolutional Networkscited by 1,154
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2016Fully-Convolutional Siamese Networks for Object Trackingcited by 566
  9. 2018SiamRPN++: Evolution of Siamese Visual Tracking with Very Deep Networkscited by 445
  10. 2019General E(2)-Equivariant Steerable CNNscited by 441
  11. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  12. 2019Learning Discriminative Model Prediction for Trackingcited by 344
29 more
  1. 2016Steerable CNNscited by 298
  2. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  3. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  4. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  5. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  6. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  7. 2020DetectoRS: Detecting Objects with Recursive Feature Pyramid and Switchable Atrous Convolutioncited by 222
  8. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  9. 2020Siamese Box Adaptive Network for Visual Trackingcited by 189
  10. 2016Deep Pyramidal Residual Networkscited by 163
  11. 2019Deeper and Wider Siamese Networks for Real-Time Visual Trackingcited by 156
  12. 2019Deep Scale-spaces: Equivariance Over Scalecited by 113
  13. 2019Scale-Equivariant Steerable Networkscited by 110
  14. 2019B-Spline CNNs on Lie Groupscited by 97
  15. 2020Group Equivariant Stand-Alone Self-Attention For Visioncited by 63
  16. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  17. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  18. 2018N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentialscited by 42
  19. 2014Scale-Invariant Convolutional Neural Networkscited by 40
  20. 2014Locally Scale-Invariant Convolutional Neural Networkscited by 34
  21. 2020Scale Equivariance Improves Siamese Trackingcited by 32
  22. 2020Scale-Equalizing Pyramid Convolution for Object Detectioncited by 25
  23. 2016Warped Convolutions: Efficient Invariance to Spatial Transformationscited by 24
  24. 2019Scale Steerable Filters for Locally Scale-Invariant Convolutional Neural Networkscited by 22
  25. 2018Scale equivariance in CNNs with vector fieldscited by 20
  26. 2017Convolutional Networks for Spherical Signalscited by 18
  27. 2019Learning to Convolve: A Generalized Weight-Tying Approachcited by 9
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 6; 2023: 13; 2024: 5; 2025: 3; 2026: 3.

35 papers.

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  1. 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
  2. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  3. 2022LieGG: Studying Learned Lie Group Generatorscited by 28
  4. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  5. 2021Dilated convolution with learnable spacingscited by 20
  6. 2023Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNNcited by 18
  7. 2021Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scalescited by 17
  8. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  9. 2022Scale Equivariant U-Netcited by 13
  10. 2023On genuine invariance learning without weight-tyingcited by 13
  11. 2023Scale-Equivariant UNet for Histopathology Image Segmentationcited by 11
  12. 2023Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fieldscited by 8
23 more
  1. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  2. 2023Color Equivariant Convolutional Networkscited by 7
  3. 2023Scale-Equivariant Deep Learning for 3D Datacited by 6
  4. 2022Scale-Equivariant Unrolled Neural Networks for Data-Efficient Accelerated MRI Reconstructioncited by 5
  5. 2023RSF-Conv: Rotation-and-Scale Equivariant Fourier Parameterized Convolution for Retinal Vessel Segmentationcited by 5
  6. 2023Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fieldscited by 5
  7. 2024Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensorscited by 5
  8. 2023Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolutioncited by 4
  9. 2023Rotation-Scale Equivariant Steerable Filterscited by 3
  10. 2024Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variationscited by 3
  11. 2022Just a Matter of Scale? Reevaluating Scale Equivariance in Convolutional Neural Networkscited by 2
  12. 2023Deep Neural Networks with Efficient Guaranteed Invariancescited by 2
  13. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  14. 2025Local Scale Equivariance with Latent Deep Equilibrium Canonicalizercited by 2
  15. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 2
  16. 2022VC dimensions of group convolutional neural networkscited by 1
  17. 2023Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural networkcited by 1
  18. 2026EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusioncited by 1
  19. 2021Wiggling Weights to Improve the Robustness of Classifierscited by 0
  20. 2024Efficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier-Bessel basescited by 0
  21. 2025Hybrid Lie semi-group and cascade structures for the generalized Gaussian derivative model for visual receptive fieldscited by 0
  22. 2026Scale-invariant Gaussian derivative residual networkscited by 0
  23. 2026MACRO: Training-free Multi-plane Attention for Closeup Render Optimizationcited by 0