mlsanityData to 7 Oct 2026

Deep Scale-spaces: Equivariance Over Scale

arXiv 1905.11697 ↗First posted 28 May 2019cs.LG cs.CV stat.MLcited by 113

Not on the map. Why?

Abstract (arXiv)

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

Key facts. Cited by 113 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 May 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 25; 2023: 26; 2024: 18; 2025: 12; 2026: 10.

113 papers.

Sort:

  1. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  2. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  3. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  4. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  5. 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
  6. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  7. 2021Self-Supervised Learning Disentangled Group Representation as Featurecited by 47
  8. 2021Learning Partial Equivariances from Datacited by 44
  9. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  10. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  11. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  12. 2023Generative Adversarial Symmetry Discoverycited by 40
38 more
  1. 2023Equivariant Adaptation of Large Pretrained Modelscited by 40
  2. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  3. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  4. 2021Equivariant neural networks for inverse problemscited by 29
  5. 2022Sample Efficiency of Data Augmentation Consistency Regularizationcited by 28
  6. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  7. 2022LieGG: Studying Learned Lie Group Generatorscited by 28
  8. 2021Commutative Lie Group VAE for Disentanglement Learningcited by 27
  9. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  10. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  11. 2022Generative Coarse-Graining of Molecular Conformationscited by 21
  12. 2022Maximum Class Separation as Inductive Bias in One Matrixcited by 21
  13. 2021Dilated convolution with learnable spacingscited by 20
  14. 2023Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNNcited by 18
  15. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  16. 2021Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scalescited by 17
  17. 2022Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecastingcited by 17
  18. 2022Equivariant Networks for Zero-Shot Coordinationcited by 16
  19. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  20. 2022Learning Instance-Specific Augmentations by Capturing Local Invariancescited by 15
  21. 2024Graph Neural PDE Solvers with Conservation and Similarity-Equivariancecited by 15
  22. 2022M"obius Convolutions for Spherical CNNscited by 13
  23. 2022Scale Equivariant U-Netcited by 13
  24. 2023On genuine invariance learning without weight-tyingcited by 13
  25. 2021Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graphcited by 11
  26. 2023Scale-Equivariant UNet for Histopathology Image Segmentationcited by 11
  27. 2023Flow Factorized Representation Learningcited by 11
  28. 2023Almost Equivariance via Lie Algebra Convolutionscited by 10
  29. 2022In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?cited by 9
  30. 2022Analysis of (sub-)Riemannian PDE-G-CNNscited by 8
  31. 2023Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fieldscited by 8
  32. 2023Riesz networks: scale invariant neural networks in a single forward passcited by 8
  33. 2023As large as it gets: Learning infinitely large Filters via Neural Implicit Functions in the Fourier Domaincited by 8
  34. 2025Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustnesscited 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. 2023Color Equivariant Convolutional Networkscited by 7
  38. 2021Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transformscited by 6

50 most cited of 113 All 113 (JSON)