mlsanityData to 14 Oct 2026

Scale equivariance in CNNs with vector fields

arXiv 1807.11783 ↗First posted 31 Jul 2018cs.CVcited by 20

Not on the map. Why?

Abstract (arXiv)

We study the effect of injecting local scale equivariance into Convolutional Neural Networks. This is done by applying each convolutional filter at multiple scales. The output is a vector field encoding for the maximally activating scale and the scale itself, which is further processed by the following convolutional layers. This allows all the intermediate representations to be locally scale equivariant. We show that this improves the performance of the model by over 20% in the scale equivariant task of regressing the scaling factor applied to randomly scaled MNIST digits. Furthermore, we find it also useful for scale invariant tasks, such as the actual classification of randomly scaled digits. This highlights the usefulness of allowing for a compact representation that can also learn relationships between different local scales by keeping internal scale equivariance.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Jul 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 3; 2023: 8; 2024: 3; 2025: 0; 2026: 1.

20 papers.

Sort:

  1. 2024Neural Operators with Localized Integral and Differential Kernelscited by 62
  2. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  3. 2021DISCO: accurate Discrete Scale Convolutionscited by 36
  4. 2021Resolution learning in deep convolutional networks using scale-space theorycited by 26
  5. 2024Clifford-Steerable Convolutional Neural Networkscited by 25
  6. 2021Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scalescited by 17
  7. 2023Scale-Equivariant UNet for Histopathology Image Segmentationcited by 11
  8. 2023Riesz networks: scale invariant neural networks in a single forward passcited by 8
  9. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  10. 2022Improving the Sample-Complexity of Deep Classification Networks with Invariant Integrationcited by 7
  11. 2023Scale-Equivariant Deep Learning for 3D Datacited by 6
  12. 2023Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictorscited by 3
8 more
  1. 2024Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variationscited by 3
  2. 2021Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?cited by 2
  3. 2022Just a Matter of Scale? Reevaluating Scale Equivariance in Convolutional Neural Networkscited by 2
  4. 2023Deep Neural Networks with Efficient Guaranteed Invariancescited by 2
  5. 2023Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural networkcited by 1
  6. 2023A study on the invariance in security whatever the dimension of images for the steganalysis by deep-learningcited by 0
  7. 2023Restore Translation Using Equivariant Neural Networkscited by 0
  8. 2026Scale-invariant Gaussian derivative residual networkscited by 0