mlsanityData to 14 Oct 2026

Truly Scale-Equivariant Deep Nets with Fourier Layers

arXiv 2311.02922 ↗First posted 6 Nov 2023cs.LG cs.CVcited by 16

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Abstract (arXiv)

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 39 of its 53 references that are in the map. First posted on arXiv 6 Nov 2023.

Builds on

39 of 53 references.

References · 39

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2016Pyramid Scene Parsing Networkcited by 2,479
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  6. 2017Deep Setscited by 1,421
  7. 2021Alias-Free Generative Adversarial Networkscited by 1,184
  8. 2016Group Equivariant Convolutional Networkscited by 1,165
  9. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  10. 2021Resolution-robust Large Mask Inpainting with Fourier Convolutionscited by 738
  11. 2014Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognitioncited by 720
  12. 2019General E(2)-Equivariant Steerable CNNscited by 446
27 more
  1. 2019Making Convolutional Networks Shift-Invariant Againcited by 391
  2. 2018Invariant and Equivariant Graph Networkscited by 346
  3. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  4. 2017Equivariance Through Parameter-Sharingcited by 141
  5. 2019Deep Scale-spaces: Equivariance Over Scalecited by 114
  6. 2019Scale-Equivariant Steerable Networkscited by 110
  7. 2020On Learning Sets of Symmetric Elementscited by 98
  8. 2019B-Spline CNNs on Lie Groupscited by 97
  9. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 92
  10. 2013Fast Training of Convolutional Networks through FFTscited by 89
  11. 2021Intriguing Findings of Frequency Selection for Image Deblurringcited by 81
  12. 2018Deep Models of Interactions Across Setscited by 69
  13. 2020Attentive Group Equivariant Convolutional Networkscited by 63
  14. 2019PIC: Permutation Invariant Critic for Multi-Agent Deep Reinforcement Learningcited by 47
  15. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  16. 2021DISCO: accurate Discrete Scale Convolutionscited by 36
  17. 2014Locally Scale-Invariant Convolutional Neural Networkscited by 34
  18. 2019Chirality Nets for Human Pose Regressioncited by 31
  19. 2019Scale Steerable Filters for Locally Scale-Invariant Convolutional Neural Networkscited by 22
  20. 2019Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filterscited by 18
  21. 2021Semantic Tracklets: An Object-Centric Representation for Visual Multi-Agent Reinforcement Learningcited by 18
  22. 2022Equivariance Discovery by Learned Parameter-Sharingcited by 18
  23. 2022Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networkscited by 18
  24. 2021Equivariant Networks for Pixelized Spherescited by 16
  25. 2023Making Vision Transformers Truly Shift-Equivariantcited by 16
  26. 2021Group Equivariant Subsamplingcited by 15
  27. 2019Building Deep, Equivariant Capsule Networkscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 7; 2026: 3.

16 papers.

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  1. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 89
  2. 2024Neural Operators with Localized Integral and Differential Kernelscited by 62
  3. 2024HyperSpace: Hypernetworks for spacing-adaptive image segmentationcited by 6
  4. 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
  5. 2025Group Downsampling with Equivariant Anti-aliasingcited by 3
  6. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 3
  7. 2024Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reductioncited by 2
  8. 2025AdS-GNN -- a Conformally Equivariant Graph Neural Networkcited by 2
  9. 2025Local Scale Equivariance with Latent Deep Equilibrium Canonicalizercited by 2
  10. 2025CLIPSym: Delving into Symmetry Detection with CLIPcited by 2
  11. 2025Alias-Free ViT: Fractional Shift Invariance via Linear Attentioncited by 2
  12. 2024Harmformer: Harmonic Networks Meet Transformers for Continuous Roto-Translation Equivariancecited by 1
4 more
  1. 2026Learning and extrapolating scale-invariant processescited by 1
  2. 2024Lost in Translation: Modern Neural Networks Still Struggle With Small Realistic Image Transformationscited by 0
  3. 2026Tunable Soft Equivariance with Guaranteescited by 0
  4. 2026MACRO: Training-free Multi-plane Attention for Closeup Render Optimizationcited by 0