mlsanityData to 14 Oct 2026

Group Equivariant Subsampling

arXiv 2106.05886 ↗First posted 10 Jun 2021cs.LG stat.MLcited by 15

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Abstract (arXiv)

Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling. We use these layers to construct group equivariant autoencoders (GAEs) that allow us to learn low-dimensional equivariant representations. We empirically verify on images that the representations are indeed equivariant to input translations and rotations, and thus generalise well to unseen positions and orientations. We further use GAEs in models that learn object-centric representations on multi-object datasets, and show improved data efficiency and decomposition compared to non-equivariant baselines.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 42 of its 55 references that are in the map. First posted on arXiv 10 Jun 2021.

Builds on

42 of 55 references.

References · 42

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30 more
  1. 2019General E(2)-Equivariant Steerable CNNscited by 446
  2. 2019MONet: Unsupervised Scene Decomposition and Representationcited by 392
  3. 2019Making Convolutional Networks Shift-Invariant Againcited by 391
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Cited by year

Citing papers per year: 2022: 4; 2023: 7; 2024: 1; 2025: 3.

15 papers.

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  1. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 39
  2. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  3. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  4. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  5. 2022Learning Instance-Specific Augmentations by Capturing Local Invariancescited by 15
  6. 2023Alias-Free Convnets: Fractional Shift Invariance via Polynomial Activationscited by 11
  7. 2023Almost Equivariance via Lie Algebra Convolutionscited by 10
  8. 2024A Generative Model of Symmetry Transformationscited by 10
  9. 2025Shifting the Paradigm: A Diffeomorphism Between Time Series Data Manifolds for Achieving Shift-Invariancy in Deep Learningcited by 5
  10. 2023Using and Abusing Equivariancecited by 4
  11. 2025Group Downsampling with Equivariant Anti-aliasingcited by 3
  12. 2023Deep Neural Networks with Efficient Guaranteed Invariancescited by 2
3 more
  1. 2025Local Scale Equivariance with Latent Deep Equilibrium Canonicalizercited by 2
  2. 2023Group Invariant Global Poolingcited by 1
  3. 2022From CNNs to Shift-Invariant Twin Models Based on Complex Waveletscited by 0