mlsanityData to 13 Oct 2026

Transversal Pooling Neural Networks

arXiv 2609.36237 ↗First posted 28 Sep 2026cs.LG math.FAcited by 0

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Abstract (arXiv)

Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce transversal pooling neural networks, which generalize spatial max pooling to affine group actions. We establish equivariance to a chosen subgroup and derive explicit stability bounds for individual pooled wavelet coefficients under affine perturbations of the input. Experimentally, we demonstrate the utility of our networks in low-data environments and for predicting tropical cyclone intensification.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 45 of its 105 references that are in the map. First posted on arXiv 28 Sep 2026.

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45 of 105 references.

References · 45

  1. 2016Group Equivariant Convolutional Networkscited by 1,157
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33 more
  1. 2019B-Spline CNNs on Lie Groupscited by 97
  2. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  3. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
  4. 2015Rotation-invariant convolutional neural networks for galaxy morphology predictioncited by 83
  5. 2016TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networkscited by 66
  6. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 66
  7. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  8. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  9. 2018Geometric Scattering for Graph Data Analysiscited by 49
  10. 2020Universal Equivariant Multilayer Perceptronscited by 49
  11. 2015A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extractioncited by 46
  12. 2018Diffusion Scattering Transforms on Graphscited by 43
  13. 2017Scaling the Scattering Transform: Deep Hybrid Networkscited by 35
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  16. 2022Geometric Scattering on Measure Spacescited by 17
  17. 2019Deep Adaptive Wavelet Networkcited by 16
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  20. 2019A Learnable ScatterNet: Locally Invariant Convolutional Layerscited by 10
  21. 2024On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theorycited by 10
  22. 2019Geometric Wavelet Scattering Networks on Compact Riemannian Manifoldscited by 7
  23. 2015Deep Convolutional Neural Networks Based on Semi-Discrete Framescited by 6
  24. 2020Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Seriescited by 5
  25. 2015Nearly optimal classification for semimetricscited by 4
  26. 2019Deep Learning for 2D and 3D Rotatable Data: An Overview of Methodscited by 4
  27. 2022Max filtering with reflection groupscited by 4
  28. 2025On Universality Classes of Equivariant Networkscited by 4
  29. 2020Local Rotation Invariance in 3D CNNscited by 3
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  31. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  32. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  33. 2026Quantitative Approximation Rates for Group Equivariant Learningcited by 1

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