mlsanityData to 7 Oct 2026

Group-invariant max filtering

arXiv 2205.14039 ↗First posted 27 May 2022cs.IT cs.DS cs.LGcited by 18

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Abstract (arXiv)

Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where V=ℝd and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where V=L2(ℝd) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 16 of its 81 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

16 of 81 references.

References · 16

  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
  2. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  3. 2015Recent Advances in Convolutional Neural Networkscited by 360
  4. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  5. 2014Phase Retrieval via Wirtinger Flow: Theory and Algorithmscited by 123
  6. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  7. 2022A Short Tutorial on The Weisfeiler-Lehman Test And Its Variantscited by 52
  8. 2015Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systemscited by 50
  9. 2018Geometric Scattering for Graph Data Analysiscited by 49
  10. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  11. 2018On Lipschitz Bounds of General Convolutional Neural Networkscited by 29
  12. 2022Permutation Invariant Representations with Applications to Graph Deep Learningcited by 20
4 more
  1. 2016Using Filter Banks in Convolutional Neural Networks for Texture Classificationcited by 15
  2. 2017Estimation under group actions: recovering orbits from invariantscited by 14
  3. 2013Invertibility and Robustness of Phaseless Reconstructioncited by 3
  4. 2021Dihedral multi-reference alignmentcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 3; 2024: 3; 2025: 7; 2026: 3.

18 papers.

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  1. 2023Neural Injective Functions for Multisets, Measures and Graphs via a Finite Witness Theoremcited by 33
  2. 2023Approximately Equivariant Graph Networkscited by 16
  3. 2022Machine learning and invariant theorycited by 13
  4. 2023Towards fully covariant machine learningcited by 10
  5. 2025Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 8
  6. 2024On the H"older Stability of Multiset and Graph Neural Networkscited by 6
  7. 2024Stability of sorting based embeddingscited by 3
  8. 2025Quick ViTs: Speeding up Vision Transformers through Equivariancecited by 3
  9. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  10. 2025Quantitative Bounds for Sorting-Based Permutation-Invariant Embeddingscited by 2
  11. 2025On the (Non) Injectivity of Piecewise Linear Janossy Poolingcited by 1
  12. 2025Toward bilipshiz geometric modelscited by 1
6 more
  1. 2026Quantitative Approximation Rates for Group Equivariant Learningcited by 1
  2. 2024Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 0
  3. 2025Classification of Firn Data via Topological Featurescited by 0
  4. 2025If you can distinguish, you can express: Galois theory, Stone--Weierstrass, machine learning, and linguisticscited by 0
  5. 2026Transversal Pooling Neural Networkscited by 0
  6. 2026Invariant Shape Analysis of Surfaces with Spherical Topologycited by 0