mlsanityData to 7 Oct 2026

VC dimensions of group convolutional neural networks

arXiv 2212.09507 ↗First posted 19 Dec 2022cs.LG math.FA stat.MLcited by 1

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Abstract (arXiv)

We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and appropriately chosen convolutional kernels, already two-parameter families of convolutional neural networks have an infinite VC dimension, despite being invariant to the action of an infinite group.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 17 of its 33 references that are in the map. First posted on arXiv 19 Dec 2022.

Builds on

17 of 33 references.

References · 17

  1. 2016Group Equivariant Convolutional Networkscited by 1,154
  2. 2019General E(2)-Equivariant Steerable CNNscited by 441
  3. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  4. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  5. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  7. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 182
  8. 2019Scale-Equivariant Steerable Networkscited by 110
  9. 2019B-Spline CNNs on Lie Groupscited by 97
  10. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
  11. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  12. 2016Understanding Deep Convolutional Networkscited by 76
5 more
  1. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  2. 2019Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spacescited by 34
  3. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  4. 2022A Theory of PAC Learnability under Transformation Invariancescited by 21
  5. 2022What is an equivariant neural network?cited by 21

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Citing papers per year: 2024: 1.

1 paper.

  1. 2024On the VC dimension of deep group convolutional neural networkscited by 1