mlsanityData to 14 Oct 2026

On the VC dimension of deep group convolutional neural networks

arXiv 2410.15800 ↗First posted 21 Oct 2024cs.LG math.ST stat.MLcited by 1

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Abstract (arXiv)

We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such as the number of layers, weights, and input dimension affect the VC dimension. We further compare the derived bounds to those known for other types of neural networks. Our findings extend previous results on the VC dimension of continuous GCNNs with two layers, thereby providing new insights into the generalization properties of GCNNs, particularly regarding the dependence on the input resolution of the data.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 26 of its 40 references that are in the map. First posted on arXiv 21 Oct 2024.

Builds on

26 of 40 references.

References · 26

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  3. 2016Group Equivariant Convolutional Networkscited by 1,165
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14 more
  1. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 92
  2. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 91
  3. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
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  5. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 73
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  7. 2019Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spacescited by 34
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  14. 2022VC dimensions of group convolutional neural networkscited by 1

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  1. 2026A Rigorous, Tractable Measure of Model Complexitycited by 0