mlsanityData to 14 Oct 2026

Homogeneous vector bundles and G-equivariant convolutional neural networks

arXiv 2105.05400 ↗First posted 12 May 2021cs.LG math.RT stat.MLcited by 21

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Abstract (arXiv)

G-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous G-space M. GCNNs are designed to respect the global symmetry in M, thereby facilitating learning. In this paper, we analyze GCNNs on homogeneous spaces M = G/K in the case of unimodular Lie groups G and compact subgroups K ≤ G. We demonstrate that homogeneous vector bundles is the natural setting for GCNNs. We also use reproducing kernel Hilbert spaces to obtain a precise criterion for expressing G-equivariant layers as convolutional layers. This criterion is then rephrased as a bandwidth criterion, leading to even stronger results for some groups.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 27 of its 56 references that are in the map. First posted on arXiv 12 May 2021.

Builds on

27 of 56 references.

References · 27

  1. 2021Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervisioncited by 3,864
  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2021EfficientNetV2: Smaller Models and Faster Trainingcited by 1,135
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
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  7. 2015An Introduction to Convolutional Neural Networkscited by 514
  8. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  9. 2018Spherical CNNscited by 456
  10. 2018Rotation Equivariant CNNs for Digital Pathologycited by 422
  11. 2021High-Performance Large-Scale Image Recognition Without Normalizationcited by 360
  12. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
15 more
  1. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  2. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  3. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 248
  4. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  5. 2017Large Kernel Matters -- Improve Semantic Segmentation by Global Convolutional Networkcited by 208
  6. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  7. 2017VNect: Real-time 3D Human Pose Estimation with a Single RGB Cameracited by 129
  8. 2018Fully Convolutional Adaptation Networks for Semantic Segmentationcited by 75
  9. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  10. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  11. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  12. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 28
  13. 2020Theoretical Aspects of Group Equivariant Neural Networkscited by 25
  14. 2019Covariance in Physics and Convolutional Neural Networkscited by 12
  15. 2019Discrete Rotation Equivariance for Point Cloud Recognitioncited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 5; 2023: 6; 2024: 3; 2025: 3; 2026: 1.

21 papers.

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  1. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 65
  2. 2023EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulationcited by 37
  3. 2022A case for using rotation invariant features in state of the art feature matcherscited by 27
  4. 2022Equivariance versus Augmentation for Spherical Imagescited by 24
  5. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  6. 2022Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spacescited by 20
  7. 2023Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariancecited by 19
  8. 2023Optimization Dynamics of Equivariant and Augmented Neural Networkscited by 18
  9. 2023EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervisioncited by 18
  10. 2021ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Cloudscited by 15
  11. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  12. 2022Equivariant Light Field Convolution and Transformercited by 2
9 more
  1. 2024Equivariant Manifold Neural ODEs and Differential Invariantscited by 2
  2. 2024Symmetries in Overparametrized Neural Networks: A Mean-Field Viewcited by 2
  3. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  4. 2025SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spherescited by 2
  5. 2025Learning Generalizable Shape Completion with SIM(3) Equivariancecited by 2
  6. 2025Learning from Frustration: Torsor CNNs on Graphscited by 2
  7. 2023Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebrascited by 1
  8. 2022In Search of Projectively Equivariant Networkscited by 0
  9. 2026Steerable Neural ODEs on Homogeneous Spacescited by 0