mlsanityData to 7 Oct 2026

Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

arXiv 2003.05425 ↗First posted 11 Mar 2020cs.LG cs.CV stat.MLcited by 90

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Abstract (arXiv)

A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs). Such GCNs utilize isotropic kernels and are therefore insensitive to the relative orientation of vertices and thus to the geometry of the mesh as a whole. We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Since the resulting features carry orientation information, we introduce a geometric message passing scheme defined by parallel transporting features over mesh edges. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.

Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Mar 2020.

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Citing papers per year: 2021: 17; 2022: 20; 2023: 20; 2024: 10; 2025: 8; 2026: 15.

90 papers.

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  1. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  2. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  3. 2023GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformerscited by 75
  4. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  5. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  6. 2023Geometric Algebra Transformercited by 46
  7. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  8. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  9. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  10. 2022Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wallcited by 29
  11. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 26
  12. 2021Roto-translated Local Coordinate Frames For Interacting Dynamical Systemscited by 24
38 more
  1. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  2. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  3. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  4. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  5. 2023Scaling Spherical CNNscited by 21
  6. 2022Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spacescited by 20
  7. 2023Machine Learning for Partial Differential Equationscited by 20
  8. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  9. 20234D Panoptic Segmentation as Invariant and Equivariant Field Predictioncited by 19
  10. 2021SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attentioncited by 18
  11. 2021Large-scale graph representation learning with very deep GNNs and self-supervisioncited by 18
  12. 2022Equivariance Discovery by Learned Parameter-Sharingcited by 18
  13. 2022Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networkscited by 18
  14. 2021Equivariant Networks for Pixelized Spherescited by 16
  15. 2023Making Vision Transformers Truly Shift-Equivariantcited by 16
  16. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  17. 2021Field Convolutions for Surface CNNscited by 14
  18. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
  19. 2021AIR-Nets: An Attention-Based Framework for Locally Conditioned Implicit Representationscited by 13
  20. 2022M"obius Convolutions for Spherical CNNscited by 13
  21. 2022Equivariant Mesh Attention Networkscited by 12
  22. 2023Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformerscited by 12
  23. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
  24. 2023Efficient Equivariant Transfer Learning from Pretrained Modelscited by 11
  25. 2021DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Cloudscited by 10
  26. 2021Mesh convolutional neural networks for wall shear stress estimation in 3D artery modelscited by 9
  27. 2022Implicit Convolutional Kernels for Steerable CNNscited by 9
  28. 2024E(3)-Equivariant Mesh Neural Networkscited by 9
  29. 2021Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizescited by 8
  30. 2022Offset equivariant networks and their applicationscited by 6
  31. 2023Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measurescited by 6
  32. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  33. 2024SE(3)-Hyena Operator for Scalable Equivariant Learningcited by 6
  34. 2025PoissonNet: A Local-Global Approach for Learning on Surfacescited by 6
  35. 2025Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogatescited by 5
  36. 2022Continual Learning for Pose-Agnostic Object Recognition in 3D Point Cloudscited by 4
  37. 2023Using and Abusing Equivariancecited by 4
  38. 2025AtlasD: Automatic Local Symmetry Discoverycited by 4

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