mlsanityData to 7 Oct 2026

E(3)-Equivariant Mesh Neural Networks

arXiv 2402.04821 ↗First posted 7 Feb 2024cs.LGcited by 9

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Abstract (arXiv)

Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric deep learning on 3D mesh. However, we observe that the complexities in many of these architectures does not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information, and further improve it to account for long-range interactions through hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive pre-processing. Our implementation is available at https://github.com/HySonLab/EquiMesh

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 34 of its 64 references that are in the map. First posted on arXiv 7 Feb 2024.

Builds on

34 of 64 references.

References · 34

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22 more
  1. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  2. 2018Tangent Convolutions for Dense Prediction in 3Dcited by 173
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  4. 2017Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Modelscited by 142
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  6. 2016Learning shape correspondence with anisotropic convolutional neural networkscited by 95
  7. 2018MeshNet: Mesh Neural Network for 3D Shape Representationcited by 95
  8. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  9. 2019SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operatorcited by 89
  10. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  11. 2021Subdivision-Based Mesh Convolution Networkscited by 60
  12. 2023On the Connection Between MPNN and Graph Transformercited by 60
  13. 2018Covariant Compositional Networks For Learning Graphscited by 54
  14. 2018TextureNet: Consistent Local Parametrizations for Learning from High-Resolution Signals on Meshescited by 45
  15. 2020Primal-Dual Mesh Convolutional Neural Networkscited by 44
  16. 2020DualConvMesh-Net: Joint Geodesic and Euclidean Convolutions on 3D Meshescited by 42
  17. 2018A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshescited by 39
  18. 2021Directional Message Passing on Molecular Graphs via Synthetic Coordinatescited by 24
  19. 2023E(n) Equivariant Message Passing Simplicial Networkscited by 23
  20. 2022Equivariant Mesh Attention Networkscited by 12
  21. 2022Laplacian2Mesh: Laplacian-Based Mesh Understandingcited by 11
  22. 2023Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networkscited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 3; 2026: 3.

9 papers.

  1. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  2. 2024E(n) Equivariant Message Passing Cellular Networkscited by 3
  3. 2024TESGNN: Temporal Equivariant Scene Graph Neural Networks for Efficient and Robust Multi-View 3D Scene Understandingcited by 2
  4. 2025HodgeFormer: Transformers for Learnable Operators on Triangular Meshes through Data-Driven Hodge Matricescited by 2
  5. 2025Thickness-aware E(3)-Equivariant 3D Mesh Neural Networkscited by 1
  6. 2025Drawback of Enforcing Equivariance and its Compensation via the Lens of Expressive Powercited by 0
  7. 2026PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchiescited by 0
  8. 2026Augmented Equivariant Mesh Networks for Anatomical Segmentationcited by 0
  9. 2026EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEscited by 0