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Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

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arxiv 2003.05425 v3 pith:J3Y7EMWT submitted 2020-03-11 cs.LG cs.CVstat.ML

Pim de Haan , Maurice Weiler , Taco Cohen , Max Welling This is my paper · ORCID
classification cs.LGcs.CVstat.ML
keywords gcnsmeshequivariantgaugeanisotropicapplycnnsconvolutions
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric Hyena Networks for Large-scale Equivariant Learning

    cs.LG 2025-05 conditional novelty 8.0 of 10

    Geometric Hyena is an equivariant long-convolutional architecture that captures global geometric context with sub-quadratic complexity and outperforms equivariant transformer baselines on several RNA and protein predi...

  2. Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes

    cs.GR 2026-07 conditional novelty 6.0 of 10

    Mass-weighted FEM attention on intrinsic mesh features is triangulation-agnostic and beats current mesh and point-cloud baselines on several geometry-learning benchmarks.

  3. Geometric deep learning for local growth prediction on abdominal aortic aneurysm surfaces

    cs.CV 2025-06 conditional novelty 6.0 of 10

    A geometric deep learning model predicts local AAA growth on 3D vessel surfaces with a median diameter error of 1.18 mm, outperforming two baselines in a 24-patient cross-validation and a 7-patient external test.

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