Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

Pim De Haan, Maurice Weiler, Taco Cohen, Max Welling

Keywords: symmetry, equivariance, mesh, geometric, convolution

Abstract: 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.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

One-sentence Summary: Expressive anisotropic mesh convolution without having to pick arbitrary kernel orientation by using gauge equivariance

Code: [ qualcomm-ai-research/gauge-equivariant-mesh-cnn](https://github.com/qualcomm-ai-research/gauge-equivariant-mesh-cnn)