  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.
