  We propose two graph neural network layers for graphs with features in a
Riemannian manifold. First, based on a manifold-valued graph diffusion
equation, we construct a diffusion layer that can be applied to an arbitrary
number of nodes and graph connectivity patterns. Second, we model a tangent
multilayer perceptron by transferring ideas from the vector neuron framework to
our general setting. Both layers are equivariant with respect to node
permutations and isometries of the feature manifold. These properties have been
shown to lead to a beneficial inductive bias in many deep learning tasks.
Numerical examples on synthetic data as well as on triangle meshes of the right
hippocampus to classify Alzheimer's disease demonstrate the very good
performance of our layers.
