  Current graph neural network (GNN) architectures naively average or sum node
embeddings into an aggregated graph representation -- potentially losing
structural or semantic information. We here introduce OT-GNN, a model that
computes graph embeddings using parametric prototypes that highlight key facets
of different graph aspects. Towards this goal, we successfully combine optimal
transport (OT) with parametric graph models. Graph representations are obtained
from Wasserstein distances between the set of GNN node embeddings and
``prototype'' point clouds as free parameters. We theoretically prove that,
unlike traditional sum aggregation, our function class on point clouds
satisfies a fundamental universal approximation theorem. Empirically, we
address an inherent collapse optimization issue by proposing a noise
contrastive regularizer to steer the model towards truly exploiting the OT
geometry. Finally, we outperform popular methods on several molecular property
prediction tasks, while exhibiting smoother graph representations.

Machine Learning;Machine Learning