  Graph neural networks (GNNs) are a powerful tool to learn representations on
graphs by iteratively aggregating features from node neighbourhoods. Many
variant models have been proposed, but there is limited understanding on both
how to compare different architectures and how to construct GNNs
systematically. Here, we propose a hierarchy of GNNs based on their aggregation
regions. We derive theoretical results about the discriminative power and
feature representation capabilities of each class. Then, we show how this
framework can be utilized to systematically construct arbitrarily powerful
GNNs. As an example, we construct a simple architecture that exceeds the
expressiveness of the Weisfeiler-Lehman graph isomorphism test. We empirically
validate our theory on both synthetic and real-world benchmarks, and
demonstrate our example's theoretical power translates to strong results on
node classification, graph classification, and graph regression tasks.

Machine Learning;Computer Vision and Pattern Recognition;Machine Learning