  Message-passing neural networks (MPNNs) have been successfully applied to
representation learning on graphs in a variety of real-world applications.
However, two fundamental weaknesses of MPNNs' aggregators limit their ability
to represent graph-structured data: losing the structural information of nodes
in neighborhoods and lacking the ability to capture long-range dependencies in
disassortative graphs. Few studies have noticed the weaknesses from different
perspectives. From the observations on classical neural network and network
geometry, we propose a novel geometric aggregation scheme for graph neural
networks to overcome the two weaknesses. The behind basic idea is the
aggregation on a graph can benefit from a continuous space underlying the
graph. The proposed aggregation scheme is permutation-invariant and consists of
three modules, node embedding, structural neighborhood, and bi-level
aggregation. We also present an implementation of the scheme in graph
convolutional networks, termed Geom-GCN (Geometric Graph Convolutional
Networks), to perform transductive learning on graphs. Experimental results
show the proposed Geom-GCN achieved state-of-the-art performance on a wide
range of open datasets of graphs. Code is available at
https://github.com/graphdml-uiuc-jlu/geom-gcn.
