Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology
This addresses the problem of understanding and improving GCN expressiveness for graph learning tasks, offering incremental enhancements to existing methods.
The paper investigates the representation power of Graph Convolutional Networks (GCNs) in learning graph topology, finding that standard GCNs are restrictive and can fail without careful design, but a modular GCN with different propagation rules and residual connections significantly improves performance, enabling distinction of graphs from different generation models for small graphs.
To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without careful design, GCNs can fail miserably even with multiple layers and nonlinear activation functions. We analyze theoretically the expressiveness of GCNs, concluding a modular GCN design, using different propagation rules with residual connections could significantly improve the performance of GCN. We demonstrate that such modular designs are capable of distinguishing graphs from different graph generation models for surprisingly small graphs, a notoriously difficult problem in network science. Our investigation suggests that, depth is much more influential than width, with deeper GCNs being more capable of learning higher order graph moments. Additionally, combining GCN modules with different propagation rules is critical to the representation power of GCNs.