Towards Bridging Generalization and Expressivity of Graph Neural Networks

We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties, e.g., shortest/longest cycle, diameter, or certain motifs, cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message passing models, and more powerful variants that exploit local graph structure (e.g., via relative orientation of messages, or local port ordering) to distinguish neighbors of each node. Our treatment includes a novel graphtheoretic formalism. Second, we provide the first data dependent generalization bounds for message passing GNNs. This analysis explicitly accounts for the local permutation invariance of GNNs. Our bounds are much tighter than existing VC-dimension based guarantees for GNNs, and are comparable to Rademacher bounds for recurrent neural networks.