A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks

In this paper, we derived generalization bounds for two primary classes of graph neural networks (GNNs), namely graph convolutional networks (GCNs) and message passing GNNs, via a PAC-Bayesian approach. Specifically, our result reveals that the maximum node degree and spectral norm of the weights govern the generalization bound. Importantly, our bound is a natural generalization of the results developed in \\cite{neyshabur2017pac} for fully-connected and convolutional neural networks. For message passing GNNs, our PAC-Bayes bound improves over the Rademacher complexity based bound in \\cite{garg2020generalization}, showing a tighter dependency on the maximum node degree and the maximum hidden dimension. The key ingredients of our proof is a perturbation analysis of GNNs and the generalization of PAC-Bayes analysis to non-homogeneous GNNs. We perform an empirical study on several real-world graph datasets and verify that our PAC-Bayes bound is tighter than others.