Graph Neural Networks are Inherently Good Generalizers: Insights by Bridging GNNs and MLPs (2212.09034v4)

Abstract: Graph neural networks (GNNs), as the de-facto model class for representation learning on graphs, are built upon the multi-layer perceptrons (MLP) architecture with additional message passing layers to allow features to flow across nodes. While conventional wisdom commonly attributes the success of GNNs to their advanced expressivity, we conjecture that this is not the main cause of GNNs' superiority in node-level prediction tasks. This paper pinpoints the major source of GNNs' performance gain to their intrinsic generalization capability, by introducing an intermediate model class dubbed as P(ropagational)MLP, which is identical to standard MLP in training, but then adopts GNN's architecture in testing. Intriguingly, we observe that PMLPs consistently perform on par with (or even exceed) their GNN counterparts, while being much more efficient in training. This finding sheds new insights into understanding the learning behavior of GNNs, and can be used as an analytic tool for dissecting various GNN-related research problems. As an initial step to analyze the inherent generalizability of GNNs, we show the essential difference between MLP and PMLP at infinite-width limit lies in the NTK feature map in the post-training stage. Moreover, by examining their extrapolation behavior, we find that though many GNNs and their PMLP counterparts cannot extrapolate non-linear functions for extremely out-of-distribution samples, they have greater potential to generalize to testing samples near the training data range as natural advantages of GNN architectures.