Graph Neural Networks are Inherently Good Generalizers: Insights by Bridging GNNs and MLPs

Chenxiao Yang, Qitian Wu, Jiahua Wang, Junchi Yan

Keywords: Graph Neural Networks, Generalization

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 provides a new perspective for understanding the learning behavior of GNNs, and can be used as an analytic tool for dissecting various GNN-related research problems including expressivity, generalization, over-smoothing and heterophily. As an initial step to analyze PMLP, we show its essential difference to MLP at infinite-width limit lies in the NTK feature map in the post-training stage. Moreover, through extrapolation analysis (i.e., generalization under distribution shifts), we find that though most GNNs and their PMLP counterparts cannot extrapolate non-linear functions for extreme out-of-distribution data, they have greater potential to generalize to testing data near the training data support as natural advantages of the GNN architecture used for inference.

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