Understanding Generalization in Node and Link Prediction

TL;DR

This paper introduces a comprehensive framework to analyze how message-passing graph neural networks (MPNNs) generalize in node and link prediction tasks, considering various architectures, loss functions, and graph structures, supported by empirical validation.

Contribution

It provides the first unified theoretical framework for understanding MPNNs' generalization in node and link prediction, accounting for diverse architectural and structural factors.

Findings

The framework applies to both inductive and transductive settings.

Empirical results validate the theoretical insights.

Graph structure significantly influences generalization performance.

Abstract

Using message-passing graph neural networks (MPNNs) for node and link prediction is crucial in various scientific and industrial domains, which has led to the development of diverse MPNN architectures. Besides working well in practical settings, their ability to generalize beyond the training set remains poorly understood. While some studies have explored MPNNs' generalization in graph-level prediction tasks, much less attention has been given to node- and link-level predictions. Existing works often rely on unrealistic i.i.d.\@ assumptions, overlooking possible correlations between nodes or links, and assuming fixed aggregation and impractical loss functions while neglecting the influence of graph structure. In this work, we introduce a unified framework to analyze the generalization properties of MPNNs in inductive and transductive node and link prediction settings, incorporating diverse architectural parameters and loss functions and quantifying the influence of graph structure. Additionally, our proposed generalization framework can be applied beyond graphs to any classification task under the inductive or transductive setting. Our empirical study supports our theoretical insights, deepening our understanding of MPNNs' generalization capabilities in these tasks.