Understanding Generalization in Node and Link Prediction

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.

Survey on Generalization Theory for Graph Neural Networks

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their ability to separate graphs and approximate functions over them, comparatively less attention has been directed toward investigating their generalization abilities, i.e., making meaningful predictions beyond the training data. Here, we systematically review the existing literature on the generalization abilities of MPNNs. We analyze the strengths and limitations of various studies in these domains, providing insights into their methodologies and findings. Furthermore, we identify potential avenues for future research, aiming to deepen our understanding of the generalization abilities of MPNNs.

Covered Forest: Fine-grained generalization analysis of graph neural networks

The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs' generalization abilities -- making meaningful predictions beyond the training set -- remain less explored. Current generalization analyses often overlook graph structure, limit the focus to specific aggregation functions, and assume the impractical, hard-to-optimize $0$-$1$ loss function. Here, we extend recent advances in graph similarity theory to assess the influence of graph structure, aggregation, and loss functions on MPNNs' generalization abilities. Our empirical study supports our theoretical insights, improving our understanding of MPNNs' generalization properties.