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# Generalization Error of Graph Neural Networks in the Mean-field Regime

*Proceedings of the 41st International Conference on Machine Learning*, PMLR 235:1359-1391, 2024.

#### Abstract

This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networksâ€™ performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.