This work provides a theoretical framework for assessing the generalization error of graph classification tasks via 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 networks' performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.

翻译：本文为超参数化场景下基于图神经网络的图分类任务泛化误差评估提供了理论框架，其中参数数量超过数据样本量。我们探讨了两种广泛应用的图神经网络：图卷积神经网络和图消息传递神经网络。在本研究之前，现有超参数化场景下的泛化误差边界缺乏信息性，限制了对超参数化网络性能的理解。我们的创新方法是在平均场机制下推导这些图神经网络泛化误差的上界。我们建立了收敛速度为 $O(1/n)$ 的上界，其中 $n$ 为图样本数量。这些上界为超参数化挑战性场景下网络对未见数据的性能提供了理论保证，并总体上有助于理解其性能表现。