We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically for MPNNs with normalized sum aggregation and mean aggregation. Our analysis is based on a data generation model incorporating a finite set of template graphons. Each graph within this framework is generated by sampling from one of the graphons with a certain degree of perturbation. In particular, we extend previous MPNN generalization results to a more realistic setting, which includes the following modifications: 1) we analyze simple random graphs with Bernoulli-distributed edges instead of weighted graphs; 2) we sample both graphs and graph signals from perturbed graphons instead of clean graphons; and 3) we analyze sparse graphs instead of dense graphs. In this more realistic and challenging scenario, we provide a generalization bound that decreases as the average number of nodes in the graphs increases. Our results imply that MPNNs with higher complexity than the size of the training set can still generalize effectively, as long as the graphs are sufficiently large.

翻译：我们研究了消息传递神经网络（MPNN）的泛化能力，MPNN是图神经网络（GNN）中常见的一类模型。我们专门为具有归一化和求和聚合以及均值聚合的MPNN推导了泛化界。我们的分析基于一个包含有限个模板图过程的数据生成模型。该框架中的每个图都是通过从某个图过程中采样并引入一定程度的扰动生成的。具体而言，我们将先前的MPNN泛化结果推广到更现实的场景，其中包含以下改进：1）我们分析具有伯努利分布边的简单随机图，而非加权图；2）我们从受扰动的图过程中采样图和图信号，而非干净图过程；3）我们分析稀疏图而非稠密图。在这一更现实且更具挑战性的场景中，我们提供了一个泛化界，该界随着图中平均节点数的增加而减小。我们的结果表明，只要图足够大，复杂度高于训练集规模的MPNN仍然可以有效地泛化。