Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.

本研究解决了图分类中难以量化图之间相似性和图表示的问题，提出了一种新颖的图参考分布学习（GRDL）方法，该方法通过将GNN层生成的潜在节点嵌入视为离散分布，避免了全局池化操作，基于最大均值差异进行直接分类。实验结果证明，GRDL在一般化能力和效率上均优于现有的GNN方法，训练和推理速度至少快10倍，为实际应用提供了强有力的理论支持和实验验证。

通过参考分布学习进行图分类：理论与实践