Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman subtree (WL-subtree) and Weisfeiler-Lehman optimal assignment (WLOA) kernels are effective in capturing similarity relationships, they rely heavily on predefined kernels and lack sufficient non-linearity for more complex data patterns. Our work aims to bridge the gap between neural network methods and kernel approaches by enabling GNNs to consistently capture relational structures in their learned representations. Given the analogy between the message-passing process of GNNs and WL algorithms, we thoroughly compare and analyze the properties of WL-subtree and WLOA kernels. We find that the similarities captured by WLOA at different iterations are asymptotically consistent, ensuring that similar graphs remain similar in subsequent iterations, thereby leading to superior performance over the WL-subtree kernel. Inspired by these findings, we conjecture that the consistency in the similarities of graph representations across GNN layers is crucial in capturing relational structures and enhancing graph classification performance. Thus, we propose a loss to enforce the similarity of graph representations to be consistent across different layers. Our empirical analysis verifies our conjecture and shows that our proposed consistency loss can significantly enhance graph classification performance across several GNN backbones on various datasets.

本研究解决了图神经网络（GNN）在捕捉图之间一致性相似性关系方面的问题。我们提出了一种新颖的方法，通过比较图核方法与GNN的消息传递过程，提出了一种一致性损失，以确保不同层次的图表示之间的相似性一致性，从而显著提升图分类性能。研究结果表明，这种一致性在图表示学习中至关重要。

探讨图表示中的一致性：从图核到图神经网络