提出路径邻居聚合方法，提升图神经网络对知识图谱逻辑规则的表达能力。
Enhancing Logical Expressiveness in Graph Neural Networks via Path-Neighbor Aggregation
- 通过聚合推理路径上的邻居嵌入，增强GNN的逻辑表达能力。
- 理论证明其在k+1跳下严格优于k跳的表达能力，且强于C-GNN。
- 在6个合成数据集和2个真实数据集上验证，逻辑推理性能显著提升。
图神经网络（GNN）能有效建模图结构信息，广泛应用于知识图谱（KG）推理。然而，现有研究主要关注单关系图的表达能力，对GNN在知识图谱中表达逻辑规则的能力讨论不足。如何提升GNN的逻辑表达能力仍是关键问题。为此，我们提出路径邻居增强型GNN（PN-GNN），通过在推理路径上聚合节点邻居嵌入来增强逻辑表达能力。首先分析现有GNN方法的表达局限性；然后从理论上研究PN-GNN的逻辑表达能力，证明其不仅严格强于C-GNN，且(k+1)跳逻辑表达能力严格优于k跳。最后在六个合成数据集和两个真实世界数据集上评估其表现。理论分析与大量实验均表明，PN-GNN在不牺牲泛化能力的前提下显著提升了逻辑规则的表达能力，在知识图谱推理任务中表现优异。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) can effectively model structural information of graphs, making them widely used in knowledge graph (KG) reasoning. However, existing studies on the expressive power of GNNs mainly focuses on simple single-relation graphs, and there is still insufficient discussion on the power of GNN to express logical rules in KGs. How to enhance the logical expressive power of GNNs is still a key issue. Motivated by this, we propose Path-Neighbor enhanced GNN (PN-GNN), a method to enhance the logical expressive power of GNN by aggregating node-neighbor embeddings on the reasoning path. First, we analyze the logical expressive power of existing GNN-based methods and point out the shortcomings of the expressive power of these methods. Then, we theoretically investigate the logical expressive power of PN-GNN, showing that it not only has strictly stronger expressive power than C-GNN but also that its $(k+1)$-hop logical expressiveness is strictly superior to that of $k$-hop. Finally, we evaluate the logical expressive power of PN-GNN on six synthetic datasets and two real-world datasets. Both theoretical analysis and extensive experiments confirm that PN-GNN enhances the expressive power of logical rules without compromising generalization, as evidenced by its competitive performance in KG reasoning tasks.
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