Enhancing Logical Expressiveness in Graph Neural Networks via Path-Neighbor Aggregation

TL;DR

The paper addresses the limited logical expressiveness of existing GNN-based KG reasoning methods, especially when moving beyond single-relational graphs. It introduces Path-Neighbor Enhanced GNN (PN-GNN), which enriches conditional message passing by aggregating neighbor embeddings along reasoning paths, using 1-hop and 2-hop path neighborhoods to balance expressiveness and efficiency. The authors prove that PN-GNN has strictly greater logical expressiveness than C-GNN, and that its (k+1)-hop capability strictly extends beyond k-hop, while maintaining generalization. Empirical results on six synthetic datasets and two real-world KG benchmarks (including transductive and inductive settings) show PN-GNN achieves strong logical-rule learning and competitive reasoning performance, often outperforming state-of-the-art baselines, and demonstrating robustness to labeling tricks. Overall, PN-GNN offers a principled way to boost logical reasoning power in KG applications without sacrificing inductive generalization, albeit with higher computational cost as hop-depth increases.

Abstract

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.

Figures (5)

• Figure 1: Schematic diagram of knowledge graph reasoning.
• Figure 2: Rules $C_3$ and $C'_3$. Here, $z_1$, $z_2$ are variables and $c$ is a constant.
• Figure 3: The rule structure that C-GNN can learn, taking 3-hop as an example.
• Figure 4: Example of the aggregation process
• Figure : Figure A.1: Schematic diagram of (k+1)-hop $T$ structure and $U$ structure

Theorems & Definitions (21)

• Theorem 1
• Theorem 2
• Corollary 3
• Definition 4
• Definition 5
• Corollary 6
• Lemma 7
• Lemma 8
• Theorem 9
• Lemma 10