We study Graph Neural Networks (GNNs)-based embedding techniques for knowledge graph (KG) reasoning. For the first time, we link the path redundancy issue in the state-of-the-art KG reasoning models based on path encoding and message passing to the transformation error in model training, which brings us new theoretical insights into KG reasoning, as well as high efficacy in practice. On the theoretical side, we analyze the entropy of transformation error in KG paths and point out query-specific redundant paths causing entropy increases. These findings guide us to maintain the shortest paths and remove redundant paths for minimized-entropy message passing. To achieve this goal, on the practical side, we propose an efficient Graph Percolation Process motivated by the percolation model in Fluid Mechanics, and design a lightweight GNN-based KG reasoning framework called Graph Percolation Embeddings (GraPE). GraPE outperforms previous state-of-the-art methods in both transductive and inductive reasoning tasks while requiring fewer training parameters and less inference time.

翻译：我们研究基于图神经网络（GNN）的知识图谱（KG）推理嵌入技术。首次将基于路径编码和消息传递的先进KG推理模型中的路径冗余问题与模型训练中的变换误差联系起来，这为KG推理带来了新的理论洞见与实践高效性。理论层面，我们分析了KG路径中变换误差的熵，指出查询特定冗余路径会导致熵增。这些发现指导我们保留最短路径并移除冗余路径以实现最小熵消息传递。为实现此目标，实践层面，我们受流体力学中渗滤模型启发，提出高效图渗滤过程，并设计了轻量级基于GNN的KG推理框架——图渗滤嵌入（GraPE）。GraPE在直推式和归纳式推理任务中均超越先前最先进方法，同时需要更少的训练参数和更短的推理时间。