Expressiveness Analysis and Enhancing Framework for Geometric Knowledge Graph Embedding Models

Existing geometric knowledge graph embedding methods employ various relational transformations, such as translation, rotation, and projection, to model different relation patterns, which aims to enhance the expressiveness of models. In contrast to current approaches that treat the expressiveness of the model as a binary issue, we aim to delve deeper into analyzing the level of difficulty in which geometric knowledge graph embedding models can represent relation patterns. In this paper, we provide a theoretical analysis framework that measures the expressiveness of the model in relation patterns by quantifying the size of the solution space of linear equation systems. Additionally, we propose a mechanism for imposing relational constraints on geometric knowledge graph embedding models by setting “traps” near relational optimal solutions, which enables the model to better converge to the optimal solution. Empirically, we analyze and compare several typical knowledge graph embedding models with different geometric algebras, revealing that some models have insufficient solution space due to their design, which leads to performance weaknesses. We also demonstrate that the proposed relational constraint operations can improve the performance of certain relation patterns. The experimental results on public benchmarks and relation pattern specified dataset are consistent with our theoretical analysis.