NagE: Non-Abelian Group Embedding for Knowledge Graphs
This work addresses knowledge graph completion for AI applications by introducing a novel theoretical foundation, though it is incremental in applying group theory to an existing problem.
The paper tackled the problem of knowledge graph embedding by revealing a hidden group algebraic structure, leading to a group-based framework where relations are embedded as group elements and entities as vectors in group action spaces, with SO3E and SU2E models achieving state-of-the-art results on benchmarks.
We demonstrated the existence of a group algebraic structure hidden in relational knowledge embedding problems, which suggests that a group-based embedding framework is essential for designing embedding models. Our theoretical analysis explores merely the intrinsic property of the embedding problem itself hence is model-independent. Motivated by the theoretical analysis, we have proposed a group theory-based knowledge graph embedding framework, in which relations are embedded as group elements, and entities are represented by vectors in group action spaces. We provide a generic recipe to construct embedding models associated with two instantiating examples: SO3E and SU2E, both of which apply a continuous non-Abelian group as the relation embedding. Empirical experiments using these two exampling models have shown state-of-the-art results on benchmark datasets.