NagE: Non-Abelian Group Embedding for Knowledge Graphs

TL;DR

This paper reveals a hidden non-Abelian group structure in knowledge graph embeddings and proposes a group theory-based framework that achieves state-of-the-art results on benchmarks.

Contribution

It introduces a novel non-Abelian group embedding framework for knowledge graphs, grounded in theoretical analysis and demonstrated with two new models.

Findings

State-of-the-art results on benchmark datasets

Theoretical analysis of intrinsic group structure in embeddings

Proposed models SO3E and SU2E using continuous non-Abelian groups

Abstract

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.