# NagE: Non-Abelian Group Embedding for Knowledge Graphs Source: [NagE: Non-Abelian Group Embedding for Knowledge Graphs]() Collection index: [llms.txt]() Data updated: 2025-10-25T14:39:36.307Z Authors: Tong Yang, Long Sha, Pengyu Hong Published: 2020-05-22T00:54:45.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Link Prediction on WN18RR originally reported recent (test)](): Link Prediction; WN18RR originally reported recent (test); MRR: 0.477. - [Link Prediction on WN18RR (test)](): Link Prediction; WN18RR (test); Hits@10: 57.4. - [Link Prediction on FB15k-237 (test)](): Link Prediction; FB15k-237 (test); Hits@10: 53. ## Original sources and implementation [Original paper]() [PDF]()