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Knowledge GeoGebra: Leveraging Geometry of Relation Embeddings in Knowledge Graph Completion

Knowledge graph embedding (KGE) models provide a low-dimensional representation of knowledge graphs in continuous vector spaces. This representation learning enables different downstream AI tasks such as link prediction for graph completion. However, most embedding models are only designed considering the algebra and geometry of the entity embedding space, the algebra of the relation embedding space, and the interaction between relation and entity embeddings. Neglecting the geometry of relation embedding limits the optimization of entity and relation distribution leading to suboptimal performance of knowledge graph completion. To address this issue, we propose a new perspective in the design of KGEs by looking into the geometry of relation embedding space. The proposed method and its variants are developed on top of an existing framework, RotatE, from which we leverage the geometry of the relation embeddings by mutating the unit circle to an ellipse, and further generalize it with the concept of a butterfly curve, consecutively. Besides the theoretical abilities of the model in preserving topological and relational patterns, the experiments on the WN18RR, FB15K-237 and YouTube benchmarks showed that this new family of KGEs can challenge or outperform state-of-the-art models.