@inproceedings{amouzouvi-etal-2024-knowledge,
    title = "Knowledge {G}eo{G}ebra: Leveraging Geometry of Relation Embeddings in Knowledge Graph Completion",
    author = "Amouzouvi, Kossi  and
      Song, Bowen  and
      Vahdati, Sahar  and
      Lehmann, Jens",
    editor = "Calzolari, Nicoletta  and
      Kan, Min-Yen  and
      Hoste, Veronique  and
      Lenci, Alessandro  and
      Sakti, Sakriani  and
      Xue, Nianwen",
    booktitle = "Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation (LREC-COLING 2024)",
    month = may,
    year = "2024",
    address = "Torino, Italia",
    publisher = "ELRA and ICCL",
    url = "https://aclanthology.org/2024.lrec-main.859",
    pages = "9832--9842",
    abstract = "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.",
}

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.
Amouzouvi, Kossi Song, Bowen Vahdati, Sahar Lehmann, Jens
Knowledge GeoGebra: Leveraging Geometry of Relation Embeddings in Knowledge Graph Completion