PolygonE: Modeling N-ary Relational Data as Gyro-Polygons in Hyperbolic Space

N-ary relational knowledge base (KBs) embedding aims to map binary and beyond-binary facts into low-dimensional vector space simultaneously. Existing approaches typically decompose n-ary relational facts into subtuples, and they generally model n-ary relational KBs in Euclidean space. However, n-ary relational facts are semantically and structurally intact; decomposition undermines the semantical and structural integrity. Moreover, compared to the binary relational KBs, n-ary ones are characterized by more abundant and complicated hierarchy structures, which could not be well expressed in Euclidean space. To address the issues, we propose a gyro-polygon embedding framework to realize n-ary fact integrity keeping and hierarchy capturing, termed PolygonE. Specifically, n-ary relational facts are modeled as gyropolygons in the hyperbolic space, where we denote entities in facts as vertexes of gyro-polygons and relations as entity translocation operations. Importantly, we design a fact plausibility measuring strategy based on the vertex-gyrocentroid geodesic to optimize the relation-adjusted gyro-polygon. Experimental results demonstrate that PolygonE shows SOTA performance on all benchmark datasets and generalizes well on binary data. Finally, we also visualize the embedding to help comprehend PolygonE’s awareness of hierarchies.

Authors

• Shiyao Yan Aerospace Information Research Institute, Chinese Academy of Sciences
• Zequn Zhang Aerospace Information Research Institute, Chinese Academy of Sciences
• Xian Sun Aerospace Information Research Institute, Chinese Academy of Sciences Key Laboratory of Target Cognition and Application Technology (TCAT) University of Chinese Academy of Sciences School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences
• Guangluan Xu Aerospace Information Research Institute, Chinese Academy of Sciences; Key Laboratory of Network Information System Technology (NIST), Aerospace Information Research Institute
• Shuchao Li
• Qing Liu
• Nayu Liu School of Computer Science and Technology, Tiangong University
• Shensi Wang

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