Beyond-triple fact representations including hyper-relational facts with auxiliary key-value pairs, temporal facts with additional timestamps, and nested facts implying relationships between facts, are gaining significant attention. However, existing link prediction models are usually designed for one specific type of facts, making it difficult to generalize to other fact representations. To overcome this limitation, we propose a Unified Hierarchical Representation learning framework (UniHR) for unified knowledge graph link prediction. It consists of a unified Hierarchical Data Representation (HiDR) module and a unified Hierarchical Structure Learning (HiSL) module as graph encoder. The HiDR module unifies hyper-relational KGs, temporal KGs, and nested factual KGs into triple-based representations. Then HiSL incorporates intra-fact and inter-fact message passing, focusing on enhancing the semantic information within individual facts and enriching the structural information between facts. Experimental results across 7 datasets from 3 types of KGs demonstrate that our UniHR outperforms baselines designed for one specific kind of KG, indicating strong generalization capability of HiDR form and the effectiveness of HiSL module. Code and data are available at https://github.com/Lza12a/UniHR.
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