Knowledge Graph Embedding (KGE) aims to map entities and relationships into a continuous vector space to facilitate reasoning and downstream tasks. Although previous KGE methods based on Euclidean, complex spaces, or hyperbolic spaces have performed well, they still struggle to effectively model Z-Paradox relation patterns which account for a large proportion in each knowledge graph. To address this issue, we propose a novel KGE method **FlorE** which integrates full Lorentz Group and directional offset operation in hyperbolic space for KGE task. Specifically, we incorporates the full Lorentz Group to enable the same relation in knowledge graph (KG) to perform indefinite isometry, thus avoiding the overlapping of entities. Meanwhile, we implement directional offset operation via exponential mapping to transform the relations to the same Lorentz manifold of the entities, thus maintaining geometric consistency for the relations and entities in KG. By integrating these two techniques, FlorE can effectively model the Z-Paradox relation patterns and improve the representation learning ability for KGs. Experiments on the five benchmark datasets demonstrate that our method achieves state-of-the-art performance. For the Z-Paradox relation patterns, the improvement achieves **26.7%**, **15.6%**, **35.4%**, **33.7%**, and **31.5%** on FB15k-237, WN18RR, CoDEx-S, CoDEx-M and CoDEx-L, respectively.

Yu Tian, Jie Xing, Ziming Li, Jiang Li, Zehua Duo, Tian Lan, Xu Liu, Guanglai Gao, Xiangdong Su. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Knowledge graph embedding techniques have emerged as a critical approach for addressing the issue of missing relations in knowledge graphs. However, existing methods often suffer from limitations, including high intra-group similarity, loss of semantic information, and insufficient inference capability, particularly in complex relation patterns such as 1-N and N-1 relations. To address these challenges, we introduce a novel KGE framework that leverages mutual information maximization to improve the semantic representation of entities and relations. By maximizing the mutual information between different components of triples, such as (h, r) and t, or (r, t) and h, the proposed method improves the model’s ability to preserve semantic dependencies while maintaining the relational structure of the knowledge graph. Extensive experiments on benchmark datasets demonstrate the effectiveness of our approach, with consistent performance improvements across various baseline models. Additionally, visualization analyses and case studies demonstrate the improved ability of the MI framework to capture complex relation patterns.