Knowledge Graph Completion with Mixed Geometry Tensor Factorization

Knowledge Graph Completion with Mixed Geometry Tensor Factorization Viacheslav Yusupov Maxim Rakhuba Evgeny Frolov HSE University HSE University AIRI HSE University Abstract In this paper, we propose a new geometric approach for knowledge graph completion via low rank tensor approximation. We augment a pretrained and well-established Euclidean model based on a Tucker tensor decomposition with a novel hyperbolic interaction term. This correction enables more nuanced capturing of distributional properties in data better aligned with real-world knowledge graphs. By combining two geometries together, our approach improves expressivity of the resulting model achieving new state-of-the-art link prediction accuracy with a significantly lower number of parameters compared to the previous Euclidean and hyperbolic models. 1 INTRODUCTION Most of the information in the world can be expressed in terms of entities and the relationships between them. This information is effectively represented in the form of a knowledge graph (d'Amato, 2021; Peng et al., 2023), which serves as a repository for storing various forms of relational data with their interconnections. Particular examples include storing user profiles on social networking platforms (Xu et al., 2018), organizing Internet resources and the links between them, constructing knowledge bases that capture user preferences to enhance the functionality of recommender systems (Wang et al., 2019a; Guo et al., 2020). With the recent emergence of large language models (LLM), knowledge graphs have become an essential tool for improving the consistency and trustworthiness of linguis-Proceedings of the 28 th International Conference on Artificial Intelligence and Statistics (AISTATS) 2025, Mai Khao, Thailand. Among notable examples of their application are fact checking (Pan et al., 2024), hallucinations mitigation (Agrawal et al., 2023), retrieval-augmented generation (Lewis et al., 2020), and generation of corpus for LLM pretraining (Agarwal et al., 2021). This utilization underscores the versatility and utility of knowledge graphs in managing complex datasets and facilitating the manipulation of interconnected information in various domains and downstream tasks. On the other hand, knowledge graphs may present an incomplete view of the world. Relations can evolve and change over time, be subject to errors, processing limitations, and gaps in available information.