Knowledge Graph Completion with Mixed Geometry Tensor Factorization

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.

@article{yusupov2025_2504.02589,
  title={ Knowledge Graph Completion with Mixed Geometry Tensor Factorization },
  author={ Viacheslav Yusupov and Maxim Rakhuba and Evgeny Frolov },
  journal={arXiv preprint arXiv:2504.02589},
  year={ 2025 }
}