# Knowledge Graph Completion with Mixed Geometry Tensor Factorization

arXiv: https://arxiv.org/abs/2504.02589 · HTML: https://mlsanity.com/paper/2504.02589/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representations](https://mlsanity.com/paper/2110.02834/) (2021)
- [Ricci Curvature of the Internet Topology](https://mlsanity.com/paper/1501.04138/) (2015)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Quality Metrics in Recommender Systems: Do We Calculate Metrics Consistently?](https://mlsanity.com/paper/2206.12858/) (2022)
- [Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks](https://mlsanity.com/paper/2008.06716/) (2020)
- [Learning Feature Interactions with Lorentzian Factorization Machine](https://mlsanity.com/paper/1911.09821/) (2019)
- [MEKER: Memory Efficient Knowledge Embedding Representation for Link Prediction and Question Answering](https://mlsanity.com/paper/2204.10629/) (2022)

## Built on by (most cited first, 3 of 3)

- [GGBall: Graph Generative Model on Poincar'e Ball](https://mlsanity.com/paper/2506.07198/) (2025)
- [Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations](https://mlsanity.com/paper/2508.11978/) (2025)
- [PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrieval](https://mlsanity.com/paper/2609.06127/) (2026)

## Abstract (arXiv)

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.