# BiQUE: Biquaternionic Embeddings of Knowledge Graphs

arXiv: https://arxiv.org/abs/2109.14401 · HTML: https://mlsanity.com/paper/2109.14401/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Commonsense Knowledge Base Completion with Structural and Semantic Context](https://mlsanity.com/paper/1910.02915/) (2019)
- [InteractE: Improving Convolution-based Knowledge Graph Embeddings by Increasing Feature Interactions](https://mlsanity.com/paper/1911.00219/) (2019)
- [Inductive Learning on Commonsense Knowledge Graph Completion](https://mlsanity.com/paper/2009.09263/) (2020)

## Built on by (most cited first, 19 of 19)

- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Towards Foundation Models for Knowledge Graph Reasoning](https://mlsanity.com/paper/2310.04562/) (2023)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [A Prompt-Based Knowledge Graph Foundation Model for Universal In-Context Reasoning](https://mlsanity.com/paper/2410.12288/) (2024)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Learning Representations of Bi-level Knowledge Graphs for Reasoning beyond Link Prediction](https://mlsanity.com/paper/2302.02601/) (2023)
- [A Simple But Powerful Graph Encoder for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2112.07791/) (2021)
- [Few-Shot Inductive Learning on Temporal Knowledge Graphs using Concept-Aware Information](https://mlsanity.com/paper/2211.08169/) (2022)
- [Re-thinking Knowledge Graph Completion Evaluation from an Information Retrieval Perspective](https://mlsanity.com/paper/2205.04105/) (2022)
- [MuCo-KGC: Multi-Context-Aware Knowledge Graph Completion](https://mlsanity.com/paper/2503.03091/) (2025)
- [Knowledge Graph Embedding with 3D Compound Geometric Transformations](https://mlsanity.com/paper/2304.00378/) (2023)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)
- [Improving Few-Shot Inductive Learning on Temporal Knowledge Graphs using Confidence-Augmented Reinforcement Learning](https://mlsanity.com/paper/2304.00613/) (2023)
- [3D Rotation and Translation for Hyperbolic Knowledge Graph Embedding](https://mlsanity.com/paper/2305.13015/) (2023)
- [Deja vu: Contrastive Historical Modeling with Prefix-tuning for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2404.00051/) (2024)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [QuatE-D: A Distance-Based Quaternion Model for Knowledge Graph Embedding](https://mlsanity.com/paper/2504.13983/) (2025)
- [Collaboration of Fusion and Independence: Hypercomplex-driven Robust Multi-Modal Knowledge Graph Completion](https://mlsanity.com/paper/2509.23714/) (2025)

## Abstract (arXiv)

Knowledge graph embeddings (KGEs) compactly encode multi-relational knowledge graphs (KGs). Existing KGE models rely on geometric operations to model relational patterns. Euclidean (circular) rotation is useful for modeling patterns such as symmetry, but cannot represent hierarchical semantics. In contrast, hyperbolic models are effective at modeling hierarchical relations, but do not perform as well on patterns on which circular rotation excels. It is crucial for KGE models to unify multiple geometric transformations so as to fully cover the multifarious relations in KGs. To do so, we propose BiQUE, a novel model that employs biquaternions to integrate multiple geometric transformations, viz., scaling, translation, Euclidean rotation, and hyperbolic rotation. BiQUE makes the best trade-offs among geometric operators during training, picking the best one (or their best combination) for each relation. Experiments on five datasets show BiQUE's effectiveness.