# Fully Hyperbolic Rotation for Knowledge Graph Embedding

arXiv: https://arxiv.org/abs/2411.03622 · HTML: https://mlsanity.com/paper/2411.03622/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Node Co-occurrence based Graph Neural Networks for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2104.07396/) (2021)
- [Zero-shot Item-based Recommendation via Multi-task Product Knowledge Graph Pre-Training](https://mlsanity.com/paper/2305.07633/) (2023)
- [Self-attention Presents Low-dimensional Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/2112.10644/) (2021)
- [Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://mlsanity.com/paper/2211.03635/) (2022)
- [L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification](https://mlsanity.com/paper/2403.06064/) (2024)
- [Two-view Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2112.09231/) (2021)
- [A Novel Word Sense Disambiguation Approach Using WordNet Knowledge Graph](https://mlsanity.com/paper/2101.02875/) (2021)

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

- [GGBall: Graph Generative Model on Poincar'e Ball](https://mlsanity.com/paper/2506.07198/) (2025)
- [Intrinsic Lorentz Neural Network](https://mlsanity.com/paper/2602.23981/) (2026)
- [Hyperbolic Residual Quantization: Discrete Representations for Data with Latent Hierarchies](https://mlsanity.com/paper/2505.12404/) (2025)

## Abstract (arXiv)

Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models only project data features into hyperbolic space for rotation, limiting their ability to fully exploit the hyperbolic space. To address this problem, we propose a novel fully hyperbolic model designed for knowledge graph embedding. Instead of feature mappings, we define the model directly in hyperbolic space with the Lorentz model. Our model considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity. We adopt the Lorentzian version distance as the scoring function for measuring the plausibility of triplets. Extensive results on standard knowledge graph completion benchmarks demonstrated that our model achieves competitive results with fewer parameters. In addition, our model get the state-of-the-art performance on datasets of CoDEx-s and CoDEx-m, which are more diverse and challenging than before. Our code is available at https://github.com/llqy123/FHRE.