# 3D Rotation and Translation for Hyperbolic Knowledge Graph Embedding

arXiv: https://arxiv.org/abs/2305.13015 · HTML: https://mlsanity.com/paper/2305.13015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [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)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (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)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [PairRE: Knowledge Graph Embeddings via Paired Relation Vectors](https://mlsanity.com/paper/2011.03798/) (2020)
- [HittER: Hierarchical Transformers for Knowledge Graph Embeddings](https://mlsanity.com/paper/2008.12813/) (2020)
- [Leveraging Knowledge Bases in LSTMs for Improving Machine Reading](https://mlsanity.com/paper/1902.09091/) (2019)
- [BiQUE: Biquaternionic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/2109.14401/) (2021)
- [LineaRE: Simple but Powerful Knowledge Graph Embedding for Link Prediction](https://mlsanity.com/paper/2004.10037/) (2020)

## Built on by (most cited first, 1 of 1)

- [Memorization, Emergence, and Explaining Reversal Failures: A Controlled Study of Relational Semantics in LLMs](https://mlsanity.com/paper/2601.02931/) (2026)

## Abstract (arXiv)

The main objective of Knowledge Graph (KG) embeddings is to learn low-dimensional representations of entities and relations, enabling the prediction of missing facts. A significant challenge in achieving better KG embeddings lies in capturing relation patterns, including symmetry, antisymmetry, inversion, commutative composition, non-commutative composition, hierarchy, and multiplicity. This study introduces a novel model called 3H-TH (3D Rotation and Translation in Hyperbolic space) that captures these relation patterns simultaneously. In contrast, previous attempts have not achieved satisfactory performance across all the mentioned properties at the same time. The experimental results demonstrate that the new model outperforms existing state-of-the-art models in terms of accuracy, hierarchy property, and other relation patterns in low-dimensional space, meanwhile performing similarly in high-dimensional space.