# Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings

arXiv: https://arxiv.org/abs/2103.14930 · HTML: https://mlsanity.com/paper/2103.14930/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 27 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (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)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (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)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [A Semantic Matching Energy Function for Learning with Multi-relational Data](https://mlsanity.com/paper/1301.3485/) (2013)
- [Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings](https://mlsanity.com/paper/1902.00913/) (2019)
- [Knowledge Association with Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2010.02162/) (2020)
- [Relation Embedding with Dihedral Group in Knowledge Graph](https://mlsanity.com/paper/1906.00687/) (2019)
- [HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/1908.04895/) (2019)

## Built on by (most cited first, 10 of 10)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Swift and Sure: Hardness-aware Contrastive Learning for Low-dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2201.00565/) (2022)
- [Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://mlsanity.com/paper/2211.03635/) (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)
- [River of No Return: Graph Percolation Embeddings for Efficient Knowledge Graph Reasoning](https://mlsanity.com/paper/2305.09974/) (2023)
- [From Wide to Deep: Dimension Lifting Network for Parameter-efficient Knowledge Graph Embedding](https://mlsanity.com/paper/2303.12816/) (2023)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation based on hyperbolic geometry is much more complicated than Euclidean operations. In this paper, based on the state-of-the-art hyperbolic-based model RotH, we develop two lightweight Euclidean-based models, called RotL and Rot2L. The RotL model simplifies the hyperbolic operations while keeping the flexible normalization effect. Utilizing a novel two-layer stacked transformation and based on RotL, the Rot2L model obtains an improved representation capability, yet costs fewer parameters and calculations than RotH. The experiments on link prediction show that Rot2L achieves the state-of-the-art performance on two widely-used datasets in low-dimensional knowledge graph embeddings. Furthermore, RotL achieves similar performance as RotH but only requires half of the training time.