---
title: "RotatE — paper by Sun et al. (2019) — summary and ideas"
description: "For training, the authors also propose self-adversarial negative sampling. 34 references, cited by 381 papers here."
authors: ["Zhiqing Sun", "Zhi-Hong Deng", "Jian-Yun Nie", "Jian Tang"]
year: 2019
venue: "arXiv:1902.10197"
source: "https://arxiv.org/abs/1902.10197"
doi: "10.48550/arxiv.1902.10197"
arxiv: "1902.10197"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/sun-2019-rotate-knowledge-graph-embedding-relational/"
---
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# RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space

**Authors:** [Zhiqing Sun](https://md.research.elamur.ai/free/en/authors/zhiqing-sun/), Zhi-Hong Deng, [Jian-Yun Nie](https://md.research.elamur.ai/free/en/authors/jian-yun-nie/) and [Jian Tang](https://md.research.elamur.ai/free/en/authors/jian-tang/) · **Year:** 2019 · **Venue:** arXiv:1902.10197 · **Licence:** [arXiv — non-exclusive licence to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1902.10197) · [PDF](https://arxiv.org/pdf/1902.10197) · [DOI 10.48550/arxiv.1902.10197](https://doi.org/10.48550/arxiv.1902.10197) · [arXiv 1902.10197](https://arxiv.org/abs/1902.10197) · [OpenAlex](https://openalex.org/W2909137510)

**Citations:** 692 citations (OpenAlex, 2026-10-14) · [381](https://md.research.elamur.ai/free/en/papers/sun-2019-rotate-knowledge-graph-embedding-relational/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary

The paper addresses the task of knowledge graph completion, that is, predicting missing links in fact bases such as Freebase or WordNet. To this end, entities and relations are represented as vectors. The authors argue that the quality of such a model depends on whether it can capture three typical properties of relations: symmetry or antisymmetry, the existence of an inverse relation, and composition. Previous models (TransE, DistMult, ComplEx and others) cover only some of these properties. The new model, RotatE, represents entities as complex vectors and each relation as a rotation of each coordinate of the head entity. The modulus of the relation components equals one, so only the phase changes. This simple mechanism suffices to formally describe all three properties, while time and memory costs grow linearly. For training, the authors also propose self-adversarial negative sampling. It assigns greater weight to false triples based on the model's current scores, and it can be applied to other models. RotatE outperforms the state-of-the-art methods of its time on several standard datasets. It has thus become a simple, scalable and theoretically grounded baseline model for knowledge graphs.

## Key points

- **Model idea:** a relation acts as element-wise multiplication by a complex number with modulus 1. Symmetric relations have phases of 0 or π, inverse pairs have conjugate vectors, and composition corresponds to the sum of phases. TransE is a limiting case of RotatE, and TorusE is a special case with a fixed modulus.
- **Evaluation data:** FB15k, WN18, FB15k-237, WN18RR, YAGO3-10 (123,182 entities, 37 relations) and Countries, a dataset created specifically to test composition.
- **Results (mean MRR over three runs with different seeds):** FB15k ≈ 0.797, WN18 ≈ 0.949, FB15k-237 ≈ 0.337, WN18RR ≈ 0.477. On YAGO3-10, MRR is 0.495 versus 0.44 for ConvE, and Hits@10 is 0.670. The variance between runs does not exceed ±0.001.
- **Ablation on FB15k-237:** self-adversarial sampling improves MRR for both RotatE and TransE (for RotatE, from 0.297 to 0.338). The negative-sampling-based loss yields a gain only for RotatE.
- **Resource:** the code is published in the `DeepGraphLearning/KnowledgeGraphEmbedding` repository on GitHub. The embedding dimension in the paper is 500–1000, and the number of negative samples ranges from 64 to 1024 depending on the dataset.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Peking University](https://md.research.elamur.ai/free/en/universities/peking-university/) — University, Beijing, China · 244 works · 39,359 citations
- [Université de Montréal](https://md.research.elamur.ai/free/en/universities/universite-de-montreal/) — University, Montreal, Canada · 68 works · 79,382 citations

📚 Shelves (5): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 16,667 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 16,194 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 16,039 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 15,891 works · [🗄️ Information Systems](https://md.research.elamur.ai/free/en/shelves/computer-science/information-systems/) · 1,437 works

🧭 Topics (1): [🕸️ Knowledge graphs & ontologies](https://md.research.elamur.ai/free/en/topics/knowledge-graphs/) · 192 works

💡 Concepts (1): [💡 Knowledge graph](https://md.research.elamur.ai/free/en/concepts/knowledge-graph/) · 49 works

## Cite

Cite as: Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie and Jian Tang. 2019. RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. arXiv:1902.10197.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{sun2019rotate,
  title = {{RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space}},
  author = {Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie and Jian Tang},
  year = {2019},
  doi = {10.48550/arxiv.1902.10197},
  eprint = {1902.10197},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1902.10197}
}
```

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*Updated 31 October 2026*