# M"obiusE: Knowledge Graph Embedding on M"obius Ring

arXiv: https://arxiv.org/abs/2101.02352 · HTML: https://mlsanity.com/paper/2101.02352/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 6 of 6)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Knowlege Graph Embedding by Flexible Translation](https://mlsanity.com/paper/1505.05253/) (2015)

## Built on by (most cited first, 4 of 4)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Negative Sampling in Knowledge Graph Representation Learning: A Review](https://mlsanity.com/paper/2402.19195/) (2024)
- [Knowledge Graph Embedding by Normalizing Flows](https://mlsanity.com/paper/2409.19977/) (2024)

## Abstract (arXiv)

In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy, called M"obiusE, in which the entities and relations are embedded to the surface of a M"obius ring. The proposition of such a strategy is inspired by the classic TorusE, in which the addition of two arbitrary elements is subject to a modulus operation. In this sense, TorusE naturally guarantees the critical boundedness of embedding vectors in KGE. However, the nonlinear property of addition operation on Torus ring is uniquely derived by the modulus operation, which in some extent restricts the expressiveness of TorusE. As a further generalization of TorusE, M"obiusE also uses modulus operation to preserve the closeness of addition operation on it, but the coordinates on M"obius ring interacts with each other in the following way: em colorred any vector on the surface of a M"obius ring moves along its parametric trace will goes to the right opposite direction after a cycle. Hence, M"obiusE assumes much more nonlinear representativeness than that of TorusE, and in turn it generates much more precise embedding results. In our experiments, M"obiusE outperforms TorusE and other classic embedding strategies in several key indicators.