# ModulE: Module Embedding for Knowledge Graphs

arXiv: https://arxiv.org/abs/2203.04702 · HTML: https://mlsanity.com/paper/2203.04702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 9 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Open Question Answering with Weakly Supervised Embedding Models](https://mlsanity.com/paper/1404.4326/) (2014)
- [HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations](https://mlsanity.com/paper/2108.05774/) (2021)

## Built on by (most cited first, 2 of 2)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

Knowledge graph embedding (KGE) has been shown to be a powerful tool for predicting missing links of a knowledge graph. However, existing methods mainly focus on modeling relation patterns, while simply embed entities to vector spaces, such as real field, complex field and quaternion space. To model the embedding space from a more rigorous and theoretical perspective, we propose a novel general group theory-based embedding framework for rotation-based models, in which both entities and relations are embedded as group elements. Furthermore, in order to explore more available KGE models, we utilize a more generic group structure, module, a generalization notion of vector space. Specifically, under our framework, we introduce a more generic embedding method, ModulE, which projects entities to a module. Following the method of ModulE, we build three instantiating models: ModulE_ℝ,mathbbC, ModulE_ℝ,mathbbH and ModulE_mathbbH,mathbbH, by adopting different module structures. Experimental results show that ModulE_mathbbH,mathbbH which embeds entities to a module over non-commutative ring, achieves state-of-the-art performance on multiple benchmark datasets.