# SpaceE: Knowledge Graph Embedding by Relational Linear Transformation in the Entity Space

arXiv: https://arxiv.org/abs/2204.10245 · HTML: https://mlsanity.com/paper/2204.10245/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [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)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [A Survey on Recent Advances in Named Entity Recognition from Deep Learning models](https://mlsanity.com/paper/1910.11470/) (2019)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Knowledge Base Completion: Baselines Strike Back](https://mlsanity.com/paper/1705.10744/) (2017)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Logician: A Unified End-to-End Neural Approach for Open-Domain Information Extraction](https://mlsanity.com/paper/1904.12535/) (2019)

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

- [Relation Geometry in Semantic Space of Language Models](https://mlsanity.com/paper/2607.26762/) (2026)

## Abstract (arXiv)

Translation distance based knowledge graph embedding (KGE) methods, such as TransE and RotatE, model the relation in knowledge graphs as translation or rotation in the vector space. Both translation and rotation are injective; that is, the translation or rotation of different vectors results in different results. In knowledge graphs, different entities may have a relation with the same entity; for example, many actors starred in one movie. Such a non-injective relation pattern cannot be well modeled by the translation or rotation operations in existing translation distance based KGE methods. To tackle the challenge, we propose a translation distance-based KGE method called SpaceE to model relations as linear transformations. The proposed SpaceE embeds both entities and relations in knowledge graphs as matrices and SpaceE naturally models non-injective relations with singular linear transformations. We theoretically demonstrate that SpaceE is a fully expressive model with the ability to infer multiple desired relation patterns, including symmetry, skew-symmetry, inversion, Abelian composition, and non-Abelian composition. Experimental results on link prediction datasets illustrate that SpaceE substantially outperforms many previous translation distance based knowledge graph embedding methods, especially on datasets with many non-injective relations. The code is available based on the PaddlePaddle deep learning platform https://www.paddlepaddle.org.cn.