# ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2206.04192 · HTML: https://mlsanity.com/paper/2206.04192/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Variational Reasoning for Question Answering with Knowledge Graph](https://mlsanity.com/paper/1709.04071/) (2017)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Unifying Knowledge Graph Learning and Recommendation: Towards a Better Understanding of User Preferences](https://mlsanity.com/paper/1902.06236/) (2019)
- [PyKEEN 1.0: A Python Library for Training and Evaluating Knowledge Graph Embeddings](https://mlsanity.com/paper/2007.14175/) (2020)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [Realistic Re-evaluation of Knowledge Graph Completion Methods: An Experimental Study](https://mlsanity.com/paper/2003.08001/) (2020)
- [On the Equivalence of Holographic and Complex Embeddings for Link Prediction](https://mlsanity.com/paper/1702.05563/) (2017)
- [New Embedded Representations and Evaluation Protocols for Inferring Transitive Relations](https://mlsanity.com/paper/1805.04690/) (2018)

## Built on by (most cited first, 13 of 13)

- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Applications of Generative AI (GAI) for Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/2405.20024/) (2024)
- [Capturing Knowledge Graphs and Rules with Octagon Embeddings](https://mlsanity.com/paper/2401.16270/) (2024)
- [MQuinE: a cure for "Z-paradox" in knowledge graph embedding models](https://mlsanity.com/paper/2402.03583/) (2024)
- [Embeddings as Epistemic States: Limitations on the Use of Pooling Operators for Accumulating Knowledge](https://mlsanity.com/paper/2210.05723/) (2022)
- [KG-BiLM: Knowledge Graph Embedding via Bidirectional Language Models](https://mlsanity.com/paper/2506.03576/) (2025)
- [On the Theoretical Limitations of Embedding-based Link Prediction](https://mlsanity.com/paper/2506.22271/) (2025)
- [Knowledge Graph Embeddings with Representing Relations as Annular Sectors](https://mlsanity.com/paper/2506.11099/) (2025)
- [CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion](https://mlsanity.com/paper/2605.11159/) (2026)
- [Scalable GNN-based Knowledge Graph Representation Learning with Efficient Message Passing](https://mlsanity.com/paper/2609.34499/) (2026)
- [Uncertainty in Representation Learning on Knowledge Graphs](https://mlsanity.com/paper/2610.06974/) (2026)

## Abstract (arXiv)

Knowledge graphs are inherently incomplete. Therefore substantial research has been directed toward knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). KG embedding models (KGEs) have yielded promising results for KGC, yet any current KGE is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent patterns jointly (e.g., hierarchy and composition), and (3) providing an intuitive interpretation of captured patterns. In this work, we propose ExpressivE, a fully expressive spatio-functional KGE that solves all these challenges simultaneously. ExpressivE embeds pairs of entities as points and relations as hyper-parallelograms in the virtual triple space ℝ2d. This model design allows ExpressivE not only to capture a rich set of inference patterns jointly but additionally to display any supported inference pattern through the spatial relation of hyper-parallelograms, offering an intuitive and consistent geometric interpretation of ExpressivE embeddings and their captured patterns. Experimental results on standard KGC benchmarks reveal that ExpressivE is competitive with state-of-the-art KGEs and even significantly outperforms them on WN18RR.