# BoxE: A Box Embedding Model for Knowledge Base Completion

arXiv: https://arxiv.org/abs/2007.06267 · HTML: https://mlsanity.com/paper/2007.06267/

## Key facts

- Cited by 105 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

## Built on by (most cited first, 30 of 105)

- [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)
- [Modeling Fine-Grained Entity Types with Box Embeddings](https://mlsanity.com/paper/2101.00345/) (2021)
- [Temporal Knowledge Graph Completion using Box Embeddings](https://mlsanity.com/paper/2109.08970/) (2021)
- [A Survey on Temporal Knowledge Graph: Representation Learning and Applications](https://mlsanity.com/paper/2403.04782/) (2024)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Hallucination Detection in Large Language Models with Metamorphic Relations](https://mlsanity.com/paper/2502.15844/) (2025)
- [How Expressive are Knowledge Graph Foundation Models?](https://mlsanity.com/paper/2502.13339/) (2025)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Bias and Fairness in Chatbots: An Overview](https://mlsanity.com/paper/2309.08836/) (2023)
- [Rethinking Knowledge Graph Evaluation Under the Open-World Assumption](https://mlsanity.com/paper/2209.08858/) (2022)
- [Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding](https://mlsanity.com/paper/2110.14450/) (2021)
- [A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2308.02457/) (2023)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Knowledge Hypergraph Embedding Meets Relational Algebra](https://mlsanity.com/paper/2102.09557/) (2021)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [QuatDE: Dynamic Quaternion Embedding for Knowledge Graph Completion](https://mlsanity.com/paper/2105.09002/) (2021)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Are Missing Links Predictable? An Inferential Benchmark for Knowledge Graph Completion](https://mlsanity.com/paper/2108.01387/) (2021)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Link Prediction with Relational Hypergraphs](https://mlsanity.com/paper/2402.04062/) (2024)
- [IME: Integrating Multi-curvature Shared and Specific Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2403.19881/) (2024)
- [Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction](https://mlsanity.com/paper/2408.08226/) (2024)
- [Flock: A Knowledge Graph Foundation Model via Learning on Random Walks](https://mlsanity.com/paper/2510.01510/) (2025)
- [A Simple But Powerful Graph Encoder for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2112.07791/) (2021)
- [NeuralKG: An Open Source Library for Diverse Representation Learning of Knowledge Graphs](https://mlsanity.com/paper/2202.12571/) (2022)

## Abstract (arXiv)

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.