# TransBox: EL++-closed Ontology Embedding

arXiv: https://arxiv.org/abs/2410.14571 · HTML: https://mlsanity.com/paper/2410.14571/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Ontology Enrichment from Texts: A Biomedical Dataset for Concept Discovery and Placement](https://mlsanity.com/paper/2306.14704/) (2023)
- [Efficient Computation of General Modules for ALC Ontologies (Extended Version)](https://mlsanity.com/paper/2305.09503/) (2023)

## Built on by (most cited first, 5 of 5)

- [Language Models as Ontology Encoders](https://mlsanity.com/paper/2507.14334/) (2025)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction](https://mlsanity.com/paper/2605.03690/) (2026)
- [DELE: Deductive EL++ Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/2411.01574/) (2024)
- [NeurOWL: An LLM-Based Neural-symbolic Framework for Incomplete OWL Ontology Reasoning](https://mlsanity.com/paper/2607.15776/) (2026)

## Abstract (arXiv)

OWL (Web Ontology Language) ontologies, which are able to represent both relational and type facts as standard knowledge graphs and complex domain knowledge in Description Logic (DL) axioms, are widely adopted in domains such as healthcare and bioinformatics. Inspired by the success of knowledge graph embeddings, embedding OWL ontologies has gained significant attention in recent years. Current methods primarily focus on learning embeddings for atomic concepts and roles, enabling the evaluation based on normalized axioms through specially designed score functions. However, they often neglect the embedding of complex concepts, making it difficult to infer with more intricate axioms. This limitation reduces their effectiveness in advanced reasoning tasks, such as Ontology Learning and ontology-mediated Query Answering. In this paper, we propose EL++-closed ontology embeddings which are able to represent any logical expressions in DL via composition. Furthermore, we develop TransBox, an effective EL++-closed ontology embedding method that can handle many-to-one, one-to-many and many-to-many relations. Our extensive experiments demonstrate that TransBox often achieves state-of-the-art performance across various real-world datasets for predicting complex axioms.