# Enhancing Geometric Ontology Embeddings for EL++ with Negative Sampling and Deductive Closure Filtering

arXiv: https://arxiv.org/abs/2405.04868 · HTML: https://mlsanity.com/paper/2405.04868/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 11 of 11)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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 Completion with Natural Language Inference and Concept Embeddings: An Analysis](https://mlsanity.com/paper/2403.17216/) (2024)
- [From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings](https://mlsanity.com/paper/2303.16519/) (2023)
- [A Self-matching Training Method with Annotation Embedding Models for Ontology Subsumption Prediction](https://mlsanity.com/paper/2402.16278/) (2024)
- [Ontology Revision based on Pre-trained Language Models](https://mlsanity.com/paper/2310.18378/) (2023)

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

- [DELE: Deductive EL++ Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/2411.01574/) (2024)

## Abstract (arXiv)

Ontology embeddings map classes, relations, and individuals in ontologies into ℝn, and within ℝn similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic EL++, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for EL++ ontologies based on high-dimensional ball representation of concept descriptions, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.