# Learning Permutation-Invariant Embeddings for Description Logic Concepts

arXiv: https://arxiv.org/abs/2303.01844 · HTML: https://mlsanity.com/paper/2303.01844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Efficient Concept Induction for Description Logics](https://mlsanity.com/paper/1812.03243/) (2018)
- [EvoLearner: Learning Description Logics with Evolutionary Algorithms](https://mlsanity.com/paper/2111.04879/) (2021)
- [Convolutional Hypercomplex Embeddings for Link Prediction](https://mlsanity.com/paper/2106.15230/) (2021)
- [Learning Concept Lengths Accelerates Concept Learning in ALC](https://mlsanity.com/paper/2107.04911/) (2021)
- [DRILL-- Deep Reinforcement Learning for Refinement Operators in ALC](https://mlsanity.com/paper/2106.15373/) (2021)
- [A Description Logic for Analogical Reasoning](https://mlsanity.com/paper/2105.04620/) (2021)

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

- [Ontolearn-A Framework for Large-scale OWL Class Expression Learning in Python](https://mlsanity.com/paper/2510.11561/) (2025)

## Abstract (arXiv)

Concept learning deals with learning description logic concepts from a background knowledge and input examples. The goal is to learn a concept that covers all positive examples, while not covering any negative examples. This non-trivial task is often formulated as a search problem within an infinite quasi-ordered concept space. Although state-of-the-art models have been successfully applied to tackle this problem, their large-scale applications have been severely hindered due to their excessive exploration incurring impractical runtimes. Here, we propose a remedy for this limitation. We reformulate the learning problem as a multi-label classification problem and propose a neural embedding model (NERO) that learns permutation-invariant embeddings for sets of examples tailored towards predicting F1 scores of pre-selected description logic concepts. By ranking such concepts in descending order of predicted scores, a possible goal concept can be detected within few retrieval operations, i.e., no excessive exploration. Importantly, top-ranked concepts can be used to start the search procedure of state-of-the-art symbolic models in multiple advantageous regions of a concept space, rather than starting it in the most general concept top. Our experiments on 5 benchmark datasets with 770 learning problems firmly suggest that NERO significantly (p-value <1%) outperforms the state-of-the-art models in terms of F1 score, the number of explored concepts, and the total runtime. We provide an open-source implementation of our approach.