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 $F_1$ 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 $F_1$ score, the number of explored concepts, and the total runtime. We provide an open-source implementation of our approach.

翻译：概念学习旨在从背景知识和输入示例中学习描述逻辑概念。其目标是学习一个覆盖所有正例、同时不覆盖任何负例的概念。这一非平凡任务通常被表述为在无限准有序概念空间中的搜索问题。尽管现有最先进模型已成功应用于解决该问题，但其大规模应用因过度探索导致不可行的运行时间而严重受限。本文我们提出了一种针对该局限性的解决方案。我们将学习问题重新表述为多标签分类问题，并提出一种神经嵌入模型（NERO），该模型学习示例集合的置换不变嵌入，专门用于预测预选描述逻辑概念的$F_1$分数。通过按预测分数降序排列这些概念，可以在少量检索操作内检测到可能的目标概念，即无需过度探索。重要的是，排名靠前的概念可用于在概念空间的多个优势区域启动现有最先进符号模型的搜索过程，而非从最一般概念$\top$开始。我们在包含770个学习问题的5个基准数据集上的实验充分表明，NERO在$F_1$分数、探索概念数量及总运行时间方面均显著优于现有最先进模型（p值<1%）。我们提供了所提方法的开源实现。