BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization

Computer Science > Artificial Intelligence [Submitted on 27 Apr 2026] BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization Bruno F. Lourenço, Hesham Morgan, Ana Ozaki, Aleksandar Pavlović, Emanuel Sallinger Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-Lite^{\mathcal{H}} that allows for convex optimization. We show that for any satisfiable DL-Lite^{\mathcal{H}} KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness properties. Comments: 28 pages. Full version of paper accepted to KR 2026 (23nd International Conference on Principles of Knowledge Representation and Reasoning). Track: KR meets Machine Learning and Explanation Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic in Computer Science (cs.LO); Optimization and Control (math.OC) Cite as: arXiv:2605.23937 [cs.AI]   (or arXiv:2605.23937v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2605.23937 Focus to learn more Submission history From: Bruno F. Lourenço [view email] [v1] Mon, 27 Apr 2026 11:45:23 UTC (302 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs cs.LG cs.LO math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)