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BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization

arXiv:2605.23937v2 Announce Type: replace Abstract: 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...

arXiv CS 9d ago

The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$

Computer Science > Data Structures and Algorithms [Submitted on 2 Jun 2026 (v1), last revised 6 Jun 2026 (this version, v2)] Title:The Grothendieck Constant is Less Than $\fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$ View PDF HTML (experimental)Abstract:We prove that the Grothendieck constant $K_G 0$. Submission history From: Pravesh K Kothari [view email][v1] Tue, 2 Jun 2026 17:59:53 UTC (829 KB)

arXiv CS 1d ago