BoxLitE: Convex Optimization for Knowledge Base Embeddings

A new knowledge base embedding model called BoxLitE has been introduced, designed for DL-Lite$^{\mathcal{H}}$ and enabling convex optimization. The model maps concepts to convex regions in vector space, allowing more general concepts to encompass more specific ones, which is useful for representing hierarchies in TBoxes. The authors prove that for any satisfiable DL-Lite$^{\mathcal{H}}$ KB, there exists a BoxLitE embedding that is weakly faithful. The approach formulates the embedding task as a convex optimization problem, leveraging convexity during learning. This work addresses a gap where convexity was rarely used in actual learning tasks despite its representational benefits. The paper is available on arXiv with ID 2605.23937.