用凸优化构建忠实的知识库嵌入，更好表达概念层级关系
BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization
- 将概念映射为向量空间中的凸区域，利用凸优化学习嵌入
- 对任何可满足的DL-Lite^H知识库，存在弱忠实的嵌入解
- 适合需要精确语义表达的逻辑推理与知识图谱应用
知识库嵌入旨在结合事实信息（ABox）的泛化能力与本体语言（TBox）所表达的概念知识。近期研究尝试将概念映射到向量空间中的凸区域，以更好地表示层次结构——更一般的概念对应更大区域，包含其下位概念。然而，凸性在实际学习中很少被充分利用。本文提出BoxLitE，一种针对DL-Lite^H知识库的嵌入模型，支持凸优化。我们证明：对任意可满足的DL-Lite^H知识库，均存在一个弱忠实的BoxLitE嵌入。作为概念验证，展示了如何将知识库嵌入任务建模为凸优化问题，并获得具备良好忠实性的嵌入。
原文摘要 · Abstract (English)
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.
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