用信息论方法自动构建精炼的教育知识图谱，提升题目生成质量。
Rate-Distortion Guided Knowledge Graph Construction from Lecture Notes Using Gromov-Wasserstein Optimal Transport
- 基于率失真理论与最优传输，将讲义转为带语义结构的度量测度空间。
- 通过优化率失真代价函数，使知识图谱在紧凑性与信息保真间取得平衡。
- 适合个性化教育系统、AI助教开发人员参考，尤其关注知识结构化。
面向任务的知识图谱（KG）可使AI学习助手自动生成高质量多选题（MCQ）。然而，将讲座笔记等非结构化教育材料转化为能捕捉关键教学内容的KG仍具挑战。本文提出一种基于率失真（RD）理论与最优传输几何的知识图谱构建与优化框架。讲座内容被建模为度量测度空间，以捕捉语义与关系结构；候选KG通过融合格罗莫夫-瓦瑟斯坦（FGW）耦合对齐，量化语义失真。率项由KG规模体现，反映复杂性与紧凑性。通过添加、合并、拆分、删除、重连等优化算子最小化率失真拉格朗日函数，生成紧凑且信息保持完整的KG。原型系统应用于数据科学讲座，生成可解释的RD曲线，结果显示，基于优化后KG生成的MCQ在15项质量指标上均优于原始讲义。该研究为个性化与AI辅助教育中的信息论驱动知识图谱优化奠定了理论基础。
原文摘要 · Abstract (English)
Task-oriented knowledge graphs (KGs) enable AI-powered learning assistant systems to automatically generate high-quality multiple-choice questions (MCQs). Yet converting unstructured educational materials, such as lecture notes and slides, into KGs that capture key pedagogical content remains difficult. We propose a framework for knowledge graph construction and refinement grounded in rate-distortion (RD) theory and optimal transport geometry. In the framework, lecture content is modeled as a metric-measure space, capturing semantic and relational structure, while candidate KGs are aligned using Fused Gromov-Wasserstein (FGW) couplings to quantify semantic distortion. The rate term, expressed via the size of KG, reflects complexity and compactness. Refinement operators (add, merge, split, remove, rewire) minimize the rate-distortion Lagrangian, yielding compact, information-preserving KGs. Our prototype applied to data science lectures yields interpretable RD curves and shows that MCQs generated from refined KGs consistently surpass those from raw notes on fifteen quality criteria. This study establishes a principled foundation for information-theoretic KG optimization in personalized and AI-assisted education.
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