Rate-Distortion Guided Knowledge Graph Construction from Lecture Notes Using Gromov-Wasserstein Optimal Transport

Abstract--T ask-oriented knowledge graphs (KGs) enable AIpowered learning assistant systems to automatically generate high-quality multiple-choice questions (MCQs). Y et 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. An AI-powered learning assistant (AILA) system [1] can automatically generate educational questions such as multiple choice questions (MCQs) from teaching materials including lecture notes and slides [2], [3]. Recent research demonstrates that integrating knowledge graphs (KGs) with large language models (LLMs) significantly improves the factual accuracy, explainability, and reasoning capabilities of LLM-powered answers [4], [5].