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

TL;DR

This paper introduces a novel framework for constructing and refining knowledge graphs from lecture notes using rate-distortion theory and Gromov-Wasserstein optimal transport, resulting in more effective educational content for AI systems.

Contribution

It presents a new method combining rate-distortion theory and optimal transport to generate and refine pedagogical knowledge graphs from unstructured lecture materials.

Findings

Refined KGs produce higher-quality MCQs than raw notes.

The framework yields interpretable rate-distortion curves.

Refinement operators improve KG compactness and information preservation.

Abstract

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.