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

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

Yuan An, Ruhma Hashmi, Michelle Rogers, Jane Greenberg and Brian K Smith
IEEE International Conference on Big Data, pp 5573-5582
08 Dec 2025
DOI: https://doi.org/10.1109/BigData66926.2025.11401838

Abstract

Complexity theory Data science Distortion Distortion measurement Knowledge graphs Prototypes Rate-distortion Education Optimization Semantics
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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