M-∂KG: A Theoretical Framework for Uncertainty Quantification in Large Language Model

Md Tauhidul Islam, Md Wahiduzzaman Suva, Md Tanzib Hosain, Nafiz Fahad, Md Kishor Morol, Dip Nandi, Mashiour Rahman, Mohammad Ali Moni

Keywords: Uncertainty quantification, medical knowledge graph, epistemic uncertainty, clinical decision support

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Abstract: Large Language Models (LLMs) have shown strong potential in healthcare, but their medical deployment remains limited by challenges in uncertainty quantification and interpretability. Although probabilistic uncertainty estimation has been widely studied, formal graph-theoretical frameworks for quantifying uncertainty in LLM reasoning are still lacking. This paper proposes a novel mathematical framework that models LLM reasoning as traversals over knowledge graphs and defines uncertainty using graph-theoretical properties. The framework decomposes uncertainty into epistemic (model) and aleatoric (data) components, derives theoretical bounds on uncertainty estimates, and enables formal comparison with existing probabilistic approaches. We further demonstrate its use in medical reasoning tasks, including diagnosis, treatment planning, and prognosis, showing that graph-based properties provide more interpretable and theoretically grounded uncertainty estimates. Finally, through mathematical analysis and simulation, we empirically validate the theoretical bounds and relationships established by the framework.

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Submission Number: 136