Can We Trust LLM's Logic? Quantifying Uncertainty, Coherence, and Robustness via a Graph-Based Framework
For researchers and practitioners using LLMs for reasoning tasks, this work provides tools to detect unfaithful reasoning and improve reliability, though it is an incremental improvement over existing self-consistency methods.
The paper introduces GRAPHEVAL, a graph-based framework for quantifying uncertainty, coherence, and robustness in LLM reasoning. It proposes GRCS, a metric that captures semantic-structural consensus and is consistently negatively correlated with reasoning faithfulness, and GSC, a decoding strategy that improves reasoning fidelity while preserving accuracy in capable models.
Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.