Can We Trust LLM's Logic? Quantifying Uncertainty, Coherence, and Robustness via a Graph-Based Framework

2026-07-08

AI Summary

Existing decoding strategies, such as Self-Consistency, rely solely on consistency among final answers and thus struggle to detect intermediate logical errors and unfaithful reasoning in large language models. This work proposes GRAPHEVAL, a framework that reframes uncertainty quantification as a reasoning fidelity problem by constructing reasoning path graphs that integrate semantic, structural, and causal information to evaluate reasoning quality. The authors introduce Graph Self-Consistency (GSC), a novel decoding strategy based on the graph median, and present the Graph Reasoning Coherence Score (GRCS)—the first metric shown to be significantly negatively correlated with reasoning unfaithfulness across both small and large models. GRCS effectively identifies mode collapse and overconfident hallucinations, while GSC enhances reasoning faithfulness without compromising—and often improving—accuracy, revealing that conventional Self-Consistency is vulnerable to misleading yet consistent “lucky guesses” from smaller models.

Abstract

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.

Problem

• Large Language Models
• reasoning faithfulness
• uncertainty quantification
• logical validity
• adversarial robustness

Innovation

• Graph-Based Reasoning
• Uncertainty Quantification
• Reasoning Faithfulness
• Self-Consistency
• Adversarial Robustness