Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty

• URL: http://arxiv.org/abs/2606.17312v1
• Date: Mon, 15 Jun 2026 21:39:47 GMT
• Title: Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty
• Abstract summary: Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently.<n>We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings.
• Score: 5.839104770457067
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

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