Audit-of-Understanding: Posterior-Constrained Inference for Mathematical Reasoning in Language Models

• URL: http://arxiv.org/abs/2510.10252v2
• Date: Sat, 18 Oct 2025 10:20:04 GMT
• Title: Audit-of-Understanding: Posterior-Constrained Inference for Mathematical Reasoning in Language Models
• Authors: Samir Abdaljalil, Erchin Serpedin, Khalid Qaraqe, Hasan Kurban,
• Abstract summary: We propose Audit-of-Understanding (AoU), a framework that constrains inference to validated premises through three phases.<n>AoU is emphposterior-constrained inference, connecting to selective prediction and rejection learning.<n>Our contributions are threefold: (i) theoretical guarantees under perfect validation, (ii) excess-risk bounds under imperfect audits, and (iii) tractability analysis.
• Score: 2.453830698820308
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) often generate reasoning traces that appear coherent but rest on unsupported assumptions, leading to hallucinated conclusions. Prior work mainly addresses factual hallucinations or relies on post-hoc verification, leaving reasoning-induced hallucinations largely unaddressed. We propose Audit-of-Understanding (AoU), a framework that constrains inference to validated premises through three phases: (1) decomposing a query into candidate assumptions, (2) auditing their support, and (3) conditioning inference only on the validated subset. Formally, AoU is \emph{posterior-constrained inference}, connecting to selective prediction and rejection learning. Our contributions are threefold: (i) theoretical guarantees under perfect validation, (ii) excess-risk bounds under imperfect audits, and (iii) tractability analysis. Empirically, AoU improves both accuracy and faithfulness on GSM8K, MultiArith, and SVAMP, achieving up to +30% gains on GSM8K, +45% on MultiArith, and consistent +20--28% improvements on SVAMP over Chain-of-Thought, Self-Consistency, and CoT-Decoding. Code is available at https://anonymous.4open.science/r/audit-of-understanding-E28B.

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