Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking

Computer Science > Artificial Intelligence [Submitted on 26 May 2026] Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking Zhenghan Song, Yunyi Li, Yulong Liu Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation, P(y=1 \mid o_{1:t}), using prefix-safe observations. Sequential Bayesian Belief Tracking (SBBT) calibrates observation likelihoods and recursively updates a two-state belief, providing a common tracker for scalar scores, text and self-verification markers, hidden clusters, token-pooling probes, and latent-trajectory features. Across generated open-weight traces on MATH-500, GSM8K, AIME 2025, and RIMO-N, probability quality and ranking separate: score-only SBBT often improves Brier, while AUROC gains require structure-aware evidence beyond strong prefix-safe baselines. In the strongest hard math setting, structure-aware observations reach +0.110 AUROC against standard prefix-safe baselines. Under a same-prefix classifier audit, MATH-500 text markers and RIMO-N self-verification signals remain positive. Together, these findings support SBBT as a calibration-aware online inference framework and expose an evidence regime: scalar scores mainly support probability quality, while structure-aware prefix signals support ranking only when strong prefix-safe baselines have not already absorbed the rank evidence. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2605.27712 [cs.AI]   (or arXiv:2605.27712v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2605.27712 Focus to learn more Submission history From: Zhenghan Song [view email] [v1] Tue, 26 May 2026 21:37:20 UTC (10,795 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)