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

Artificial Intelligence 2026-05-28 v1

Abstract

Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation, P(y=1o1:t)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.

Keywords

Cite

@article{arxiv.2605.27712,
  title  = {Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking},
  author = {Zhenghan Song and Yunyi Li and Yulong Liu},
  journal= {arXiv preprint arXiv:2605.27712},
  year   = {2026}
}
R2 v1 2026-07-22T07:35:45.597Z