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

Researchers introduced Sequential Bayesian Belief Tracking (SBBT), a framework that estimates the likelihood of a correct final answer from partial reasoning traces by calibrating observation likelihoods and updating a two-state belief. Testing on open-weight model traces across multiple math benchmarks revealed that score-only SBBT improved probability quality (Brier scores), but gains in ranking accuracy (AUROC) required structure-aware evidence beyond strong prefix-safe baselines. In the hardest math setting, structure-aware observations achieved a +0.110 AUROC improvement over standard prefix-safe baselines, demonstrating that scalar scores and structural signals serve distinct roles in reliability estimation.

arXiv:2605.27712v1 Announce Type: new Abstract: 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.