Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking
On the map: LLM reasoning → Test-time compute and efficient thinking
Abstract (arXiv)
Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation, P(y=1 mid o1: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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 26 of its 44 references that are in the map. First posted on arXiv 26 May 2026.
Builds on
26 of 44 references.
Closest ancestors · 6
Same direction, newest first
- 2026Monitoring the Internal Monologue: Probe Trajectories Reveal Reasoning Dynamics18 May
- 2025Tracing the Traces: Latent Temporal Signals for Efficient and Accurate Reasoning12 Oct
- 2025Overclocking LLM Reasoning: Monitoring and Controlling Thinking Path Lengths in LLMs8 Jun
- 2025Dynamic Early Exit in Reasoning Models22 Apr
- 2025Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification7 Apr
- 2022Language Models (Mostly) Know What They Know11 Jul
Other references · 20
- 2024The Llama 3 Herd of Modelscited by 14,192
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
- 2021Training Verifiers to Solve Math Word Problemscited by 9,743
- 2025Qwen3 Technical Reportcited by 8,195
- 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
- 2023Let's Verify Step by Stepcited by 3,598
- 2016Understanding intermediate layers using linear classifier probescited by 1,279
- 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,057
- 2022Solving math word problems with process- and outcome-based feedbackcited by 871
- 2021Probing Classifiers: Promises, Shortcomings, and Advancescited by 831
- 2023FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performancecited by 791
- 2022Discovering Latent Knowledge in Language Models Without Supervisioncited by 733
8 more
- 2022Teaching Models to Express Their Uncertainty in Wordscited by 731
- 2024Improve Mathematical Reasoning in Language Models by Automated Process Supervisioncited by 426
- 2022Confident Adaptive Language Modelingcited by 297
- 2022Conformal Risk Controlcited by 290
- 2024ProcessBench: Identifying Process Errors in Mathematical Reasoningcited by 277
- 2026Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMscited by 115
- 2024Calibrating Reasoning in Language Models with Internal Consistencycited by 27
- 2025RIMO: An Easy-to-Evaluate, Hard-to-Solve Olympiad Benchmark for Advanced Mathematical Reasoningcited by 3
Built on by
Citing papers per year: 2026: 1.
1 paper.
Similar, not cited
Close in wording, no citation either way
- 2026Unsupervised Confidence Calibration for Reasoning LLMs from a Single Generation
- 2025ReasonBENCH: Benchmarking the (In)Stability of LLM Reasoning
- 2026SELFDOUBT: Uncertainty Quantification for Reasoning LLMs via the Hedge-to-Verify Ratio
- 2025Martingale Score: An Unsupervised Metric for Bayesian Rationality in LLM Reasoning
- 2026Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning
- 2026When Many Answers Are Valid, Voting Fails: Symbolic Verification for Best-of-K Causal Reasoning in LLMs
- 2026Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution
- 2026The Error You See Is Not the Error You Made: Progression-aware Reasoning Origin for Reasoning Error Localization