mlsanityData to 14 Oct 2026

PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains

arXiv 2508.21787 ↗First posted 29 Aug 2025cs.CL cs.AIcited by 10

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 57 of its 72 references that are in the map. First posted on arXiv 29 Aug 2025.

Builds on

57 of 72 references.

Closest ancestors · 14

Same direction, newest first

  1. 2025Inverse Scaling in Test-Time Compute19 Jul
  2. 2025How Well Can Reasoning Models Identify and Recover from Unhelpful Thoughts?12 Jun
  3. 2025Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoning23 May
  4. 2025Scalable Best-of-N Selection for Large Language Models via Self-Certainty25 Feb
  5. 2025Confidence Improves Self-Consistency in LLMs10 Feb
  6. 2025s1: Simple test-time scaling31 Jan
  7. 2024Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs30 Dec
  8. 2024Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling30 Aug
  9. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  10. 2023Universal Self-Consistency for Large Language Model Generation29 Nov
  11. 2023SelfCheck: Using LLMs to Zero-Shot Check Their Own Step-by-Step Reasoning1 Aug
  12. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
2 more
  1. 2023Self-Refine: Iterative Refinement with Self-Feedback30 Mar
  2. 2022Language Models (Mostly) Know What They Know11 Jul

Other references · 43

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  4. 2025Qwen3 Technical Reportcited by 8,820
  5. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  6. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2024GPT-4o System Cardcited by 4,588
  9. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  10. 2023Let's Verify Step by Stepcited by 3,789
  11. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
  12. 2020Learning to summarize from human feedbackcited by 2,588
31 more
  1. 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,998
  2. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,392
  3. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,210
  4. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  5. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 878
  6. 2023Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generationcited by 819
  7. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 812
  8. 2023SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Modelscited by 810
  9. 2020Towards a Human-like Open-Domain Chatbotcited by 470
  10. 2024The Platonic Representation Hypothesiscited by 382
  11. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 320
  12. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 313
  13. 2025MathArena: Evaluating LLMs on Uncontaminated Math Competitionscited by 297
  14. 2023Fine-tuning Language Models for Factualitycited by 221
  15. 2023Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hackingcited by 200
  16. 2023TheoremQA: A Theorem-driven Question Answering datasetcited by 192
  17. 2025When More is Less: Understanding Chain-of-Thought Length in LLMscited by 183
  18. 2024Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantificationcited by 162
  19. 2023Controlled Decoding from Language Modelscited by 135
  20. 2023LM-Polygraph: Uncertainty Estimation for Language Modelscited by 131
  21. 2025Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignmentcited by 97
  22. 2021Generate & Rank: A Multi-task Framework for Math Word Problemscited by 82
  23. 2024Calibrating Large Language Models with Sample Consistencycited by 73
  24. 2025A Survey of Uncertainty Estimation Methods on Large Language Modelscited by 62
  25. 2025Great Models Think Alike and this Undermines AI Oversightcited by 58
  26. 2024Variational Best-of-N Alignmentcited by 51
  27. 2024Understanding Chain-of-Thought in LLMs through Information Theorycited by 37
  28. 2024A Simple Model of Inference Scaling Lawscited by 36
  29. 2024DeCoRe: Decoding by Contrasting Retrieval Heads to Mitigate Hallucinationscited by 25
  30. 2024CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoningcited by 16
  31. 2025Theorem Prover as a Judge for Synthetic Data Generationcited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 6.

10 papers.

  1. 2026Uncertainty Quantification in LLM Agents: Foundations, Emerging Challenges, and Opportunitiescited by 20
  2. 2025DTS: Enhancing Large Reasoning Models via Decoding Tree Sketchingcited by 6
  3. 2025LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervisioncited by 6
  4. 2026Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisationcited by 4
  5. 2025From <Answer> to <Think>: Multidimensional Supervision of Reasoning Process for LLM Optimizationcited by 3
  6. 2026Reasoning or Fluency? Dissecting Probabilistic Confidence in Best-of-N Selectioncited by 2
  7. 2025When Retrieval Succeeds and Fails: Rethinking Retrieval-Augmented Generation for LLMscited by 1
  8. 2026Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Modelscited by 1
  9. 2026Fork-Think with Confidencecited by 1
  10. 2026Compare to Correct: Pairwise-Guided Logit Adjustment for LLM Test-Time Scalingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Sample Smart, Not Hard: Correctness-First Decoding for Better Reasoning in LLMs
  2. 2026CALIBER: Calibrating Confidence Before and After Reasoning in Language Models
  3. 2026Probability is Not Enough: Exploring and Counting Divergent Tokens for Reasoning Uncertainty Quantification in LLMs
  4. 2026Unsupervised Confidence Calibration for Reasoning LLMs from a Single Generation
  5. 2026How Reliable are Confidence Estimators for Large Reasoning Models? A Systematic Benchmark on High-Stakes Domains
  6. 2025CER: Confidence Enhanced Reasoning in LLMs
  7. 2025Let the Model Distribute Its Doubt: Confidence Estimation through Verbalized Probability Distribution
  8. 2026ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models