mlsanityData to 7 Oct 2026

On the Provable Performance Guarantee of Efficient Reasoning Models

arXiv 2510.09133 ↗First posted 10 Oct 2025cs.AI cs.LG math.STcited by 6

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

Abstract (arXiv)

Large reasoning models (LRMs) have achieved remarkable progress in complex problem-solving tasks. Despite this success, LRMs typically suffer from high computational costs during deployment, highlighting a need for efficient inference. A practical direction of efficiency improvement is to switch the LRM between thinking and non-thinking modes dynamically. However, such approaches often introduce additional reasoning errors and lack statistical guarantees for the performance loss, which are critical for high-stakes applications. In this work, we propose Probably Approximately Correct (PAC) reasoning that controls the performance loss under the user-specified tolerance. Specifically, we construct an upper confidence bound on the performance loss and determine a threshold for switching to the non-thinking model. Theoretically, using the threshold to switch between the thinking and non-thinking modes ensures bounded performance loss in a distribution-free manner. Our comprehensive experiments on reasoning benchmarks show that the proposed method can save computational budgets and control the user-specified performance loss.

Key facts. Cited by 6 papers 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 54 of its 64 references that are in the map. First posted on arXiv 10 Oct 2025.

Builds on

54 of 64 references.

Closest ancestors · 12

Same direction, newest first

  1. 2025Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models4 Aug
  2. 2025Thinker: Learning to Think Fast and Slow27 May
  3. 2025Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens23 May
  4. 2025ThinkSwitcher: When to Think Hard, When to Think Fast20 May
  5. 2025FlashThink: An Early Exit Method For Efficient Reasoning20 May
  6. 2025Thinkless: LLM Learns When to Think19 May
  7. 2025A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law5 May
  8. 2025Dynamic Early Exit in Reasoning Models22 Apr
  9. 2025Reasoning Models Can Be Effective Without Thinking14 Apr
  10. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models20 Mar
  11. 2025Thinking Slow, Fast: Scaling Inference Compute with Distilled Reasoners27 Feb
  12. 2024DynaThink: Fast or Slow? A Dynamic Decision-Making Framework for Large Language Models1 Jul

Other references · 42

  1. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  2. 2025Qwen3 Technical Reportcited by 8,195
  3. 2021Evaluating Large Language Models Trained on Codecited by 8,053
  4. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  5. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  6. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  7. 2017On Calibration of Modern Neural Networkscited by 4,860
  8. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,710
  9. 2023Let's Verify Step by Stepcited by 3,598
  10. 2022OPT: Open Pre-trained Transformer Language Modelscited by 3,464
  11. 2017TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehensioncited by 2,895
  12. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,748
30 more
  1. 2018CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledgecited by 1,793
  2. 2023SGLang: Efficient Execution of Structured Language Model Programscited by 1,107
  3. 2023Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMscited by 946
  4. 2023Reasoning with Language Model is Planning with World Modelcited by 846
  5. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 788
  6. 2024RouteLLM: Learning to Route LLMs with Preference Datacited by 633
  7. 2020Recipes for building an open-domain chatbotcited by 593
  8. 2024From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipelinecited by 484
  9. 2025The Lessons of Developing Process Reward Models in Mathematical Reasoningcited by 402
  10. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 381
  11. 2022Conformal Risk Controlcited by 290
  12. 2025Chain of Draft: Thinking Faster by Writing Lesscited by 290
  13. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 278
  14. 2021Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Controlcited by 256
  15. 2025ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoningcited by 186
  16. 2020Estimating means of bounded random variables by bettingcited by 164
  17. 2023Conformal Language Modelingcited by 163
  18. 2024On Verbalized Confidence Scores for LLMscited by 83
  19. 2020Admissible anytime-valid sequential inference must rely on nonnegative martingalescited by 43
  20. 2025The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giantscited by 37
  21. 2019Bootstrapping Upper Confidence Boundcited by 36
  22. 2025Fast-Slow Thinking GRPO for Large Vision-Language Model Reasoningcited by 34
  23. 2025Beyond GPT-5: Making LLMs Cheaper and Better via Performance-Efficiency Optimized Routingcited by 32
  24. 2025Think More, Hallucinate Less: Mitigating Hallucinations via Dual Process of Fast and Slow Thinkingcited by 29
  25. 2020Confidence sequences for sampling without replacementcited by 23
  26. 2024Localized Adaptive Risk Controlcited by 16
  27. 2024Automatically Adaptive Conformal Risk Controlcited by 16
  28. 2024HDFlow: Enhancing LLM Complex Problem-Solving with Hybrid Thinking and Dynamic Workflowscited by 13
  29. 2025DynamicMind: A Tri-Mode Thinking System for Large Language Modelscited by 5
  30. 2019A New Confidence Interval for the Mean of a Bounded Random Variablecited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 5.

6 papers.

  1. 2026Conformal Thinking: Risk Control for Reasoning on a Compute Budgetcited by 9
  2. 2025A note on conditional PAC-efficient reasoning in large language model routingcited by 3
  3. 2026Anytime Safe PAC Efficient Reasoningcited by 1
  4. 2026Conditional Performance Guarantee for Large Reasoning Modelscited by 0
  5. 2026The Exceedance Design Effect: Effective Sample Size for Thresholds under Clusteringcited by 0
  6. 2026On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Efficient Inference for Large Reasoning Models: A Survey
  2. 2025How Far Are We from Optimal Reasoning Efficiency?
  3. 2025THINK-Bench: Evaluating Thinking Efficiency and Chain-of-Thought Quality of Large Reasoning Models
  4. 2025When to Continue Thinking: Adaptive Thinking Mode Switching for Efficient Reasoning
  5. 2025Thought Manipulation: External Thought Can Be Efficient for Large Reasoning Models
  6. 2025Efficient Reasoning Models: A Survey
  7. 2025Trade-offs in Large Reasoning Models: An Empirical Analysis of Deliberative and Adaptive Reasoning over Foundational Capabilities
  8. 2025Optimizing Length Compression in Large Reasoning Models