mlsanityData to 7 Oct 2026

Scaling of Capability and Efficiency at Inference Time in Large Reasoning Models

arXiv 2609.27166 ↗First posted 22 Sep 2026cs.LG physics.soc-phcited by 0

On the map: LLM reasoning → Test-time compute and efficient thinking also fits: Prompting and chain-of-thought reasoning

Abstract (arXiv)

Capability and efficiency are two key dimensions of reasoning in large language models (LLMs). Capability refers to the ability to solve a given problem correctly, whereas efficiency refers to the ability to do so with limited resources. When LLMs use Chain-of-Thought (CoT) reasoning to solve problems of controlled hardness, both the number of problems solved correctly and the number of tokens required to reach a correct answer depend on problem hardness and model size. However, how these factors jointly shape capability and efficiency remains poorly understood. Here, we use hierarchical Bayesian models to evaluate the capability and efficiency of LLMs from the DeepSeek-R1-Distill model family across four classes of arithmetic and algorithmic reasoning problems. At a fixed model size, the probability of correctly solving an instance decays approximately exponentially with instance size, our proxy for problem hardness. The decay scale grows sublinearly with model size, indicating that larger models are more capable, but that capability gains diminish with scale. Output length grows as a power law with instance size, which serves as a proxy for difficulty. However, the parameters of this power law do not vary systematically with model size, suggesting that larger models do not become more efficient. Together, these findings reveal potential limitations of naive scaling as a strategy for developing more capable AI systems: capability improves with diminishing returns, while efficiency shows little to no improvement.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 57 of its 65 references that are in the map. First posted on arXiv 22 Sep 2026.

Builds on

57 of 65 references.

Closest ancestors · 11

Same direction, newest first

  1. 2026Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models7 Apr
  2. 2026Reasoning about Reasoning: BAPO Bounds on Chain-of-Thought Token Complexity in LLMs2 Feb
  3. 2025When Reasoning Meets Its Laws19 Dec
  4. 2025Inverse Scaling in Test-Time Compute19 Jul
  5. 2025The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity7 Jun
  6. 2025Let Me Think! A Long Chain-of-Thought Can Be Worth Exponentially Many Short Ones27 May
  7. 2025The First Impression Problem: Internal Bias Triggers Overthinking in Reasoning Models22 May
  8. 2025Lost in Transmission: When and Why LLMs Fail to Reason Globally13 May
  9. 2025Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs30 Apr
  10. 2025A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?31 Mar
  11. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning25 Feb

Other references · 46

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  3. 2020Scaling Laws for Neural Language Modelscited by 6,411
  4. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
  5. 2017Deep reinforcement learning from human preferencescited by 3,846
  6. 2021Finetuned Language Models Are Zero-Shot Learnerscited by 3,747
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  9. 2022Training Compute-Optimal Large Language Modelscited by 2,927
  10. 2022Emergent Abilities of Large Language Modelscited by 2,483
  11. 2019Fine-Tuning Language Models from Human Preferencescited by 2,124
  12. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,193
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  4. 2023Instruction Tuning for Large Language Models: A Surveycited by 617
  5. 2023RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedbackcited by 615
  6. 2017Deep Learning Scaling is Predictable, Empiricallycited by 556
  7. 2024GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Modelscited by 533
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  10. 2018Pyro: Deep Universal Probabilistic Programmingcited by 379
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  12. 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 288
  13. 2022Predictability and Surprise in Large Generative Modelscited by 209
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  15. 2019Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyrocited by 187
  16. 2025ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoningcited by 186
  17. 2025When More is Less: Understanding Chain-of-Thought Length in LLMscited by 182
  18. 2025A Survey of Reinforcement Learning for Large Reasoning Modelscited by 175
  19. 2023What Formal Languages Can Transformers Express? A Surveycited by 120
  20. 2024A Dynamical Model of Neural Scaling Lawscited by 105
  21. 2022Broken Neural Scaling Lawscited by 102
  22. 2025The Art of Scaling Reinforcement Learning Compute for LLMscited by 91
  23. 2025Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contaminationcited by 81
  24. 2025Reinforcement Learning from Human Feedbackcited by 53
  25. 2025Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzlescited by 53
  26. 2024Selecting Large Language Model to Fine-tune via Rectified Scaling Lawcited by 33
  27. 2025What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoTcited by 24
  28. 2025Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoningcited by 23
  29. 2024Does RLHF Scale? Exploring the Impacts From Data, Model, and Methodcited by 22
  30. 2025Beyond Accuracy: Dissecting Mathematical Reasoning for LLMs Under Reinforcement Learningcited by 7
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  32. 2025Are Language Models Efficient Reasoners? A Perspective from Logic Programmingcited by 4
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