mlsanityData to 7 Oct 2026

s1: Simple test-time scaling

arXiv 2501.19393 ↗First posted 31 Jan 2025cs.CL cs.AI cs.LGcited by 1,311

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

Abstract (arXiv)

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1-32B exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1-32B with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1

Key facts. Cited by 1,311 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 58 of its 68 references that are in the map. First posted on arXiv 31 Jan 2025.

Builds on

58 of 68 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025T1: Advancing Language Model Reasoning through Reinforcement Learning and Inference Scaling20 Jan
  2. 2024O1 Replication Journey -- Part 2: Surpassing O1-preview through Simple Distillation, Big Progress or Bitter Lesson?25 Nov
  3. 2024O1 Replication Journey: A Strategic Progress Report -- Part 18 Oct
  4. 2024Interpretable Contrastive Monte Carlo Tree Search Reasoning2 Oct
  5. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  6. 2024Stream of Search (SoS): Learning to Search in Language1 Apr
  7. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
  8. 2023Self-Evaluation Guided Beam Search for Reasoning1 May

Other references · 50

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,355
  3. 2020Scaling Laws for Neural Language Modelscited by 6,411
  4. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  5. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  6. 2023Let's Verify Step by Stepcited by 3,598
  7. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,748
  8. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,970
  9. 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 1,906
  10. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  11. 2023LIMA: Less Is More for Alignmentcited by 1,080
  12. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 946
38 more
  1. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 895
  2. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 724
  3. 2023AGIEval: A Human-Centric Benchmark for Evaluating Foundation Modelscited by 701
  4. 2017Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problemscited by 642
  5. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 618
  6. 2023Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Modelscited by 551
  7. 2022Complexity-Based Prompting for Multi-Step Reasoningcited by 387
  8. 2023Llemma: An Open Language Model For Mathematicscited by 385
  9. 2024Quiet-STaR: Language Models Can Teach Themselves to Think Before Speakingcited by 292
  10. 2024OLMoE: Open Mixture-of-Experts Language Modelscited by 291
  11. 2024Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Modelscited by 260
  12. 2024HelpSteer2: Open-source dataset for training top-performing reward modelscited by 232
  13. 2024FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AIcited by 227
  14. 2024DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Datacited by 225
  15. 2023Planning with Large Language Models for Code Generationcited by 179
  16. 2024Lessons from the Trenches on Reproducible Evaluation of Language Modelscited by 172
  17. 2024BRIGHT: A Realistic and Challenging Benchmark for Reasoning-Intensive Retrievalcited by 153
  18. 2024From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Modelscited by 136
  19. 2019JEC-QA: A Legal-Domain Question Answering Datasetcited by 115
  20. 2023SciEval: A Multi-Level Large Language Model Evaluation Benchmark for Scientific Researchcited by 112
  21. 2025Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thoughtcited by 108
  22. 2023Cumulative Reasoning with Large Language Modelscited by 94
  23. 2024o1-Coder: an o1 Replication for Codingcited by 77
  24. 2023Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Modelscited by 76
  25. 2025Agent-R: Training Language Model Agents to Reflect via Iterative Self-Trainingcited by 74
  26. 2024Can Language Models Solve Olympiad Programming?cited by 70
  27. 2024OlympicArena: Benchmarking Multi-discipline Cognitive Reasoning for Superintelligent AIcited by 70
  28. 2025RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?cited by 60
  29. 2023Don't throw away your value model! Generating more preferable text with Value-Guided Monte-Carlo Tree Search decodingcited by 59
  30. 2023Rewarding Chatbots for Real-World Engagement with Millions of Userscited by 58
  31. 2024Thinking LLMs: General Instruction Following with Thought Generationcited by 45
  32. 2021From LSAT: The Progress and Challenges of Complex Reasoningcited by 43
  33. 2023KCTS: Knowledge-Constrained Tree Search Decoding with Token-Level Hallucination Detectioncited by 43
  34. 2024A Simple Model of Inference Scaling Lawscited by 36
  35. 2025O1 Replication Journey -- Part 3: Inference-time Scaling for Medical Reasoningcited by 34
  36. 2023When Do Program-of-Thoughts Work for Reasoning?cited by 19
  37. 2024LLM-as-an-Interviewer: Beyond Static Testing Through Dynamic LLM Evaluationcited by 12
  38. 2024Multimodal Structured Generation: CVPR's 2nd MMFM Challenge Technical Reportcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 890; 2026: 421.

1,311 papers.

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  1. 2025InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiencycited by 1,419
  2. 2025Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Modelscited by 653
  3. 2025Dream 7B: Diffusion Large Language Modelscited by 515
  4. 2025Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAscited by 491
  5. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Modelscited by 456
  6. 2025DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learningcited by 398
  7. 2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learningcited by 381
  8. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 381
  9. 2025ReTool: Reinforcement Learning for Strategic Tool Use in LLMscited by 377
  10. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 319
  11. 2025VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learningcited by 315
  12. 2025Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agentscited by 294
38 more
  1. 2025OpenThoughts: Data Recipes for Reasoning Modelscited by 287
  2. 2026Reinforcement Learning via Self-Distillationcited by 285
  3. 2025Learning to Reason under Off-Policy Guidancecited by 266
  4. 2025ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memorycited by 253
  5. 2025MMaDA: Multimodal Large Diffusion Language Modelscited by 241
  6. 2025AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoningcited by 234
  7. 2025MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agentscited by 226
  8. 2025Dynamic Early Exit in Reasoning Modelscited by 217
  9. 2025A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?cited by 215
  10. 2025Deep Think with Confidencecited by 199
  11. 2025ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learningcited by 187
  12. 2025Reasoning Models Can Be Effective Without Thinkingcited by 182
  13. 2025d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learningcited by 178
  14. 2025Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyondcited by 175
  15. 2025Hierarchical Reasoning Modelcited by 167
  16. 2025UI-R1: Enhancing Efficient Action Prediction of GUI Agents by Reinforcement Learningcited by 166
  17. 2025AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning datasetcited by 165
  18. 2025The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoningcited by 160
  19. 2025The Surprising Effectiveness of Negative Reinforcement in LLM Reasoningcited by 158
  20. 2025DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Modelscited by 154
  21. 2025ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learningcited by 152
  22. 2025Llama-Nemotron: Efficient Reasoning Modelscited by 151
  23. 2026Entropy-Aware On-Policy Distillation of Language Modelscited by 151
  24. 2025GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoningcited by 147
  25. 2025SoTA with Less: MCTS-Guided Sample Selection for Data-Efficient Visual Reasoning Self-Improvementcited by 144
  26. 2025VisualPRM: An Effective Process Reward Model for Multimodal Reasoningcited by 134
  27. 2025SafeChain: Safety of Language Models with Long Chain-of-Thought Reasoning Capabilitiescited by 133
  28. 2025General-Reasoner: Advancing LLM Reasoning Across All Domainscited by 132
  29. 2025A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyondcited by 131
  30. 2025AbstentionBench: Reasoning LLMs Fail on Unanswerable Questionscited by 129
  31. 2025Thought Anchors: Which LLM Reasoning Steps Matter?cited by 126
  32. 2025Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systemscited by 125
  33. 2025Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretrainingcited by 123
  34. 2025OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cyclescited by 122
  35. 2025Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuningcited by 121
  36. 2025Safety Tax: Safety Alignment Makes Your Large Reasoning Models Less Reasonablecited by 120
  37. 2025Long-Context Autoregressive Video Modeling with Next-Frame Predictioncited by 119
  38. 2025Process Reward Models That Thinkcited by 118

50 most cited of 1,311 All 1,311 (JSON)

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  1. 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility
  2. 2025Are We Scaling the Right Thing? A System Perspective on Test-Time Scaling
  3. 2025Iterative Deepening Sampling as Efficient Test-Time Scaling
  4. 2025Rethinking Inference-Time Scaling: Efficiency Limits and Linguistic Signals
  5. 2026Efficient Test-Time Scaling via Temporal Reasoning Aggregation
  6. 2025SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling
  7. 2025Scaling over Scaling: Exploring Test-Time Scaling Plateau in Large Reasoning Models
  8. 2024A Comparative Study on Reasoning Patterns of OpenAI's o1 Model