s1: Simple test-time scaling

arxiv:2501.19393

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Reasoning and the "physics" of language models · 2025-01-31

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1. Part 1
2. Part 2
3. Part 3

Contents

• s1 : Simple test-time scaling
• Abstract
• Keywords:
• 1 Introduction
• 2 Reasoning data curation to create s1K
• 2.1 Initial collection of 59K samples
• Curation of existing datasets
• New datasets in quantitative reasoning
• 2.2 Final selection of 1K samples
• Quality
• Difficulty
• Diversity
• 3 Test-time scaling
• 3.1 Method
• Budget forcing
• Baselines
• 3.2 Metrics
• 4 Results
• 4.1 Setup
• Training
• Evaluation
• Other models
• 4.2 Performance
• Test-time scaling
• Sample-efficiency
• 5 Ablations
• 5.1 Data Quantity, Diversity, and Difficulty
• 5.2 Test-time scaling methods
• Budget forcing
• Rejection sampling
• 6 Discussion and related work
• 6.1 Sample-efficient reasoning
• Models
• Benchmarks and methods
• 6.2 Test-time scaling
• Methods
• Limits to further test-time scaling
• Parallel scaling as a solution
• Impact Statement
• Acknowledgements
• Appendix A s1.1
• Appendix B Evaluation determinism
• Appendix C s1K details
• C.1 s1K summary
• C.2 Dataset composition for full 59K questions
• C.3 s1K grading prompt
• C.4 s1K diversity selection
• C.5 Decontamination
• Appendix D Training details
• D.1 Training Ablations: Sequence length
• D.2 Training Samples
• Appendix E Test-time scaling details
• E.1 Sequential scaling ablations
• Token-conditional control
• Step-conditional control
• Class-conditional control
• E.2 Examples for rejection sampling ablation
• Appendix F Version Control
• Instructions for reporting errors