{"id":"arxiv:2501.19393","title":"s1: Simple test-time scaling","date":"2025-01-31","section":"Reasoning and the \"physics\" of language models","quality":null,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/","source_url":"https://arxiv.org/abs/2501.19393","text_available":true,"authors":["Niklas Muennighoff","Zitong Yang","Weijia Shi","Xiang Lisa Li"],"outgoing":[{"source":"arxiv:2501.19393","target":"arxiv:2001.08361","evidence":"id","id":"arxiv:2001.08361","title":"Scaling Laws for Neural Language Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/82302458a6d03bc051b2e4fdb8277893a81d4bd6a029969045df6a8380904eac/"},{"source":"arxiv:2501.19393","target":"arxiv:2206.04615","evidence":"title","id":"arxiv:2206.04615","title":"Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/70882486c1f8c46cb7b26cf100847f770eb7b39b69dee56b8a21141141ef814d/"},{"source":"arxiv:2501.19393","target":"arxiv:2407.21783","evidence":"id","id":"arxiv:2407.21783","title":"The Llama 3 Herd of Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/de3cebb4c28bc5d41a843279f219dca14476284991ea5c7c0aeab7068a40e306/"},{"source":"arxiv:2501.19393","target":"arxiv:2502.03387","evidence":"id","id":"arxiv:2502.03387","title":"LIMO: Less is More for Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/714392528bb842fb3a61cee5367942f697536f0131b0fcac85c6eb8d2212125c/"}],"incoming":[{"source":"arxiv:2503.00735","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2503.00735","title":"LADDER: Self-Improving LLMs Through Recursive Problem Decomposition","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/65b264030233bf2bcd17284eb9a521e6e38d4ee83eb7fec6587e4c047199f227/"},{"source":"arxiv:2503.02875","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2503.02875","title":"The First Few Tokens Are All You Need: An Efficient and Effective Unsupervised Prefix Fine-Tuning Method for Reasoning Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/b9349378a2ea40a7998ba364a4587c40dff3cc9b22750e14b3b21e296a4ecb12/"},{"source":"arxiv:2505.15134","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2505.15134","title":"The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/12b01b403e280a32d41fd991a27fa30f33315e09f0f42a4f43e9bece5ad9c53d/"},{"source":"arxiv:2505.22954","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2505.22954","title":"Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/c29f716871f80314868b5647692de387f26e12166b93bd362915fd272b6e081c/"},{"source":"arxiv:2506.06632","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2506.06632","title":"Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/79fda9609f9b88bb71f71f531b63ea6b5237d1c889b7ae59e9ca07c12dbe70d1/"},{"source":"arxiv:2506.21734","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2506.21734","title":"Hierarchical Reasoning Model","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/3604312101ff09ab9903e7d6a32c7b2b8a9a7ece6a9d145d04ea01c9d13ffa3a/"},{"source":"arxiv:2507.12856","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2507.12856","title":"Supervised Fine Tuning on Curated Data is Reinforcement Learning (and can be improved)","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/5f6c1906eaa67369d9ff15b974756b89141d1b4cf9d7c0f6554e0d56f26e79be/"},{"source":"arxiv:2509.20317","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2509.20317","title":"SIM-CoT: Supervised Implicit Chain-of-Thought","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/72b64dd6a30c71d99920cafabbb2c909d03febab8991eeaf3c091b16cb7ed348/"},{"source":"arxiv:2512.13961","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2512.13961","title":"Olmo 3","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/8daa11a9729da9879a7e95c15d4eef3bab8579d2885a14102ed09db111221802/"},{"source":"arxiv:2601.18734","target":"arxiv:2501.19393","evidence":"id","id":"arxiv:2601.18734","title":"Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/8a352e37fa79840a4f35f86ebc39661cfc34fbfc4391cd020a69af158c63485a/"},{"source":"arxiv:2601.20802","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2601.20802","title":"Reinforcement Learning via Self-Distillation","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6073ec3d17b9a932a68e79ae078928f4635e40fc79cfcbc31709715d1f1e1ffa/"},{"source":"arxiv:2604.19341","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2604.19341","title":"Structured Scaling of AI Discovery Across Diverse Scientific Domains","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/33ad3375247f86197210840a19064548b997e8617475e606d7a7ac2cda64740e/"},{"source":"arxiv:2605.07654","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2605.07654","title":"Reliable Chain-of-Thought via Prefix Consistency","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/715ed2b4b2f355b771111eb0e65e113f100dc33739423a76307e8ece18b57d18/"},{"source":"arxiv:2609.30652","target":"arxiv:2501.19393","evidence":"title","id":"arxiv:2609.30652","title":"Recursive Self-Improvement via On-Policy Distillation for Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/9e52af299c264dd7185057305368429cdf42deb165dd5e3fc0f9cf6ef1d612bf/"}],"text_parts":[{"start":0,"end":15899,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html"},{"start":15899,"end":31457,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html"},{"start":31457,"end":44075,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html"}],"contents":[{"title":"s1 : Simple test-time scaling","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Abstract","offset":33,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Keywords:","offset":1331,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"1 Introduction","offset":1349,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"2 Reasoning data curation to create s1K","offset":5814,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"2.1 Initial collection of 59K samples","offset":5987,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Curation of existing datasets","offset":6454,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"New datasets in quantitative reasoning","offset":7161,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"2.2 Final selection of 1K samples","offset":8359,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Quality","offset":8700,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Difficulty","offset":9242,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Diversity","offset":10414,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"3 Test-time scaling","offset":11607,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"3.1 Method","offset":11631,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Budget forcing","offset":12179,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Baselines","offset":12866,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"3.2 Metrics","offset":13603,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"4 Results","offset":15629,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"4.1 Setup","offset":15643,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Training","offset":15658,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Evaluation","offset":15882,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-1.html#text"},{"title":"Other models","offset":17383,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"4.2 Performance","offset":18525,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Test-time scaling","offset":18546,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Sample-efficiency","offset":19502,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"5 Ablations","offset":20265,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"5.1 Data Quantity, Diversity, and Difficulty","offset":20281,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"5.2 Test-time scaling methods","offset":21767,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Budget forcing","offset":21802,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Rejection sampling","offset":22979,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"6 Discussion and related work","offset":23824,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"6.1 Sample-efficient reasoning","offset":23858,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Models","offset":23894,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Benchmarks and methods","offset":25227,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"6.2 Test-time scaling","offset":26617,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Methods","offset":26644,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Limits to further test-time scaling","offset":28411,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Parallel scaling as a solution","offset":29713,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Impact Statement","offset":30922,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Acknowledgements","offset":31436,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-2.html#text"},{"title":"Appendix A s1.1","offset":31949,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Appendix B Evaluation determinism","offset":32533,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Appendix C s1K details","offset":33498,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"C.1 s1K summary","offset":33525,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"C.2 Dataset composition for full 59K questions","offset":33546,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"C.3 s1K grading prompt","offset":33598,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"C.4 s1K diversity selection","offset":33849,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"C.5 Decontamination","offset":34130,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Appendix D Training details","offset":34364,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"D.1 Training Ablations: Sequence length","offset":35734,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"D.2 Training Samples","offset":36788,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Appendix E Test-time scaling details","offset":36873,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"E.1 Sequential scaling ablations","offset":36914,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Token-conditional control","offset":36952,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Step-conditional control","offset":38602,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Class-conditional control","offset":41482,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"E.2 Examples for rejection sampling ablation","offset":42885,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Appendix F Version Control","offset":42935,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"},{"title":"Instructions for reporting errors","offset":43111,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/part-3.html#text"}],"text_code_points":44075,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/2a88818f7605b71cd0160831faebd51b3274c24ffd29626b4d519390b4bffffe/source.md"}