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s1: Simple test-time scaling

Written for the Research library (claude-opus-5-5) from the paper text. Original — aclanthology.org/2025.emnlp-main.1025.pdf

Summary

The paper looks for the least machinery needed to reproduce what OpenAI's o1 showed: a model that gets more accurate when it is allowed to think longer at inference time. The authors skip large-scale reinforcement learning. They fine-tune Qwen2.5-32B-Instruct with plain supervised learning on s1K, which has only 1,000 questions. Each question comes with a reasoning trace distilled from Gemini Thinking. The questions were filtered from a larger pool on three criteria together: quality, difficulty and diversity. Difficulty meant both Qwen2.5-7B and Qwen2.5-32B failed the question, with longer traces preferred. Diversity meant spreading the set across 50 MSC-based domains. At inference the authors add budget forcing. When a token limit is reached, they insert the end-of-thinking delimiter to stop the reasoning. To make the model think longer, they block that delimiter and append "Wait", which often leads the model to recheck and fix earlier steps. The resulting s1-32B beats o1-preview on competition math, and its accuracy rises in a controllable way as it gets more compute. The work matters because it is cheap, fully open (model, data and code) and gives future reasoning research a clear baseline.

Key points

  • s1K was drawn from 59,029 questions across 16 sources, including NuminaMATH, OlympicArena, OmniMath and AGIEval. It also uses two new sets: s1-prob, with 182 probability problems from Stanford Statistics PhD qualifying exams, and s1-teasers, with 23 hard brain-teasers from quant-trading interviews. The data was decontaminated against MATH500, GPQA Diamond and AIME24 using 8-gram overlap.
  • Fine-tuning took 26 minutes on 16 H100 GPUs. s1-32B beats o1-preview by up to 27% on MATH and AIME24. With budget forcing, AIME24 accuracy rises from 50% to 57%, above what the model reaches without intervention.
  • In ablations, picking examples at random, by longest trace, or by diversity alone cost about 30% on AIME24 on average. Training on the full 59K pool gave no substantial gain over the curated 1K.
  • Limitations: gains eventually level off, and sequential scaling is capped by the context window. Parallel methods (majority voting, REBASE tree search) complement it. A later variant, s1K-1.1, uses DeepSeek r1 traces, and all experiments use Qwen-family models.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Mathematics & statistics

Cited by

511 papers of our library cite it (of the 140673 whose bibliographies we read); 7 of them have a page here, 504 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.emnlp-main.1025 · arXiv 2501.19393

@inproceedings{muennighoff2025s1,
  title = {{s1: Simple test-time scaling}},
  author = {Muennighoff, Niklas and Yang, Zitong and Shi, Weijia and Li, Xiang Lisa and Fei-Fei, Li and Hajishirzi, Hannaneh and Zettlemoyer, Luke and Liang, Percy and Candès, Emmanuel and Hashimoto, Tatsunori},
  booktitle = {Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing},
  year = {2025},
  doi = {10.18653/v1/2025.emnlp-main.1025},
  eprint = {2501.19393},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.18653/v1/2025.emnlp-main.1025}
}

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