rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912180390068224 |
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| author | Guan, Xinyu Zhang, Li Lyna Liu, Yifei Shang, Ning Sun, Youran Zhu, Yi Yang, Fan Yang, Mao |
| author_facet | Guan, Xinyu Zhang, Li Lyna Liu, Yifei Shang, Ning Sun, Youran Zhu, Yi Yang, Fan Yang, Mao |
| contents | We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids naïve step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking Guan, Xinyu Zhang, Li Lyna Liu, Yifei Shang, Ning Sun, Youran Zhu, Yi Yang, Fan Yang, Mao Computation and Language We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids naïve step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar. |
| title | rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2501.04519 |