---
title: "Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers"
description: "The authors, from Microsoft Research Asia and Harvard, propose rStar, which works purely at… 43 references, cited by 71 papers here."
authors: ["Zhenting Qi", "Mingyuan Ma", "Jiahang Xu", "Li Lyna Zhang", "Fan Yang", "Mao Yang"]
year: 2024
venue: "arXiv:2408.06195"
source: "https://arxiv.org/abs/2408.06195"
doi: "10.48550/arxiv.2408.06195"
arxiv: "2408.06195"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/qi-2024-mutual-reasoning-makes-smaller-llms/"
---
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# Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers

**Authors:** [Zhenting Qi](https://md.research.elamur.ai/free/en/authors/zhenting-qi/), Mingyuan Ma, [Jiahang Xu](https://md.research.elamur.ai/free/en/authors/jiahang-xu/), [Li Lyna Zhang](https://md.research.elamur.ai/free/en/authors/li-lyna-zhang/), [Fan Yang](https://md.research.elamur.ai/free/en/authors/fan-yang/) and [Mao Yang](https://md.research.elamur.ai/free/en/authors/mao-yang/) · **Year:** 2024 · **Venue:** arXiv:2408.06195 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2408.06195) · [PDF](https://arxiv.org/pdf/2408.06195) · [DOI 10.48550/arxiv.2408.06195](https://doi.org/10.48550/arxiv.2408.06195) · [arXiv 2408.06195](https://arxiv.org/abs/2408.06195) · [OpenAlex](https://openalex.org/W4402387391)

**Citations:** 3 citations (OpenAlex, 2026-10-14) · [71](https://md.research.elamur.ai/free/en/papers/qi-2024-mutual-reasoning-makes-smaller-llms/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Small language models (SLMs) are often weak at multi-step reasoning. The usual fix is fine-tuning on data produced by a stronger model such as GPT-4. Self-improvement methods that avoid a teacher, such as RAP, tend to fail on small models for two reasons: they explore the solution space poorly, and they cannot reliably judge their own steps. The authors, from Microsoft Research Asia and Harvard, propose rStar, which works purely at inference time and needs no training and no stronger model. A target SLM builds candidate solutions with Monte Carlo Tree Search (MCTS) over a broadened set of human-inspired step types, such as asking a sub-question or restating the problem. A second SLM of comparable strength then acts as a checker. It receives part of each candidate path and finishes it independently, and paths whose answers both models agree on are preferred. The authors call this mutual consistency. Across five SLMs and five benchmarks, 32 MCTS rounds lift accuracy dramatically, sometimes to the level of domain-specific fine-tuning. This makes strong reasoning feasible with small open models alone.

## Key points
- Benchmarks: GSM8K, GSM-Hard, MATH, SVAMP and StrategyQA, tested on five SLMs including LLaMA2-7B, Mistral-7B, LLaMA3-8B and LLaMA3-8B-Instruct.
- GSM8K accuracy gains: LLaMA2-7B rose from 12.51% to 63.91%, Mistral-7B from 36.46% to 81.88%, LLaMA3-8B from 47.23% to 85.52%, and LLaMA3-8B-Instruct from 74.53% to 91.13%.
- Motivation: after 32 rounds of RAP, only about 24% of LLaMA2-7B's GSM8K trajectories were correct. Naive self-rewarding by SLMs performed roughly at chance level (Appendix A.1).
- The action space goes beyond single-action MCTS methods like RAP and AlphaMath. It includes stepwise thoughts, sub-question decomposition and question rephrasing, the last of which splits a question into explicit conditions.
- rStar outperforms few-shot CoT, self-consistency, RAP, ToT, self-evaluation and self-verification. It also avoids training a reward model, which could overfit to specific tasks.

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

## Institutions

- [Harvard University](https://md.research.elamur.ai/free/en/universities/harvard-university/) — University, Cambridge, United States · 126 works · 45,130 citations
- [Microsoft Research Asia](https://md.research.elamur.ai/free/en/companies/microsoft-research-asia/) — Company, Beijing, China · 82 works · 61,484 citations

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🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 3,894 works · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,685 works

## Cite

Cite as: Zhenting Qi, Mingyuan Ma, Jiahang Xu, Li Lyna Zhang, Fan Yang and Mao Yang. 2024. Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers. arXiv:2408.06195.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{qi2024mutual,
  title = {{Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers}},
  author = {Zhenting Qi, Mingyuan Ma, Jiahang Xu, Li Lyna Zhang, Fan Yang and Mao Yang},
  year = {2024},
  doi = {10.48550/arxiv.2408.06195},
  eprint = {2408.06195},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2408.06195}
}
```

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*Updated 2 November 2026*