# Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers

arXiv: https://arxiv.org/abs/2408.06195 · HTML: https://mlsanity.com/paper/2408.06195/

## Key facts

- Cited by 138 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 25 of 25)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [Take a Step Back: Evoking Reasoning via Abstraction in Large Language Models](https://mlsanity.com/paper/2310.06117/) (2023)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Self-Discover: Large Language Models Self-Compose Reasoning Structures](https://mlsanity.com/paper/2402.03620/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation](https://mlsanity.com/paper/2311.04254/) (2023)
- [Self-Verification Improves Few-Shot Clinical Information Extraction](https://mlsanity.com/paper/2306.00024/) (2023)
- [MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time](https://mlsanity.com/paper/2405.16265/) (2024)
- [Large Language Models Can Self-Correct with Key Condition Verification](https://mlsanity.com/paper/2405.14092/) (2024)

## Built on by (most cited first, 30 of 138)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Mulberry: Empowering MLLM with o1-like Reasoning and Reflection via Collective Monte Carlo Tree Search](https://mlsanity.com/paper/2412.18319/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2503.09501/) (2025)
- [o1-Coder: an o1 Replication for Coding](https://mlsanity.com/paper/2412.00154/) (2024)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [A Survey on (M)LLM-Based GUI Agents](https://mlsanity.com/paper/2504.13865/) (2025)
- [Archon: An Architecture Search Framework for Inference-Time Techniques](https://mlsanity.com/paper/2409.15254/) (2024)
- [SpecReason: Fast and Accurate Inference-Time Compute via Speculative Reasoning](https://mlsanity.com/paper/2504.07891/) (2025)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search](https://mlsanity.com/paper/2502.02508/) (2025)
- [When Thinking Fails: The Pitfalls of Reasoning for Instruction-Following in LLMs](https://mlsanity.com/paper/2505.11423/) (2025)
- [Scaling of Search and Learning: A Roadmap to Reproduce o1 from Reinforcement Learning Perspective](https://mlsanity.com/paper/2412.14135/) (2024)
- [VLM-R3: Region Recognition, Reasoning, and Refinement for Enhanced Multimodal Chain-of-Thought](https://mlsanity.com/paper/2505.16192/) (2025)
- [MT-R1-Zero: Advancing LLM-based Machine Translation via R1-Zero-like Reinforcement Learning](https://mlsanity.com/paper/2504.10160/) (2025)
- [SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning](https://mlsanity.com/paper/2504.19162/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Unveiling the Key Factors for Distilling Chain-of-Thought Reasoning](https://mlsanity.com/paper/2502.18001/) (2025)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)
- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Search and Refine During Think: Facilitating Knowledge Refinement for Improved Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2505.11277/) (2025)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [ReARTeR: Retrieval-Augmented Reasoning with Trustworthy Process Rewarding](https://mlsanity.com/paper/2501.07861/) (2025)
- [MCTS-Judge: Test-Time Scaling in LLM-as-a-Judge for Code Correctness Evaluation](https://mlsanity.com/paper/2502.12468/) (2025)
- [TemplateRL: Structured Template-Guided Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2505.15692/) (2025)

## Abstract (arXiv)

This paper introduces rStar, a self-play mutual reasoning approach that significantly improves reasoning capabilities of small language models (SLMs) without fine-tuning or superior models. rStar decouples reasoning into a self-play mutual generation-discrimination process. First, a target SLM augments the Monte Carlo Tree Search (MCTS) with a rich set of human-like reasoning actions to construct higher quality reasoning trajectories. Next, another SLM, with capabilities similar to the target SLM, acts as a discriminator to verify each trajectory generated by the target SLM. The mutually agreed reasoning trajectories are considered mutual consistent, thus are more likely to be correct. Extensive experiments across five SLMs demonstrate rStar can effectively solve diverse reasoning problems, including GSM8K, GSM-Hard, MATH, SVAMP, and StrategyQA. Remarkably, rStar boosts GSM8K accuracy from 12.51% to 63.91% for LLaMA2-7B, from 36.46% to 81.88% for Mistral-7B, from 74.53% to 91.13% for LLaMA3-8B-Instruct. Code will be available at https://github.com/zhentingqi/rStar.