# MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time

arXiv: https://arxiv.org/abs/2405.16265 · HTML: https://mlsanity.com/paper/2405.16265/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 25 May 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text](https://mlsanity.com/paper/2310.06786/) (2023)
- [A Confederacy of Models: a Comprehensive Evaluation of LLMs on Creative Writing](https://mlsanity.com/paper/2310.08433/) (2023)
- [SocialIQA: Commonsense Reasoning about Social Interactions](https://mlsanity.com/paper/1904.09728/) (2019)
- [Levin Tree Search with Context Models](https://mlsanity.com/paper/2305.16945/) (2023)

## Built on by (most cited first, 30 of 41)

- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [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)
- [Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers](https://mlsanity.com/paper/2408.06195/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Multi-Agent Collaboration via Evolving Orchestration](https://mlsanity.com/paper/2505.19591/) (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)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning](https://mlsanity.com/paper/2501.15602/) (2025)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [MCTS-Judge: Test-Time Scaling in LLM-as-a-Judge for Code Correctness Evaluation](https://mlsanity.com/paper/2502.12468/) (2025)
- [LiteSearch: Efficacious Tree Search for LLM](https://mlsanity.com/paper/2407.00320/) (2024)
- [Think More, Hallucinate Less: Mitigating Hallucinations via Dual Process of Fast and Slow Thinking](https://mlsanity.com/paper/2501.01306/) (2025)
- [MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervision](https://mlsanity.com/paper/2505.13427/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2410.13857/) (2024)
- [Enhancing Multi-Step Reasoning Abilities of Language Models through Direct Q-Function Optimization](https://mlsanity.com/paper/2410.09302/) (2024)
- [On the Emergence of Thinking in LLMs I: Searching for the Right Intuition](https://mlsanity.com/paper/2502.06773/) (2025)
- [Accelerating Large Language Model Reasoning via Speculative Search](https://mlsanity.com/paper/2505.02865/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [When Does Verification Pay Off? A Closer Look at LLMs as Solution Verifiers](https://mlsanity.com/paper/2512.02304/) (2025)
- [BEATS: Optimizing LLM Mathematical Capabilities with BackVerify and Adaptive Disambiguate based Efficient Tree Search](https://mlsanity.com/paper/2409.17972/) (2024)
- [Don't Get Lost in the Trees: Streamlining LLM Reasoning by Overcoming Tree Search Exploration Pitfalls](https://mlsanity.com/paper/2502.11183/) (2025)
- [Temporal Sampling for Forgotten Reasoning in LLMs](https://mlsanity.com/paper/2505.20196/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [Temporal Consistency for LLM Reasoning Process Error Identification](https://mlsanity.com/paper/2503.14495/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)

## Abstract (arXiv)

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.