# BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning

arXiv: https://arxiv.org/abs/2501.03226 · HTML: https://mlsanity.com/paper/2501.03226/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (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)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [ChatGLM-Math: Improving Math Problem-Solving in Large Language Models with a Self-Critique Pipeline](https://mlsanity.com/paper/2404.02893/) (2024)
- [Progressive Multimodal Reasoning via Active Retrieval](https://mlsanity.com/paper/2412.14835/) (2024)
- [What Makes In-context Learning Effective for Mathematical Reasoning: A Theoretical Analysis](https://mlsanity.com/paper/2412.12157/) (2024)

## Built on by (most cited first, 21 of 21)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Spatial-SSRL: Enhancing Spatial Understanding via Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/2510.27606/) (2025)
- [CapRL: Stimulating Dense Image Caption Capabilities via Reinforcement Learning](https://mlsanity.com/paper/2509.22647/) (2025)
- [Unlocking General Long Chain-of-Thought Reasoning Capabilities of Large Language Models via Representation Engineering](https://mlsanity.com/paper/2503.11314/) (2025)
- [Advancing Complex Video Object Segmentation via Progressive Concept Construction](https://mlsanity.com/paper/2507.15852/) (2025)
- [Feature Extraction and Steering for Enhanced Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2505.15634/) (2025)
- [STAR-Bench: Probing Deep Spatio-Temporal Reasoning as Audio 4D Intelligence](https://mlsanity.com/paper/2510.24693/) (2025)
- [Process or Result? Manipulated Ending Tokens Can Mislead Reasoning LLMs to Ignore the Correct Reasoning Steps](https://mlsanity.com/paper/2503.19326/) (2025)
- [Enhancing Test-Time Scaling of Large Language Models with Hierarchical Retrieval-Augmented MCTS](https://mlsanity.com/paper/2507.05557/) (2025)
- [Visual Self-Refine: A Pixel-Guided Paradigm for Accurate Chart Parsing](https://mlsanity.com/paper/2602.16455/) (2026)
- [Guideline Forest: Retrieval-Augmented Reasoning with Branching Experience-Induced Guidelines](https://mlsanity.com/paper/2506.07820/) (2025)
- [FinHEAR: Human Expertise and Adaptive Risk-Aware Temporal Reasoning for Financial Decision-Making](https://mlsanity.com/paper/2506.09080/) (2025)
- [From Perception to Reasoning: Deep Thinking Empowers Multimodal Large Language Models](https://mlsanity.com/paper/2511.12861/) (2025)
- [Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance](https://mlsanity.com/paper/2602.22583/) (2026)
- [SciDocBench: A Workflow-Centered Benchmark and Data Pipeline for Scientific Document Understanding](https://mlsanity.com/paper/2609.05141/) (2026)
- [Reward Model Generalization for Compute-Aware Test-Time Reasoning](https://mlsanity.com/paper/2505.18065/) (2025)
- [From Implicit Exploration to Structured Reasoning: Leveraging Guideline and Refinement for LLMs](https://mlsanity.com/paper/2509.06284/) (2025)
- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)
- [When LLM Meets Tree Search: A Systematic View of Inference as Search in Large Language Models](https://mlsanity.com/paper/2608.30395/) (2026)
- [SpatialASM: Internalizing Active Mentalization for Spatial Reasoning](https://mlsanity.com/paper/2610.13832/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated impressive ability in solving complex mathematical problems with multi-step reasoning and can be further enhanced with well-designed in-context learning (ICL) examples. However, this potential is often constrained by two major challenges in ICL: granularity mismatch and irrelevant information. We observe that while LLMs excel at decomposing mathematical problems, they often struggle with reasoning errors in fine-grained steps. Moreover, ICL examples retrieved at the question level may omit critical steps or even mislead the model with irrelevant details. To address this issue, we propose BoostStep, a method that enhances reasoning accuracy through step-aligned ICL, a novel mechanism that carefully aligns retrieved reference steps with the corresponding reasoning steps. Additionally, BoostStep incorporates an effective "first-try" strategy to deliver exemplars highly relevant to the current state of reasoning. BoostStep is a flexible and powerful method that integrates seamlessly with chain-of-thought (CoT) and tree search algorithms, refining both candidate selection and decision-making. Empirical results show that BoostStep improves GPT-4o's CoT performance by 4.6% across mathematical benchmarks, significantly surpassing traditional few-shot learning's 1.2%. Moreover, it can achieve an additional 7.5% gain combined with tree search. Surprisingly, it enhances state-of-the-art LLMs to solve challenging math problems using simpler examples. It improves DeepSeek-R1-671B's performance on AIME by 2.2%, leveraging simple examples only from the MATH dataset.