# BEATS: Optimizing LLM Mathematical Capabilities with BackVerify and Adaptive Disambiguate based Efficient Tree Search

arXiv: https://arxiv.org/abs/2409.17972 · HTML: https://mlsanity.com/paper/2409.17972/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 30 of 32)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Buffer of Thoughts: Thought-Augmented Reasoning with Large Language Models](https://mlsanity.com/paper/2406.04271/) (2024)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)

## Built on by (most cited first, 13 of 13)

- [Can We Generate Images with CoT? Let's Verify and Reinforce Image Generation Step by Step](https://mlsanity.com/paper/2501.13926/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [MM-Verify: Enhancing Multimodal Reasoning with Chain-of-Thought Verification](https://mlsanity.com/paper/2502.13383/) (2025)
- [Zero-Shot Verification-guided Chain of Thoughts](https://mlsanity.com/paper/2501.13122/) (2025)
- [CMCTS: A Constrained Monte Carlo Tree Search Framework for Mathematical Reasoning in Large Language Model](https://mlsanity.com/paper/2502.11169/) (2025)
- [Can Test-Time Scaling Improve World Foundation Model?](https://mlsanity.com/paper/2503.24320/) (2025)
- [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)
- [Rethinking Text-to-SQL: Dynamic Multi-turn SQL Interaction for Real-world Database Exploration](https://mlsanity.com/paper/2510.26495/) (2025)
- [Canvas-of-Thought: Grounding Reasoning via Mutable Structured States](https://mlsanity.com/paper/2602.10494/) (2026)
- [End-to-End Bangla AI for Solving Math Olympiad Problem Benchmark: Leveraging Large Language Model Using Integrated Approach](https://mlsanity.com/paper/2501.04425/) (2025)
- [From Implicit Exploration to Structured Reasoning: Leveraging Guideline and Refinement for LLMs](https://mlsanity.com/paper/2509.06284/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.