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

TL;DR

BEATS is a novel method that enhances LLMs' mathematical problem-solving by guiding iterative reasoning, verifying answers with back-verification, and optimizing search with pruning trees, significantly outperforming previous models on benchmarks.

Contribution

The paper introduces BEATS, combining iterative prompting, back-verification, and efficient tree search to substantially improve LLMs' mathematical reasoning capabilities.

Findings

Qwen2-7b-Instruct's score increased from 36.94 to 61.52

Outperforms GPT-4's score of 42.5 on the MATH benchmark

Demonstrates effective use of back-verification and pruning in LLM reasoning

Abstract

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.