Enhancing Mathematical Reasoning in LLMs by Stepwise Correction

TL;DR

This paper introduces Stepwise Correction (StepCo), a novel prompting method for LLMs that iteratively verifies and revises reasoning steps, significantly improving mathematical problem-solving accuracy and efficiency.

Contribution

The paper presents StepCo, a new prompting approach that enhances LLM reasoning by stepwise correction, outperforming existing methods in accuracy and token efficiency.

Findings

StepCo achieves 94.1% accuracy on eight datasets with GPT-4o.

It outperforms Best-of-N by +2.4 accuracy points.

Token consumption is reduced by 77.8%.

Abstract

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.