Logo PRP

Get an A in Math: Progressive Rectification Prompting

Zhenyu Wu1, Meng Jiang2, Chao Shen†,1

1Xi'an Jiaotong University, 2University of Notre Dame

†Corresponding to: chaoshen@xjtu.edu.cn
arXiv Code Twitter Examples
geometric reasoning

Overview of Progressive Rectification Prompting (PRP) method. PRP first generates an initial answer. PRP then iterates a verify-then-rectify process to progressively rectify the LLM-generated answer to find the correct one.

Introduction

We propose a novel method named Progressive Rectification Prompting (PRP) to improve average accuracy on eight MWP datasets from 77.3 to 90.5. Given an initial answer from CoT, PRP iterates a verify-then-rectify process to progressively identify incorrect answers and rectify the reasoning paths. With the most likely correct answer, the LLM predicts a masked numerical value in the question; if the prediction does not match the masked value, the answer is likely incorrect. Then the LLM is prompted to re-generate the reasoning path hinted with a set of incorrect answers to prevent itself from repeating previous mistakes. PRP achieves the best performance compared against the CoT methods.

Experiment Results

Comparison with Baseline Methods

We conduct comprehensive experiments on eight math word problem datasets, including AddSub, SingleOp, MultiArith, SingleEq, SVAMP, GSM8K, GSM-IC2-1K, and GSM-ICM-1K. We compare our method with six baseline methods: Direct, Zero-Shot-CoT, Plan-and-Solve (PS), Manual-CoT, Auto-CoT, and Progressive-Hint Prompting (PHP-CoT). The Direct baseline concatenates a question with the prompt ''The answer is'' as the LLM input. We use text-davinci-003 as the backend large language model, which is one of the most widely-used LLMs with public APIs. The few-shot baselines, including Manual-CoT, Auto-CoT, and PHP-CoT employ demonstration examples as suggested in the original papers. Regarding the evaluation metric, we use accuracy to evaluate the performance of MWP solving.

Method (text-davinci-003) AddSub MultiArith SVAMP GSM8K SingleEq SingleOp GSM-IC2-1K GSM-ICM-1K Average
Direct 89.3 25.8 65.2 15.0 84.6 92.1 22.8 9.0 50.5
Zero-Shot-CoT 84.8 87.0 74.3 60.8 89.5 89.1 70.7 62.5 77.3
PS 88.1 87.2 72.0 58.2 89.2 89.5 70.9 63.5 77.3
PRP (Ours) 94.7 96.3 86.2 73.6 96.5 96.1 93.1 87.1 90.5
Manual-CoT 87.8 91.5 76.7 56.9 91.3 93.7 73.9 60.6 79.1
Auto-CoT 90.6 95.1 77.8 58.9 90.9 94.4 74.3 65.2 80.9
PHP-CoT 91.1 94.0 81.3 57.5 93.5 94.5 75.3 60.9 81.0

Accuracy comparison on eight MWP datasets. The best and second best results are boldfaced and underlined, respectively. All indicators are presented in percentages.

Break-down Analysis of PRP

As the number of iterations increases, the accuracy improves across all eight MWP datasets. In this paper, we set the maximum iteration number to 5. Note that the bigger maximum iteration number may lead to better performance, but here we set it to 5 to achieve a trade-off between efficiency and effectiveness.

For datasets such as SingleOp, MultiArith, and SingleEq, the average number of iterations is less than 2.5. This is because the problem statements in these datasets are shorter and contain no irrelevant context. As a result, the PRP method can quickly obtain the final answer within a few iterations. In contrast, the PRP method requires more iterations on the SVAMP, GSM8K, GSM-IC2-1K and GSM-ICM-1K datasets. This can be attributed to longer problem statements and more irrelevant context in the problems.

geometric reasoning

Break-down analysis of PRP. (a) Accuracy of PRP method on different datasets with different number of iterations. (b) The average number of iterations for PRP method across different datasets.

Examples

BibTeX


      @inproceedings{wu2024prp,
        title={Get an A in Math: Progressive Rectification Prompting},
        author={Wu, Zhenyu and Jiang, Meng and Shen, Chao},
        booktitle={The Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI 2024)},
        year={2024}
      }