Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with
  Code-based Self-Verification
Authors: name: Aojun Zhou, name: Ke Wang, name: Zimu Lu, name: Weikang Shi, name: Sichun Luo, name: Zipeng Qin, name: Shaoqing Lu, name: Anya Jia, name: Linqi Song, name: Mingjie Zhan, name: Hongsheng Li

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has
brought significant advancements in addressing math reasoning problems. In
particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter,
shows remarkable performance on challenging math datasets. In this paper, we
explore the effect of code on enhancing LLMs' reasoning capability by
introducing different constraints on the Code Usage Frequency of GPT-4
Code Interpreter. We found that its success can be largely attributed to its
powerful skills in generating and executing code, evaluating the output of code
execution, and rectifying its solution when receiving unreasonable outputs.
Based on this insight, we propose a novel and effective prompting method,
explicit code-based self-verification~(CSV), to further
boost the mathematical reasoning potential of GPT-4 Code Interpreter. This
method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to
use code to self-verify its answers. In instances where the verification state
registers as ``False'', the model shall automatically amend its solution,
analogous to our approach of rectifying errors during a mathematics
examination. Furthermore, we recognize that the states of the verification
result indicate the confidence of a solution, which can improve the
effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we
achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to
84.3\%).