Rationales for Answers to Simple Math Word Problems Confuse Large Language Models (2024)

Abstract: Recently, large language models (LLMs) have demonstrated breakthrough mathematical problem-solving capabilities in grade school math word problems (MWP). For example, on the MWP benchmark GSM8K, the accuracy of GPT-3.5-Turbo and MetaMath-70B reaches 80.80% and 82.30%, respectively. One question arises, does it mean that LLMs have truly mastered related mathematical problem-solving abilities? In this paper, by presenting two types of benchmarks, where MCGSM8K aims at selecting one correct solution from four solutions, while GSM8K-Judgement judges whether a solution to a given question is true or false, we demonstrate that the ability of most LLMs to evaluate the mathematical reasoning process of MWP is far from sufficient. To compensate for this issue, we propose hybrid supervised fine-tuning data from the training data of GSM8K, MCGSM8K, and GSM8K-Judgement, which significantly improves performance on the proposed reasoning process evaluation benchmarks. For example, fine-tuning improves the performance of LLaMA-2-13B from 33.51% to 70.89% on MCGSM8K. In conclusion, we experimentally demonstrate that most LLMs have limited ability to evaluate the mathematical reasoning process of MWP, which can be enhanced through fine-tuning.

## introduction it is reported that general close-source large language models (llms) have demonstrated promising performance on several mathematical word problems (mwp) benchmarks, e.g., @xcite and @xcite achieving the accuracy of 92.00% and 80.80% on grade school mwp benchmark gsm8k @xcite , respectively. with the development of prompt-based methods @xcite and finetuning-based methods @xcite @xcite , mathematical specialized llms tuned on specific tasks also exhibit competitive performance. for example, metamath-70b @xcite , wizardmath-70b @xcite , and mammoth-70b @xcite achieves 82.30%, 81.60%, and 76.90% on gsm8k, respectively. now, one question arises, does the excellent performance demonstrate that these llms truly master related mathematical problem-solving abilities, such as the ability to evaluate the mathematical reasoning process of mwp? ## mcgsm8k in this section, we describe in detail the process of constructing the benchmark mcgsm8k, which consists of multiple-choice questions with each question from the original test set of gsm8k and each option containing a solution. our primary objective is to guarantee the reliability of mcgsm8k, ensuring that correct options are indeed correct and incorrect options are demonstrably wrong. to achieve this, we derive correct options directly from gsm8k, incorporating both the validated answer and its accompanying rationale, which are manually annotated to ensure accuracy. conversely, incorrect options are generated by llms, comprising wrong answers distinct from the ground-truth answer, each accompanied by a plausible rationale. on the premise that the reliability of the dataset is guaranteed, we further enhance the challenge and difficulty of the dataset. thus, we 1) use multiple advanced open-source llms to generate numerous candidate solutions with wrong answers, 2) maintain the diversity of incorrect option differences based on rouge-l @xcite scores and k-means cluster (wong, 1979), and 3) ensure the confusability of the incorrect options with the correct option based on similarity ranking. ## conclusion in this paper, we focus on exploring the ability of llms to evaluate the mathematical reasoning processes of mwp. to achieve this, we utilize incorrect solutions generated by multiple advanced llms to curate two benchmarks. one is mcgsm8k and its two variants, a new type of multiple-choice question dataset, in which each option contains a solution to solve the problem. the other one is gsm8k-judgement, which judges whether a solution to a given problem is true or false. the poor performance of llms on mcgsm8k confirms the incapable ability of most llms in mathematical reasoning process evaluation. in particular, the performance on gsm8k-judgement exhibits that it is easier to identify incorrect solutions. however, merely fine-tuning with correct solutions improves the performance in evaluating correct solutions, but leads to a huge drop in evaluating incorrect solutions. fine-tuning models on the proposed training data greatly improves the mathematical process evaluation ability. exploring the relation between the ability of mathematical problem-solving and mathematical reasoning process evaluation is left to future work.