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.

Multi-path voting methods like Self-consistency have been used to mitigate reasoning errors in large language models caused by factual errors and illusion generation. However, these methods require excessive computing resources as they generate numerous reasoning paths for each problem. And our experiments show that on the arithmetic reasoning task, SVAMP, half of the problems fail to obtain noticeable accuracy gains when voting with more than three paths. In this paper, we propose a novel multi-path voting technique called Dynamic Voting, which effectively reduces the number of reasoning paths during multi-path voting while preserving accuracies by applying early exiting for problems that large language models can confidently solve. Experimental evaluations on arithmetic, commonsense, and symbolic reasoning tasks under few-shot and zero-shot settings demonstrate that Dynamic Voting achieves comparable accuracies employing significantly fewer reasoning paths. Notably, one of our Dynamic Voting strategies outperforms Self-consistency using only 24.7% of the number of paths on the LetterConcat task in the few-shot setting. Furthermore, Dynamic Voting showcases strong robustness in threshold selection. It also demonstrates excellent generalizability when combined with other voting techniques, different models, and diverse prompts.

Unsupervised paraphrase generation is a challenging task that benefits a variety of downstream NLP applications. Current unsupervised methods for paraphrase generation typically employ round-trip translation or denoising, which require translation corpus and result in paraphrases overly similar to the original sentences in surface structure. Most of these methods lack explicit control over the similarity between the original and generated sentences, and the entities are also less correctly kept. To obviate the reliance on translation data and prompt greater variations in surface structure, we propose a self-supervised pseudo-data construction method that generates diverse pseudo-paraphrases in distinct surface structures for a given sentence. To control the similarity and generate accurate entities, we propose an unsupervised paraphrasing model that encodes the sentence meaning and the entities with discrete and continuous variables, respectively. The similarity can be controlled by sampling discrete variables and the entities are kept substantially accurate due to the specific modeling of entities using continuous variables. Experimental results on two benchmark datasets demonstrate the advantages of our pseudo-data construction method compared to round-trip translation, and the superiority of our paraphrasing model over the state-of-the-art unsupervised methods.