Large Language Models (LLMs) have shown excellent performance in language
understanding, text generation, code synthesis, and many other tasks, while
they still struggle in complex multi-step reasoning problems, such as
mathematical reasoning. In this paper, through a newly proposed arithmetical
puzzle problem, we show that the model can perform well on multi-step reasoning
tasks via fine-tuning on high-quality synthetic data. Experimental results with
the open-llama-3B model on three different test datasets show that not only the
model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also
demonstrates certain generalization capabilities on the out-of-domain datasets.
Specifically, this paper has designed two out-of-domain datasets in the form of
extending the numerical range and the composing components of the arithmetical
puzzle problem separately. The fine-tuned models have shown encouraging
performance on these two far more difficult tasks with the zero-shot pass@1 at
0.33 and 0.35, respectively.

通过对高质量合成数据的微调，本文通过提出的算术难题问题展示出大型语言模型在多步推理任务上的出色表现，并通过开源的 3B 模型在三个不同的测试数据集上实验结果表明，这种模型不仅在域内数据集上能够达到 0.44 的零样本一次通过率 @1，而且还在域外数据集上展现出一定的泛化能力，对于扩展数字范围和算术难题问题的组合组件分别设计了两个域外数据集，在这两个更难的任务上，经过微调的模型展示出令人鼓舞的表现，零样本一次通过率 @1 分别为 0.33 和 0.35。