Small-scale models offer various computational advantages, and yet to which extent size is critical for problem-solving abilities remains an open question. Specifically for solving grade school math, the smallest model size so far required to break the 80\% barrier on the GSM8K benchmark remains to be 34B. Our work studies how high-quality datasets may be the key for small language models to acquire mathematical reasoning. We introduce \texttt{TinyGSM}, a synthetic dataset of 12.3M grade school math problems paired with Python solutions, generated fully by GPT-3.5. After finetuning on \texttt{TinyGSM}, we find that a duo of a 1.3B generation model and a 1.3B verifier model can achieve 81.5\% accuracy, outperforming existing models that are orders of magnitude larger. This also rivals the performance of the GPT-3.5 ``teacher'' model (77.4\%), from which our model's training data is generated. Our approach is simple and has two key components: 1) the high-quality dataset \texttt{TinyGSM}, 2) the use of a verifier, which selects the final outputs from multiple candidate generations.

通过使用小规模模型并结合高质量的数据集，我们的研究探索了如何提升小型语言模型在解决小学数学问题时的数学推理能力，并通过引入 TinyGSM 数据集和验证器的方法，实现了在 GSM8K 基准测试中超过 80% 的准确率，同时在模型规模上远远超过现有模型。

TinyGSM: 使用小型语言模型在GSM8k上达到80%以上