  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.
