  Large language models (LLMs) have seen considerable advancements in natural
language understanding tasks, yet there remains a gap to bridge before
attaining true artificial general intelligence, especially concerning
shortcomings in mathematical reasoning capabilities. We postulate that the
inherent nature of LLM training, which focuses on predicting probabilities of
next token, presents challenges in effectively modeling mathematical reasoning
that demands exact calculations, both from data-driven and theoretical
standpoints. In this paper, we address this challenge by enriching the data
landscape and introducing a novel math dataset, enhanced with a capability to
utilize a Python code interpreter. This dataset is derived from GSM8K and MATH
and has been further refined through a combination of GPT-4 annotations, human
review, and self-training processes, where the errors in the original GSM8K
training set have been fixed. Additionally, we propose a tentative, easily
replicable protocol for the fine-tuning of math-specific LLMs, which has led to
a significant improvement in the performance of a 7B-parameter LLM on the GSM8K
and MATH datasets. We are committed to advancing the field of mathematical
reasoning in LLMs and, to that end, we have made source code for data
generation / training / inference, and the model checkpoints publicly available
at \url{https://github.com/MARIO-Math-Reasoning/MARIO}. We hope this will
facilitate further research and development within the community.
