Augmenting Math Word Problems via Iterative Question Composing
This addresses the problem of limited mathematical reasoning capabilities in open-source LLMs for competition-level tasks, representing a strong specific gain.
The paper tackles the challenge of solving competition-level math problems with open-source LLMs by introducing the MMIQC dataset, which includes synthetic question-response pairs, and shows that fine-tuned models achieve a 45.0% accuracy on the MATH benchmark, exceeding the previous open-source SOTA by 8.2%.
Despite the advancements in large language models (LLMs) for mathematical reasoning, solving competition-level math problems remains a significant challenge, especially for open-source LLMs without external tools. We introduce the MMIQC dataset, comprising a mixture of processed web data and synthetic question-response pairs, aimed at enhancing the mathematical reasoning capabilities of base language models. Models fine-tuned on MMIQC consistently surpass their counterparts in performance on the MATH benchmark across various model sizes. Notably, Qwen-72B-MMIQC achieves a 45.0% accuracy, exceeding the previous open-source state-of-the-art by 8.2% and outperforming the initial version GPT-4 released in 2023. Extensive evaluation results on Hungarian high school finals suggest that such improvement can generalize to unseen data. Our ablation study on MMIQC reveals that a large part of the improvement can be attributed to our novel augmentation method, Iterative Question Composing (IQC), which involves iteratively composing new questions from seed problems using an LLM and applying rejection sampling through another LLM.