SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models
This addresses the challenge of enhancing generalization in LLMs for mathematical problem-solving, moving beyond narrow datasets to leverage diverse expert-written resources.
The paper tackles the problem of improving large language models' code-assisted mathematical reasoning by proposing a novel paradigm that uses a code-based critic model for data construction and quality control, achieving gains of up to +5.7% on in-domain and +4.4% on out-of-domain benchmarks.
There is a growing trend of teaching large language models (LLMs) to solve mathematical problems through coding. Existing studies primarily focus on prompting powerful, closed-source models to generate seed training data followed by in-domain data augmentation, equipping LLMs with considerable capabilities for code-aided mathematical reasoning. However, continually training these models on augmented data derived from a few datasets such as GSM8K may impair their generalization abilities and restrict their effectiveness to a narrow range of question types. Conversely, the potential of improving such LLMs by leveraging large-scale, expert-written, diverse math question-answer pairs remains unexplored. To utilize these resources and tackle unique challenges such as code response assessment, we propose a novel paradigm that uses a code-based critic model to guide steps including question-code data construction, quality control, and complementary evaluation. We also explore different alignment algorithms with self-generated instruction/preference data to foster continuous improvement. Experiments across both in-domain (up to +5.7%) and out-of-domain (+4.4%) benchmarks in English and Chinese demonstrate the effectiveness of the proposed paradigm.