Arrows of Math Reasoning Data Synthesis for Large Language Models: Diversity, Complexity and Correctness
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915463668170752 |
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| author | Chen, Sirui Tian, Changxin Hu, Binbin Chen, Kunlong Liu, Ziqi Zhang, Zhiqiang Zhou, Jun |
| author_facet | Chen, Sirui Tian, Changxin Hu, Binbin Chen, Kunlong Liu, Ziqi Zhang, Zhiqiang Zhou, Jun |
| contents | Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose a novel program-assisted synthesis framework that systematically generates a high-quality mathematical corpus with guaranteed diversity, complexity, and correctness. This framework integrates mathematical knowledge systems and domain-specific tools to create executable programs. These programs are then translated into natural language problem-solution pairs and vetted by a bilateral validation mechanism that verifies solution correctness against program outputs and ensures program-problem consistency. We have generated 12.3 million such problem-solving triples. Experiments demonstrate that models fine-tuned on our data significantly improve their inference capabilities, achieving state-of-the-art performance on several benchmark datasets and showcasing the effectiveness of our synthesis approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arrows of Math Reasoning Data Synthesis for Large Language Models: Diversity, Complexity and Correctness Chen, Sirui Tian, Changxin Hu, Binbin Chen, Kunlong Liu, Ziqi Zhang, Zhiqiang Zhou, Jun Computation and Language Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose a novel program-assisted synthesis framework that systematically generates a high-quality mathematical corpus with guaranteed diversity, complexity, and correctness. This framework integrates mathematical knowledge systems and domain-specific tools to create executable programs. These programs are then translated into natural language problem-solution pairs and vetted by a bilateral validation mechanism that verifies solution correctness against program outputs and ensures program-problem consistency. We have generated 12.3 million such problem-solving triples. Experiments demonstrate that models fine-tuned on our data significantly improve their inference capabilities, achieving state-of-the-art performance on several benchmark datasets and showcasing the effectiveness of our synthesis approach. |
| title | Arrows of Math Reasoning Data Synthesis for Large Language Models: Diversity, Complexity and Correctness |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2508.18824 |