Neuro-Symbolic Data Generation for Math Reasoning
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912147109314560 |
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| author | Li, Zenan Zhou, Zhi Yao, Yuan Li, Yu-Feng Cao, Chun Yang, Fan Zhang, Xian Ma, Xiaoxing |
| author_facet | Li, Zenan Zhou, Zhi Yao, Yuan Li, Yu-Feng Cao, Chun Yang, Fan Zhang, Xian Ma, Xiaoxing |
| contents | A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neuro-Symbolic Data Generation for Math Reasoning Li, Zenan Zhou, Zhi Yao, Yuan Li, Yu-Feng Cao, Chun Yang, Fan Zhang, Xian Ma, Xiaoxing Artificial Intelligence A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts. |
| title | Neuro-Symbolic Data Generation for Math Reasoning |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2412.04857 |