How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918067054837760 |
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| author | Feng, Guhao Yang, Kai Gu, Yuntian Ai, Xinyue Luo, Shengjie Sun, Jiacheng He, Di Li, Zhenguo Wang, Liwei |
| author_facet | Feng, Guhao Yang, Kai Gu, Yuntian Ai, Xinyue Luo, Shengjie Sun, Jiacheng He, Di Li, Zhenguo Wang, Liwei |
| contents | Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous theoretical analysis of LLMs' mathematical abilities, with a specific focus on their arithmetic performances. We identify numerical precision as a key factor that influences their effectiveness in arithmetical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication, unless the model size grows super-polynomially with respect to the input length. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes. We further support our theoretical findings through empirical experiments that explore the impact of varying numerical precision on arithmetic tasks, providing valuable insights for improving the mathematical reasoning capabilities of LLMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs Feng, Guhao Yang, Kai Gu, Yuntian Ai, Xinyue Luo, Shengjie Sun, Jiacheng He, Di Li, Zhenguo Wang, Liwei Machine Learning Artificial Intelligence Computation and Language Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous theoretical analysis of LLMs' mathematical abilities, with a specific focus on their arithmetic performances. We identify numerical precision as a key factor that influences their effectiveness in arithmetical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication, unless the model size grows super-polynomially with respect to the input length. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes. We further support our theoretical findings through empirical experiments that explore the impact of varying numerical precision on arithmetic tasks, providing valuable insights for improving the mathematical reasoning capabilities of LLMs. |
| title | How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2410.13857 |