How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs Article Swipe

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Guhao Feng , Kai Yang , Y. Gu , Xinyue Ai , Shengjie Luo , Jian Sun , David He , Zhenguo Li , Lijia Wang ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2410.13857

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.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2410.13857
PDF: https://arxiv.org/pdf/2410.13857
OA Status: green
Cited By: 2
Related Works: 10
OpenAlex ID: https://openalex.org/W4403580251

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DOI: https://doi.org/10.48550/arxiv.2410.13857

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Title: How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-10-17

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Authors: Guhao Feng, Kai Yang, Y. Gu, Xinyue Ai, Shengjie Luo, Jian Sun, David He, Zhenguo Li, Lijia Wang

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Landing page: https://arxiv.org/abs/2410.13857

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PDF URL: https://arxiv.org/pdf/2410.13857

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Concepts: Computer science, Management science, Economics

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Cited by: 2

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Citations by year (recent): 2025: 1, 2024: 1

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Related works (count): 10

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