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        <title>Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks</title>
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    <abstract>The ability (and inability) of large language models (LLMs) to perform arithmetic tasks has been the subject of much theoretical and practical debate. We show that LLMs are frequently able to correctly and confidently predict the first digit of n-digit by m-digit multiplication tasks without using chain of thought reasoning, despite these tasks require compounding operations to solve. Simultaneously, LLMs in practice often fail to correctly or confidently predict the last digit of an n-digit by m-digit multiplication, a task equivalent to 1-digit by 1-digit multiplication which can be easily learned or memorized. We show that the latter task can be solved more robustly when the LLM is conditioned on all of the correct higher-order digits, which on average increases the confidence of the correct last digit on 5-digit by 5-digit multiplication tasks using Llama 2-13B by over 230% (0.13→0.43) and Mistral-7B by 150% (0.22→0.55).</abstract>
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        <date>2024-08</date>
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            <start>85</start>
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%0 Conference Proceedings
%T Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks
%A Gambardella, Andrew
%A Iwasawa, Yusuke
%A Matsuo, Yutaka
%Y Ku, Lun-Wei
%Y Martins, Andre
%Y Srikumar, Vivek
%S Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)
%D 2024
%8 August
%I Association for Computational Linguistics
%C Bangkok, Thailand
%F gambardella-etal-2024-language
%X The ability (and inability) of large language models (LLMs) to perform arithmetic tasks has been the subject of much theoretical and practical debate. We show that LLMs are frequently able to correctly and confidently predict the first digit of n-digit by m-digit multiplication tasks without using chain of thought reasoning, despite these tasks require compounding operations to solve. Simultaneously, LLMs in practice often fail to correctly or confidently predict the last digit of an n-digit by m-digit multiplication, a task equivalent to 1-digit by 1-digit multiplication which can be easily learned or memorized. We show that the latter task can be solved more robustly when the LLM is conditioned on all of the correct higher-order digits, which on average increases the confidence of the correct last digit on 5-digit by 5-digit multiplication tasks using Llama 2-13B by over 230% (0.13→0.43) and Mistral-7B by 150% (0.22→0.55).
%R 10.18653/v1/2024.acl-short.8
%U https://aclanthology.org/2024.luhme-short.8/
%U https://doi.org/10.18653/v1/2024.acl-short.8
%P 85-91

Markdown (Informal)

[Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks](https://aclanthology.org/2024.luhme-short.8/) (Gambardella et al., ACL 2024)

• Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks (Gambardella et al., ACL 2024)

ACL

• Andrew Gambardella, Yusuke Iwasawa, and Yutaka Matsuo. 2024. Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 85–91, Bangkok, Thailand. Association for Computational Linguistics.