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 to 0.43) and
Mistral-7B by 150% (0.22 to 0.55).

大型语言模型在进行算术任务中对多位数乘法的可信准确预测能力较强，而对单位数乘法可信准确预测的能力较差，但在给出正确的高位数字作为条件下，后者任务的可信准确预测能力可以大幅提升。