Recent works have shown the benefits to LLMs from fine-tuning golden-standard
Chain-of-Thought (CoT) rationales or using them as correct examples in few-shot
prompting. While humans can indeed imitate correct examples, learning from our
mistakes is another vital aspect of human cognition. Hence, a question
naturally arises: \textit{can LLMs learn and benefit from their mistakes,
especially for their reasoning? } This study investigates this problem from
both the prompting and model-tuning perspectives. We begin by introducing
\textsc{CoTErrorSet}, a new benchmark with 609,432 questions, each designed
with both correct and error references, and demonstrating the types and reasons
for making such mistakes. To explore the effectiveness of those mistakes, we
design two methods: (1) \textbf{Self-rethinking} prompting guides LLMs to
rethink whether they have made similar previous mistakes; and (2)
\textbf{Mistake tuning} involves finetuning models in both correct and
incorrect reasoning domains, rather than only tuning models to learn ground
truth in traditional methodology. We conduct a series of experiments to prove
LLMs can obtain benefits from mistakes in both directions. Our two methods
offer potentially cost-effective strategies by leveraging errors to enhance
reasoning capabilities, which costs significantly less than creating
meticulously hand-crafted golden references. We ultimately make a thorough
analysis of the reasons behind LLMs' errors, which provides directions that
future research needs to overcome. \textsc{CoTErrorSet} will be published soon
on \texttt{Anonymity Link}.

这项研究从提示和模型调整的角度探究 LLMs 是否能够从错误中学习和受益，特别是在推理方面，通过引入 CoTErrorSet 基准测试，设计了自我反思提示和错误调整两种方法，证明 LLMs 能够从错误中受益，进而增强其推理能力，并对 LLMs 错误原因进行了深入分析。