  Chain-of-Thought (CoT) serves as a critical emerging ability in LLMs,
especially when it comes to logical reasoning. Attempts have been made to
induce such ability in small models as well by distilling from the data with
CoT generated by Large Language Models (LLMs). However, existing methods often
simply generate and incorporate more data from LLMs and fail to note the
importance of efficiently utilizing existing CoT data. We here propose a new
training paradigm AS-ES (Abstractive Segments - Extractive Segments) learning,
which exploits the inherent information in CoT for iterative generation.
Experiments show that our methods surpass the direct seq2seq training on
CoT-extensive tasks like MWP and PET summarization, without data augmentation
or altering the model itself. Furthermore, we explore the reason behind the
inefficiency of small models in learning CoT and provide an explanation of why
AS-ES learning works, giving insights into the underlying mechanism of CoT.
