What Happened in LLMs Layers when Trained for Fast vs. Slow Thinking: A
  Gradient Perspective
Authors: name: Ming Li, name: Yanhong Li, name: Tianyi Zhou

What makes a difference in the post-training of LLMs? We investigate the
training patterns of different layers in large language models (LLMs), through
the lens of gradient, when training with different responses and initial
models. We are specifically interested in how fast vs. slow thinking affects
the layer-wise gradients, given the recent popularity of training LLMs on
reasoning paths such as chain-of-thoughts (CoT) and process rewards. In our
study, fast thinking without CoT leads to larger gradients and larger
differences of gradients across layers than slow thinking (Detailed CoT),
indicating the learning stability brought by the latter. Moreover, pre-trained
LLMs are less affected by the instability of fast thinking than
instruction-tuned LLMs. Additionally, we study whether the gradient patterns
can reflect the correctness of responses when training different LLMs using
slow vs. fast thinking paths. The results show that the gradients of slow
thinking can distinguish correct and irrelevant reasoning paths. As a
comparison, we conduct similar gradient analyses on non-reasoning knowledge
learning tasks, on which, however, trivially increasing the response length
does not lead to similar behaviors of slow thinking. Our study strengthens
fundamental understandings of LLM training and sheds novel insights on its
efficiency and stability, which pave the way towards building a generalizable
System-2 agent. Our code, data, and gradient statistics can be found in:
https://github.com/MingLiiii/Layer_Gradient.