This study investigates the gradient patterns of different layers in large language models (LLMs) during instruction tuning. The researchers compare the gradients of LLMs trained using "fast thinking" (without chain-of-thought reasoning) versus "slow thinking" (with detailed chain-of-thought reasoning). The study examines how these training methods affect gradient stability, response correctness, and the ability to distinguish between correct and irrelevant responses. They further analyze the impact of different initial models (pre-trained vs. instruction-tuned) on gradient behavior. The results show that "slow thinking" leads to more stable and efficient training, while "fast thinking" results in larger gradients and greater fluctuation across layers. The researchers also find that "slow thinking" helps distinguish correct responses from irrelevant responses, but this ability is not as pronounced in "fast thinking" training. Finally, the study explores the effects of response length and popularity on gradient patterns in knowledge-learning tasks, demonstrating that increasing response length alone does not necessarily mimic the effects of "slow thinking."