  Large language models (LLMs) open up new horizons for sequential
recommendations, owing to their remarkable language comprehension and
generation capabilities. However, there are still numerous challenges that
should be addressed to successfully implement sequential recommendations
empowered by LLMs. Firstly, user behavior patterns are often complex, and
relying solely on one-step reasoning from LLMs may lead to incorrect or
task-irrelevant responses. Secondly, the prohibitively resource requirements of
LLM (e.g., ChatGPT-175B) are overwhelmingly high and impractical for real
sequential recommender systems. In this paper, we propose a novel Step-by-step
knowLedge dIstillation fraMework for recommendation (SLIM), paving a promising
path for sequential recommenders to enjoy the exceptional reasoning
capabilities of LLMs in a "slim" (i.e., resource-efficient) manner. We
introduce CoT prompting based on user behavior sequences for the larger teacher
model. The rationales generated by the teacher model are then utilized as
labels to distill the downstream smaller student model (e.g., LLaMA2-7B). In
this way, the student model acquires the step-by-step reasoning capabilities in
recommendation tasks. We encode the generated rationales from the student model
into a dense vector, which empowers recommendation in both ID-based and
ID-agnostic scenarios. Extensive experiments demonstrate the effectiveness of
SLIM over state-of-the-art baselines, and further analysis showcasing its
ability to generate meaningful recommendation reasoning at affordable costs.
