Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models

TL;DR

This paper challenges the traditional view of RKL and FKL divergences in LLM knowledge distillation, showing they share objectives and proposing an adaptive method that improves model performance and response diversity.

Contribution

It provides a theoretical and empirical analysis of RKL and FKL in LLM KD, revealing their similarities and differences, and introduces an adaptive divergence method that enhances distillation outcomes.

Findings

RKL and FKL share the same optimization objective after sufficient training.

RKL emphasizes distribution tails, FKL emphasizes the head initially.

Adaptive Kullback-Leibler (AKL) improves task performance and response diversity.

Abstract

Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that neither mode-seeking nor mean-seeking properties manifest in KD for LLMs. Instead, RKL and FKL are found to share the same optimization objective and both converge after a sufficient number of epochs. However, due to practical constraints, LLMs are seldom trained for such an extensive number of epochs. Meanwhile, we further find that RKL focuses on the tail part of the distributions, while FKL focuses on the head part at the beginning epochs. Consequently, we propose a simple yet effective Adaptive Kullback-Leiber (AKL) divergence method, which adaptively allocates weights to combine FKL and RKL. Metric-based and GPT-4-based evaluations demonstrate that the proposed AKL outperforms the baselines across various tasks and improves the diversity and quality of generated responses. Codes are available at \href{https://github.com/wutaiqiang/LLM_KD_AKL}{github}.