SinKD: Sinkhorn Distance Minimization for Knowledge Distillation
Xiao Cui, Yulei Qin, Yuting Gao, Enwei Zhang, Zihan Xu, Tong Wu, Ke Li, Xing Sun, Wengang Zhou, Houqiang Li
Abstract
Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse KL (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when a distribution overlap exists between the teacher and the student. In this article, we show that the aforementioned KL, RKL, and JS divergences, respectively, suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse natural language processing (NLP) tasks. We propose the Sinkhorn KD (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between distributions of teacher and student models. Besides, thanks to the properties of the Sinkhorn metric, we get rid of sample-wise KD that restricts the perception of divergences inside each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture the geometric intricacies of distributions across samples in the high-dimensional space. A comprehensive evaluation of GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art (SOTA) methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures. Codes and models are available at https://github.com/2018cx/SinKD.