SinKD: Sinkhorn Distance Minimization for Knowledge Distillation

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.