  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 Kullback-Leibler (RKL),
and Jensen-Shannon (JS) divergences. However, due to limitations inherent in
their assumptions and definitions, these measures fail to deliver effective
supervision when few distribution overlap exists between the teacher and the
student. In this paper, 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 NLP
tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the
Sinkhorn distance to ensure a nuanced and precise assessment of the disparity
between teacher and student distributions. Besides, profit by properties of the
Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception
of divergence in each teacher-student sample pair. Instead, we propose a
batch-wise reformulation to capture geometric intricacies of distributions
across samples in the high-dimensional space. Comprehensive evaluation on GLUE
and SuperGLUE, in terms of comparability, validity, and generalizability,
highlights our superiority over state-of-the-art methods on all kinds of LLMs
with encoder-only, encoder-decoder, and decoder-only architectures.
