  Knowledge distillation has become one of the most important model compression
techniques by distilling knowledge from larger teacher networks to smaller
student ones. Although great success has been achieved by prior distillation
methods via delicately designing various types of knowledge, they overlook the
functional properties of neural networks, which makes the process of applying
those techniques to new tasks unreliable and non-trivial. To alleviate such
problem, in this paper, we initially leverage Lipschitz continuity to better
represent the functional characteristic of neural networks and guide the
knowledge distillation process. In particular, we propose a novel Lipschitz
Continuity Guided Knowledge Distillation framework to faithfully distill
knowledge by minimizing the distance between two neural networks' Lipschitz
constants, which enables teacher networks to better regularize student networks
and improve the corresponding performance. We derive an explainable
approximation algorithm with an explicit theoretical derivation to address the
NP-hard problem of calculating the Lipschitz constant. Experimental results
have shown that our method outperforms other benchmarks over several knowledge
distillation tasks (e.g., classification, segmentation and object detection) on
CIFAR-100, ImageNet, and PASCAL VOC datasets.
