  In this paper we revisit the efficacy of knowledge distillation as a function
matching and metric learning problem. In doing so we verify three important
design decisions, namely the normalisation, soft maximum function, and
projection layers as key ingredients. We theoretically show that the projector
implicitly encodes information on past examples, enabling relational gradients
for the student. We then show that the normalisation of representations is
tightly coupled with the training dynamics of this projector, which can have a
large impact on the students performance. Finally, we show that a simple soft
maximum function can be used to address any significant capacity gap problems.
Experimental results on various benchmark datasets demonstrate that using these
insights can lead to superior or comparable performance to state-of-the-art
knowledge distillation techniques, despite being much more computationally
efficient. In particular, we obtain these results across image classification
(CIFAR100 and ImageNet), object detection (COCO2017), and on more difficult
distillation objectives, such as training data efficient transformers, whereby
we attain a 77.2% top-1 accuracy with DeiT-Ti on ImageNet. Code and models are
publicly available.
