  Knowledge distillation transfers the knowledge from a cumbersome teacher to a
small student. Recent results suggest that the student-friendly teacher is more
appropriate to distill since it provides more transferable knowledge. In this
work, we propose the novel framework, "prune, then distill," that prunes the
model first to make it more transferrable and then distill it to the student.
We provide several exploratory examples where the pruned teacher teaches better
than the original unpruned networks. We further show theoretically that the
pruned teacher plays the role of regularizer in distillation, which reduces the
generalization error. Based on this result, we propose a novel neural network
compression scheme where the student network is formed based on the pruned
teacher and then apply the "prune, then distill" strategy. The code is
available at https://github.com/ososos888/prune-then-distill
