  Knowledge distillation is a technique for improving the performance of a
simple "student" model by replacing its one-hot training labels with a
distribution over labels obtained from a complex "teacher" model. While this
simple approach has proven widely effective, a basic question remains
unresolved: why does distillation help? In this paper, we present a statistical
perspective on distillation which addresses this question, and provides a novel
connection to extreme multiclass retrieval techniques. Our core observation is
that the teacher seeks to estimate the underlying (Bayes) class-probability
function. Building on this, we establish a fundamental bias-variance tradeoff
in the student's objective: this quantifies how approximate knowledge of these
class-probabilities can significantly aid learning. Finally, we show how
distillation complements existing negative mining techniques for extreme
multiclass retrieval, and propose a unified objective which combines these
ideas.
