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# A statistical perspective on distillation

*Proceedings of the 38th International Conference on Machine Learning*, PMLR 139:7632-7642, 2021.

#### Abstract

Knowledge distillation is a technique for improving a “student” model by replacing its one-hot training labels with a label distribution obtained from a “teacher” model. Despite its broad success, several basic questions — e.g., Why does distillation help? Why do more accurate teachers not necessarily distill better? — have received limited formal study. In this paper, we present a statistical perspective on distillation which provides an answer to these questions. Our core observation is that a “Bayes teacher” providing the true class-probabilities can lower the variance of the student objective, and thus improve performance. We then establish a bias-variance tradeoff that quantifies the value of teachers that approximate the Bayes class-probabilities. This provides a formal criterion as to what constitutes a “good” teacher, namely, the quality of its probability estimates. Finally, we illustrate how our statistical perspective facilitates novel applications of distillation to bipartite ranking and multiclass retrieval.