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arXiv 2002.05715cs.LGstat.ML

Self-Distillation Amplifies Regularization in Hilbert Space

DeepMind;Google Research(谷歌研究);EECS Dept., University of California at Berkeley(加州大学伯克利分校电气工程与计算机科学系);University of California at Berkeley(加州大学伯克利分校);Google(谷歌)

Hossein Mobahi, Mehrdad Farajtabar, Peter L. Bartlett

英文摘要:

Knowledge distillation introduced in the deep learning context is a method to transfer knowledge from one architecture to another. In particular, when the architectures are identical, this is called self-distillation. The idea is to feed in predictions of the trained model as new target values for retraining (and iterate this loop possibly a few times). It has been empirically observed that the self-distilled model often achieves higher accuracy on held out data. Why this happens, however, has been a mystery: the self-distillation dynamics does not receive any new information about the task and solely evolves by looping over training. To the best of our knowledge, there is no rigorous understanding of this phenomenon. This work provides the first theoretical analysis of self-distillation. We focus on fitting a nonlinear function to training data, where the model space is Hilbert space and fitting is subject to $\ell_2$ regularization in this function space. We show that self-distillation iterations modify regularization by progressively limiting the number of basis functions that can be used to represent the solution. This implies (as we also verify empirically) that while a few rounds of self-distillation may reduce over-fitting, further rounds may lead to under-fitting and thus worse performance.

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