Self-Distillation Amplifies Regularization in Hilbert Space

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 why this happens. 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 L2 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.

Comments

There's unfortunately not much to read here yet...

Discover the Best of Machine Learning.

Ever having issues keeping up with everything that's going on in Machine Learning? That's where we help. We're sending out a weekly digest, highlighting the Best of Machine Learning.

Join over 900 Machine Learning Engineers receiving our weekly digest.

Best of Machine LearningBest of Machine Learning

Discover the best guides, books, papers and news in Machine Learning, once per week.

Twitter