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arXiv · 2203.14649

Knowledge Distillation: Bad Models Can Be Good Role Models

Gal Kaplun·Eran Malach·Preetum Nakkiran·Shai Shalev-Shwartz
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Abstract

Large neural networks trained in the overparameterized regime are able to fit noise to zero train error. Recent work \citep{nakkiran2020distributional} has empirically observed that such networks behave as "conditional samplers" from the noisy distribution. That is, they replicate the noise in the train data to unseen examples. We give a theoretical framework for studying this conditional sampling behavior in the context of learning theory. We relate the notion of such samplers to knowledge distillation, where a student network imitates the outputs of a teacher on unlabeled data. We show that samplers, while being bad classifiers, can be good teachers. Concretely, we prove that distillation from samplers is guaranteed to produce a student which approximates the Bayes optimal classifier. Finally, we show that some common learning algorithms (e.g., Nearest-Neighbours and Kernel Machines) can generate samplers when applied in the overparameterized regime.

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Gal Kaplun, Eran Malach, Preetum Nakkiran, Shai Shalev-Shwartz. 2022-03-28. Knowledge Distillation: Bad Models Can Be Good Role Models. https://arxiv.org/abs/2203.14649

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