Knowledge Distillation: Bad Models Can Be Good Role Models
This provides a theoretical foundation for using noisy models in distillation, which could improve efficiency in machine learning by leveraging bad models for training better ones.
The paper tackles the problem of overparameterized neural networks fitting noise and behaving as conditional samplers, showing that such models, despite being poor classifiers, can serve as effective teachers in knowledge distillation to approximate the Bayes optimal classifier.
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.