Rethinking Soft Labels for Knowledge Distillation: A Bias–Variance Tradeoff Perspective

Helong Zhou, Liangchen Song, Jiajie Chen, Ye Zhou, Guoli Wang, Junsong Yuan, Qian Zhang

Keywords: Knowledge distillation, soft labels, teacher-student model

Abstract: Knowledge distillation is an effective approach to leverage a well-trained network or an ensemble of them, named as the teacher, to guide the training of a student network. The outputs from the teacher network are used as soft labels for supervising the training of a new network. Recent studies (M ̈uller et al., 2019; Yuan et al., 2020) revealed an intriguing property of the soft labels that making labels soft serves as a good regularization to the student network. From the perspective of statistical learning, regularization aims to reduce the variance, however how bias and variance change is not clear for training with soft labels. In this paper, we investigate the bias-variance tradeoff brought by distillation with soft labels. Specifically, we observe that during training the bias-variance tradeoff varies sample-wisely. Further, under the same distillation temperature setting, we observe that the distillation performance is negatively associated with the number of some specific samples, which are named as regularization samples since these samples lead to bias increasing and variance decreasing. Nevertheless, we empirically find that completely filtering out regularization samples also deteriorates distillation performance. Our discoveries inspired us to propose the novel weighted soft labels to help the network adaptively handle the sample-wise bias-variance tradeoff. Experiments on standard evaluation benchmarks validate the effectiveness of our method. Our code is available in the supplementary.

One-sentence Summary: For knowledge distillation, we analyze the regularization effect introduced by soft labels from a bias-variance perspective and propose weighted soft labels to handle the tradeoff.

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Data: [CIFAR-100](https://paperswithcode.com/dataset/cifar-100), [ImageNet](https://paperswithcode.com/dataset/imagenet)