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

TL;DR

This paper investigates the bias-variance tradeoff in knowledge distillation with soft labels, revealing sample-wise variations and proposing weighted soft labels to improve distillation performance.

Contribution

It introduces a novel perspective on bias-variance tradeoff in soft label distillation and proposes weighted soft labels for adaptive handling of sample-wise bias-variance dynamics.

Findings

Bias-variance tradeoff varies sample-wisely during training.

Distillation performance negatively correlates with the number of certain samples.

Weighted soft labels improve distillation effectiveness.

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 \citep{muller2019does,yuan2020revisiting} 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 at \url{https://github.com/bellymonster/Weighted-Soft-Label-Distillation}.