Rethinking Soft Labels for Knowledge Distillation: A Bias-Variance Tradeoff Perspective (2102.00650v1)

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}.

• The paper examines the bias-variance tradeoff in KD by analyzing how soft labels act as regularizers at a sample-specific level.
• It identifies regularization samples that reduce variance but may introduce bias, thereby affecting distillation efficacy.
• The paper proposes weighted soft labels that adaptively assign sample weights, achieving superior performance on benchmarks like CIFAR-100 and ImageNet.

Analysis of Soft Labels in Knowledge Distillation: A Bias-Variance Perspective

The paper "Rethinking Soft Labels for Knowledge Distillation: A Bias-Variance Tradeoff Perspective" by Zhou et al. critically examines the mechanics of knowledge distillation (KD) by focusing on the implications of using soft labels, an aspect previously highlighted for its regularization properties. Despite empirical and theoretical support for the efficacy of soft labels in KD, this paper questions how exactly these labels balance bias and variance during the training of neural networks.

Core Contributions

1. Bias-Variance Tradeoff in KD: The authors delve into the traditional bias-variance tradeoff, analyzing it through the lens of neural networks trained with soft labels. They argue that while the intrinsic school of thought suggests soft labels primarily act as regularizers, their impact must be carefully balanced across samples to achieve optimal distillation performance. The paper emphasizes a crucial observation: during training, this tradeoff isn't static but varies at the sample level.
2. Regularization Samples Identification: A significant contribution of this paper is the identification of regularization samples - those that primarily contribute to reducing variance at the expense of introducing bias. Zhou et al. provide experimental data showing that an abundance of such samples, particularly when sourced from label-smoothed teachers, correlates with reduced distillation efficacy. This underpins their hypothesis that simply filtering or naively handling these samples might not always yield improvements, due to their partial value in informing distillation.
3. Proposed Weighted Soft Labels: In response to findings regarding the aforementioned sample-specific tradeoffs, the authors introduce "weighted soft labels". This approach involves adaptively assigning weights to samples based on their bias-variance characteristics, with the aim of ameliorating the negative effects of excess regularization while capitalizing on the informative value of soft labels. The paper validates this approach through rigorous experimentation, showcasing improved performance benchmarks on datasets like CIFAR-100 and ImageNet.

Numerical Results and Implications

Through extensive experiments, Zhou et al. demonstrate the improved accuracy of models trained with weighted soft labels compared to those using standard KD approaches. Notably, their approach surpasses existing state-of-the-art methods in both homogeneous architecture distillation as well as heterogeneous scenarios.

Theoretical and Practical Implications

The insights provided in this research offer a new dimension to the understanding of knowledge distillation, extending beyond conventional perspectives of KD as merely a tool for model compression or acceleration. By framing soft labels within the bias-variance paradigm, Zhou et al. enhance our theoretical understanding of how distillation shapes learning dynamics. Practically, the proposed methodology facilitates more nuanced training protocols that can yield better-performing, well-calibrated models, essential for real-world applications where model robustness and interpretability are paramount.

Future Directions

Looking ahead, the work prompts new avenues for exploring bias-variance interplay in KD across various model architectures and dataset complexities. It raises questions about the potential for leveraging such tradeoffs at different abstraction levels within neural networks or even across multimodal frameworks. Further research could involve extending these principles to other domains like reinforcement learning or unsupervised learning, where KD is also gaining traction.

In summary, this paper presents a thorough examination of the role of soft labels within the knowledge distillation process, recontextualizing their impact through the bias-variance tradeoff. This approach not only enriches the theoretical underpinnings of KD but also introduces practical improvements that underscore the value of balancing sample-relative tradeoffs in training deep learning models.