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arXiv · 2305.13948

Decoupled Kullback-Leibler Divergence Loss

Jiequan Cui·Zhuotao Tian·Zhisheng Zhong·Xiaojuan Qi·Bei Yu·Hanwang Zhang
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Abstract

In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of 1) a weighted Mean Square Error (wMSE) loss and 2) a Cross-Entropy loss incorporating soft labels. Thanks to the decomposed formulation of DKL loss, we have identified two areas for improvement. Firstly, we address the limitation of KL/DKL in scenarios like knowledge distillation by breaking its asymmetric optimization property. This modification ensures that the $\mathbf{w}$MSE component is always effective during training, providing extra constructive cues. Secondly, we introduce class-wise global information into KL/DKL to mitigate bias from individual samples. With these two enhancements, we derive the Improved Kullback-Leibler (IKL) Divergence loss and evaluate its effectiveness by conducting experiments on CIFAR-10/100 and ImageNet datasets, focusing on adversarial training, and knowledge distillation tasks. The proposed approach achieves new state-of-the-art adversarial robustness on the public leaderboard -- RobustBench and competitive performance on knowledge distillation, demonstrating the substantial practical merits. Our code is available at https://github.com/jiequancui/DKL.

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Jiequan Cui, Zhuotao Tian, Zhisheng Zhong, Xiaojuan Qi, Bei Yu, Hanwang Zhang. 2024-10-27. Decoupled Kullback-Leibler Divergence Loss. https://arxiv.org/abs/2305.13948

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