There is a growing concern about applying batch normalization (BN) in
adversarial training (AT), especially when the model is trained on both
adversarial samples and clean samples (termed Hybrid-AT). With the assumption
that adversarial and clean samples are from two different domains, a common
practice in prior works is to adopt Dual BN, where BN and BN are used for
adversarial and clean branches, respectively. A popular belief for motivating
Dual BN is that estimating normalization statistics of this mixture
distribution is challenging and thus disentangling it for normalization
achieves stronger robustness. In contrast to this belief, we reveal that
disentangling statistics plays a less role than disentangling affine parameters
in model training. This finding aligns with prior work (Rebuffi et al., 2023),
and we build upon their research for further investigations. We demonstrate
that the domain gap between adversarial and clean samples is not very large,
which is counter-intuitive considering the significant influence of adversarial
perturbation on the model accuracy. We further propose a two-task hypothesis
which serves as the empirical foundation and a unified framework for Hybrid-AT
improvement. We also investigate Dual BN in test-time and reveal that affine
parameters characterize the robustness during inference. Overall, our work
sheds new light on understanding the mechanism of Dual BN in Hybrid-AT and its
underlying justification.

在对抗训练中应用批归一化（BN）时存在越来越多的关注，尤其是当模型在对抗样本和干净样本上进行训练时（即混合式对抗训练）；本研究揭示了统计数据的分离对模型训练起到的作用较小，而分离仿射参数则起到了更大的作用；通过研究表明对抗样本与干净样本之间的领域差距较小，这与对抗扰动对模型准确性的显著影响不一致；我们进一步提出了一个双任务假设，作为混合式对抗训练改进的经验证据和统一框架；同时，我们还探讨了测试时的对偶 BN 并揭示仿射参数在推理过程中刻画了模型的鲁棒性，从而为我们理解混合式对抗训练中对偶 BN 的机制及其潜在的理论基础提供了新的视角。