Deep neural networks (DNNs) are notoriously vulnerable to adversarial attacks that place carefully crafted perturbations on normal examples to fool DNNs. To better understand such attacks, a characterization of the features carried by adversarial examples is needed. In this paper, we tackle this challenge by inspecting the subspaces of sample features through spectral analysis. We first empirically show that the features of either clean signals or adversarial perturbations are redundant and span in low-dimensional linear subspaces respectively with minimal overlap, and the classical low-dimensional subspace projection can suppress perturbation features out of the subspace of clean signals. This makes it possible for DNNs to learn a subspace where only features of clean signals exist while those of perturbations are discarded, which can facilitate the distinction of adversarial examples. To prevent the residual perturbations that is inevitable in subspace learning, we propose an independence criterion to disentangle clean signals from perturbations. Experimental results show that the proposed strategy enables the model to inherently suppress adversaries, which not only boosts model robustness but also motivates new directions of effective adversarial defense.

通过谱分析来检查样本特征的子空间，我们首先从实证角度表明干净信号或对抗扰动的特征分别是冗余的，而且在低维线性子空间中重叠较少，并且经典的低维子空间投影可以将扰动特征压缩到干净信号的子空间之外，从而使得深度神经网络可以学习一个只包含干净信号特征的子空间，抛弃扰动特征，从而能够区分对抗性样本。为了防止子空间学习中不可避免的残余扰动，我们提出一种独立性准则来区分干净信号和扰动。实验结果表明，所提出的策略能够本质上抑制对抗者，不仅提高了模型的鲁棒性，而且还给出了有效对抗防御的新方向。

子空间防御：通过学习纯净信号的子空间来排除对抗性扰动