Adversarial training (AT) is one of the most effective ways for improving the robustness of deep convolution neural networks (CNNs). Just like common network training, the effectiveness of AT relies on the design of basic network components. In this paper, we conduct an in-depth study on the role of the basic ReLU activation component in AT for robust CNNs. We find that the spatially-shared and input-independent properties of ReLU activation make CNNs less robust to white-box adversarial attacks with either standard or adversarial training. To address this problem, we extend ReLU to a novel Sparta activation function (Spatially attentive and Adversarially Robust Activation), which enables CNNs to achieve both higher robustness, i.e., lower error rate on adversarial examples, and higher accuracy, i.e., lower error rate on clean examples, than the existing state-of-the-art (SOTA) activation functions. We further study the relationship between Sparta and the SOTA activation functions, providing more insights about the advantages of our method. With comprehensive experiments, we also find that the proposed method exhibits superior cross-CNN and cross-dataset transferability. For the former, the adversarially trained Sparta function for one CNN (e.g., ResNet-18) can be fixed and directly used to train another adversarially robust CNN (e.g., ResNet-34). For the latter, the Sparta function trained on one dataset (e.g., CIFAR-10) can be employed to train adversarially robust CNNs on another dataset (e.g., SVHN). In both cases, Sparta leads to CNNs with higher robustness than the vanilla ReLU, verifying the flexibility and versatility of the proposed method.
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