  In recent years, neural networks have demonstrated outstanding effectiveness
in a large amount of applications.However, recent works have shown that neural
networks are susceptible to adversarial examples, indicating possible flaws
intrinsic to the network structures. To address this problem and improve the
robustness of neural networks, we investigate the fundamental mechanisms behind
adversarial examples and propose a novel robust training method via regulating
adversarial gradients. The regulation effectively squeezes the adversarial
gradients of neural networks and significantly increases the difficulty of
adversarial example generation.Without any adversarial example involved, the
robust training method could generate naturally robust networks, which are
near-immune to various types of adversarial examples. Experiments show the
naturally robust networks can achieve optimal accuracy against Fast Gradient
Sign Method (FGSM) and C\&W attacks on MNIST, Cifar10, and Google Speech
Command dataset. Moreover, our proposed method also provides neural networks
with consistent robustness against transferable attacks.
