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.

通过限制神经网络的对抗梯度并增加对抗性样本生成的难度，提高了神经网络的鲁棒性，使其能够抵御各种类型的对抗性攻击，特别是迁移攻击。

通过正则化对抗梯度实现神经网络的鲁棒训练