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In recent years, neural networks have demonstrated outstanding effectivenessin a large amount of applications.However, recent works have shown that neuralnetworks are susceptible to adversarial examples, indicating possible flawsintrinsic to the network structures. To address this problem and improve therobustness of neural networks, we investigate the fundamental mechanisms behindadversarial examples and propose a novel robust training method via regulatingadversarial gradients. The regulation effectively squeezes the adversarialgradients of neural networks and significantly increases the difficulty ofadversarial example generation.Without any adversarial example involved, therobust training method could generate naturally robust networks, which arenear-immune to various types of adversarial examples. Experiments show thenaturally robust networks can achieve optimal accuracy against Fast GradientSign Method (FGSM) and C\&W attacks on MNIST, Cifar10, and Google SpeechCommand dataset. Moreover, our proposed method also provides neural networkswith consistent robustness against transferable attacks.

Towards Robust Training of Neural Networks by Regularizing Adversarial Gradients