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The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the representation space, by integrating a margin-based triplet embedding regularization term into the classification objective, so that the obtained model learns to resist adversarial examples. The regularization term consists of two steps optimizations which find potential perturbations and punish them by a large margin in an iterative way. Experimental results on MNIST, CASIA-WebFace, VGGFace2 and MS-Celeb-1M reveal that our approach increases the robustness of the network against both feature and label adversarial attacks in simple object classification and deep face recognition.The code is available at https://github.com/ zhongyy/Adversarial_MTER