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Deep Neural Networks (DNNs) classifiers performance degrades under adversarial attacks, such attacks are indistinguishably perturbed relative to the original data. Providing robustness to adversarial attacks is an important challenge in DNN training, which has led to extensive research. In this paper, we harden DNN classifiers under the adversarial attacks by regularizing their deep internal representation space with Multi-class Triplet regularization method. This method enables DNN classifier to learn a feature representation that detects similarities between adversarial and clean images and brings similar images close to their original class and pushes dissimilar images away from their false classes. This training process with our Multi-class Triplet regularization method in combination with Gaussian noise injection proves to be more robust in detecting adversarial attacks exceeding that of adversarial training on strong iterative attacks.

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