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This paper presents a novel model training solution, denoted asAdaptive-Gravity, for enhancing the robustness of deep neural networkclassifiers against adversarial examples. We conceptualize the modelparameters/features associated with each class as a mass characterized by itscentroid location and the spread (standard deviation of the distance) offeatures around the centroid. We use the centroid associated with each clusterto derive an anti-gravity force that pushes the centroids of different classesaway from one another during network training. Then we customized an objectivefunction that aims to concentrate each class's features toward theircorresponding new centroid, which has been obtained by anti-gravity force. Thismethodology results in a larger separation between different masses and reducesthe spread of features around each centroid. As a result, the samples arepushed away from the space that adversarial examples could be mapped to,effectively increasing the degree of perturbation needed for making anadversarial example. We have implemented this training solution as an iterativemethod consisting of four steps at each iteration: 1) centroid extraction, 2)anti-gravity force calculation, 3) centroid relocation, and 4) gravitytraining. Gravity's efficiency is evaluated by measuring the correspondingfooling rates against various attack models, including FGSM, MIM, BIM, and PGDusing LeNet and ResNet110 networks, benchmarked against MNIST and CIFAR10classification problems. Test results show that Gravity not only functions as apowerful instrument to robustify a model against state-of-the-art adversarialattacks but also effectively improves the model training accuracy.

Adaptive-Gravity: A Defense Against Adversarial Samples