Radial Basis Feature Transformation to Arm CNNs Against Adversarial Attacks

The linear and non-flexible nature of deep convolutional models makes them vulnerable to carefully crafted adversarial perturbations. To tackle this problem, in this paper, we propose a nonlinear radial basis convolutional feature transformation by learning the Mahalanobis distance function that maps the input convolutional features from the same class into tight clusters. In such a space, the clusters become compact and well-separated, which prevent small adversarial perturbations from forcing a sample to cross the decision boundary. We test the proposed method on three publicly available image classification and segmentation data-sets namely, MNIST, ISBI ISIC skin lesion, and NIH ChestX-ray14. We evaluate the robustness of our method to different gradient (targeted and untargeted) and non-gradient based attacks and compare it to several non-gradient masking defense strategies. Our results demonstrate that the proposed method can boost the performance of deep convolutional neural networks against adversarial perturbations without accuracy drop on clean data.