Approximate Manifold Defense Against Multiple Adversarial Perturbations

Existing defenses against adversarial attacks are typically tailored to a specific perturbation type. Using adversarial training to defend against multiple types of perturbation requires expensive adversarial examples from different perturbation types at each training step. In contrast, manifold-based defense incorporates a generative network to project an input sample onto the clean data manifold. This approach eliminates the need to generate expensive adversarial examples while achieving robustness against multiple perturbation types. However, the success of this approach relies on whether the generative network can capture the complete clean data manifold, which remains an open problem for complex input domain. In this work, we devise an approximate manifold defense mechanism, called RBF-CNN, for image classification. Instead of capturing the complete data manifold, we use an RBF layer to learn the density of small image patches. RBF-CNN also utilizes a reconstruction layer that mitigates any minor adversarial perturbations. Further, incorporating our proposed reconstruction process for training improves the adversarial robustness of our RBF-CNN models. Experiment results on MNIST and CIFAR-10 datasets indicate that RBF-CNN offers robustness for multiple perturbations without the need for expensive adversarial training.