Generalized Adversarial Training in Riemannian Space Adversarial examples, referred to as augmented data points generated by imperceptible perturbations of input samples, have recently drawn much attention. Wellcrafted adversarial examples may even mislead stateoftheart deep neural network (DNN) models to make wrong predictions easily. To alleviate this problem, many studies have focused on investigating how adversarial examples can be generated andor effectively handled. All existing works tackle this problem in the Euclidean space. In this paper, we extend the learning of adversarial examples to the more general Riemannian space over DNNs. The proposed work is important in that (1) it is a generalized learning methodology since Riemmanian space will be degraded to the Euclidean space in a special case; (2) it is the first work to tackle the adversarial example problem tractably through the perspective of Riemannian geometry; (3) from the perspective of geometry, our method leads to the steepest direction of the loss function, by considering the second order information of the loss function. We also provide a theoretical study showing that our proposed method can truly find the descent direction for the loss function, with a comparable computational time against traditional adversarial methods. Finally, the proposed framework demonstrates superior performance over traditional counterpart methods, using benchmark data including MNIST, CIFAR10 and SVHN.

Generation of Low Distortion Adversarial Attacks via Convex Programming As deep neural networks (DNNs) achieve extraordinary performance in a wide range of tasks, testing their robustness under adversarial attacks becomes paramount. Adversarial attacks, also known as adversarial examples, are used to measure the robustness of DNNs and are generated by incorporating imperceptible perturbations into the input data with the intention of altering a DNNu0027s classification. In prior work in this area, most of the proposed optimization based methods employ gradient descent to find adversarial examples. In this paper, we present an innovative method which generates adversarial examples via convex programming. Our experiment results demonstrate that we can generate adversarial examples with lower distortion and higher transferability than the Cu0026W attack, which is the current stateoftheart adversarial attack method for DNNs. We achieve 100% attack success rate on both the original undefended models and the adversariallytrained models. Our distortions of the L_inf attack are respectively 31% and 18% lower than the Cu0026W attack for the best case and average case on the CIFAR10 data set.