Recent work has shown that state-of-the-art models are highly vulnerable to adversarial perturbations of the input. We propose cowboy, an approach to detecting and defending against adversarial attacks by using both the discriminator and generator of a GAN trained on the same dataset. We show that the discriminator consistently scores the adversarial samples lower than the real samples across multiple attacks and datasets. We provide empirical evidence that adversarial samples lie outside of the data manifold learned by the GAN. Based on this, we propose a cleaning method which uses both the discriminator and generator of the GAN to project the samples back onto the data manifold. This cleaning procedure is independent of the classifier and type of attack and thus can be deployed in existing systems.
Projected Gradient Descent Method @cite_27 Projected Gradient Descent Method(PGDM) is an optimization based attack which finds a point, @math , that lies within the @math -ball of @math such that it minimizes the probability of the true label @math .
@cite_27
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Proximal gradient descent (PGD) and stochastic proximal gradient descent (SPGD) are popular methods for solving regularized risk minimization problems in machine learning and statistics. In this paper, we propose and analyze an accelerated variant of these methods in the mini-batch setting. This method incorporates two acceleration techniques: one is Nesterov's acceleration method, and the other is a variance reduction for the stochastic gradient. Accelerated proximal gradient descent (APG) and proximal stochastic variance reduction gradient (Prox-SVRG) are in a trade-off relationship. We show that our method, with the appropriate mini-batch size, achieves lower overall complexity than both APG and Prox-SVRG. In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, fits into the framework of RC-FDM. We prove linear convergence for both R-FDM and RC-FDM under the weak strong convexity assumption. Moreover, we show that the duality gap converges linearly for RC-FDM, which implies that the duality gap also converges linearly for SDCA applied to the SVM dual problem. In this paper, we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the diagonal quadratic approximation method DQAM of Mulvey and Ruszczynski [A diagonal quadratic approximation method for large scale linear programs, Oper. Res. Lett. 12 1992, pp. 205–215] and the parallel coordinate descent method PCDM of Richtarik and Takac [Parallel coordinate descent methods for big data optimization. Technical report, November 2012. arXiv:1212.0873]. We show that the two methods are equivalent for feasibility problems up to the selection of a step-size parameter. Furthermore, we prove an improved complexity bound for PCDM under strong convexity, and show that this bound is at least 8L′ Lω−12 times better than the best known bound for DQAM, where ω is the degree of partial separability and L’ and L are the maximum and average of the block Lipschitz constants of the gradient of the quadratic penalty appearing in the augmented Lagrangian. Mathematical optimization plays a fundamental role in solving many problems in computer vision (e.g., camera calibration, image alignment, structure from motion). It is generally accepted that second order descent methods are the most robust, fast, and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of computer vision, second order descent methods have two main drawbacks: 1) the function might not be analytically differentiable and numerical approximations are impractical, and 2) the Hessian may be large and not positive definite. Recently, Supervised Descent Method (SDM), a method that learns the “weighted averaged gradients” in a supervised manner has been proposed to solve these issues. However, SDM is a local algorithm and it is likely to average conflicting gradient directions. This paper proposes Global SDM (GSDM), an extension of SDM that divides the search space into regions of similar gradient directions. GSDM provides a better and more efficient strategy to minimize non-linear least squares functions in computer vision problems. We illustrate the effectiveness of GSDM in two problems: non-rigid image alignment and extrinsic camera calibration.