Network Moments: Extensions and Sparse-Smooth Attacks
The impressive performance of deep neural networks (DNNs) has immensely strengthened the line of research that aims at theoretically analyzing their effectiveness. This has incited research on the reaction of DNNs to noisy input, namely developing adversarial input attacks and strategies that lead to robust DNNs to these attacks. To that end, in this paper, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network (Affine, ReLU, Affine) subject to Gaussian input. In particular, we generalize the second-moment expression of Bibi et al. to arbitrary input Gaussian distributions, dropping the zero-mean assumption. We show that the new variance expression can be efficiently approximated leading to much tighter variance estimates as compared to the preliminary results of Bibi et al. Moreover, we experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, where we investigate the effect of the linearization sensitivity on the accuracy of the moment estimates. Lastly, we show that the derived expressions can be used to construct sparse and smooth Gaussian adversarial attacks (targeted and non-targeted) that tend to lead to perceptually feasible input attacks.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Active and sparse methods in smoothed model checking
Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functi…
Active LearningmodelMahNMF: Manhattan Non-negative Matrix Factorization
Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence…
Convex-constrained Sparse Additive Modeling and Its Extensions
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integ…
Additive modelsregression(De)Randomized Smoothing for Certifiable Defense against Patch Attacks
Patch adversarial attacks on images, in which the attacker can distort pixels within a region of bounded size, are an important threat model since they provide a quantitative model for physical adversarial attacks. In th…
Exploring Sparsity and Smoothness of Arbitrary $\ell_p$ Norms in Adversarial Attacks
Adversarial attacks against deep neural networks are commonly constructed under $\ell_p$ norm constraints, most often using $p=1$, $p=2$ or $p=\infty$, and potentially regularized for specific demands such as sparsity or…