The Madry Lab recently hosted a competition designed to test the robustness of their adversarially trained MNIST model. Attacks were constrained to perturb each pixel of the input image by a scaled maximal L∞ distortion = 0.3. This decision discourages the use of attacks which are not optimized on the L∞ distortion metric. Our experimental results demonstrate that by relaxing the L∞ constraint ...

The β-skeleton {Gβ(V )} for a point set V is a family of geometric graphs, defined by the notion of neighborhoods parameterized by real number 0 < β < ∞. By using the distance-based version definition of β-skeletons we study those graphs for a set of points in R d space with l1 and l∞ metrics. We present algorithms for the entire spectrum of β values and we discuss properties of lens-based and ...

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the `1,2 and the `1,∞ version have been studied in detail and efficient algorithms exist, there are still open questions regarding other `1,p variants. We characterize conditions for solutions of the `1,p GroupLasso for all p-norms with 1 ≤ p ≤ ∞, and we present a unified active set algorithm. For a...

Numerical experiments in literature on compressed sensing have indicated that the reweighted l1 minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for sparse signal via weighted l1 minimization from the insight of the classical NSP (null space property) and RIC (restricted isometry constant) bound. We first int...

In this paper we present a robust method for simultaneous registration of multiple 3D scans. Rigid registration is an important task in many applications such as surface reconstruction, navigation and computer aided design. The goal of 3-D (rigid) registration is to align surfaces through a (rigid) transformation. A large number of existing registration algorithms are dependent on finding match...

We suggest an elementary harmonic analysis approach to canceling and weakly differential operators, which allows us extend these notions the anisotropic setting replace operators with Fourier multiplies mild smoothness regularity. In this more general of multipliers, we prove inequality $$\|f\|_{L_\infty} \lesssim \|Af\|_{L_1}$$ if $$A$$ is a operator order $$d$$ $$\|f\|_{L_2} $$d/2$$ , provide...