arXiv research

Random smoothing struggles to certify high-dimensional image robustness.

We improve image perturbation defenses using a better-defined Wasserstein threat model.

Adversarial training yields robust models against a specific threat model, e.g., $L_\infty$ adversarial examples. Typically robustness does not generalize to previously unseen threat models, e.g., other $L_p$ norms, or larger perturbations. Our confidence-calibrated adversarial training (CCAT) tackles this problem by b…

Researchers redefine $\ell^\infty$-cohomology for groups and spaces, linking it to amenability, hyperbolicity, and algorithmic undecidability.

The paper studies the asymptotic behavior of adversarial training under $\ell_\infty$-perturbation.

Enhances robustness of AT frameworks to multiple perturbations without increasing training complexity.

New neural network design resists small $\ell_\infty$-norm adversarial perturbations.

RobustBench aims to standardize adversarial robustness evaluation in image classification.

Proposes a new method for joint sample and feature selection in multi-view data.

We provide recovery guarantees for compressible signals that have been corrupted with noise and extend the framework introduced in \cite{bafna2018thwarting} to defend neural networks against $\ell_0$-norm, $\ell_2$-norm, and $\ell_{\infty}$-norm attacks. Our results are general as they can be applied to most unitary tr…

Semantify-NN verifies neural network robustness against semantic perturbations.

AdamW optimizes a constrained loss with $\ell_\infty$ norm constraint.

The paper derives upper bounds on the MLE error for BTL model under general graphs.

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in a framework of maximizing the weighted feature contributions subject to a $\ell…

Efficiently performs robust and sparse kernel regression.

Improved training boosts certified robustness of L-infinity distance nets.

The paper analyzes kNN density estimation's convergence rates under different conditions.

The paper tackles multi-armed bandits with vector losses, focusing on minimizing the $\ell^\infty$-norm of relative losses.

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have been employed to obtain models which are robust on the training set. However, the …

Localized uncertainty attacks target uncertain regions to create imperceptible adversarial examples.

New method defends against unseen threat models using perceptual adversarial training.

New surfaces near a sphere violate Minkowski inequality.

This paper tackles robustness of ensemble stumps and trees under general ℓ_p norm perturbations.

In this paper we consider the problem of grouped variable selection in high-dimensional regression using $\ell_1-\ell_q$ regularization ($1\leq q \leq \infty$), which can be viewed as a natural generalization of the $\ell_1-\ell_2$ regularization (the group Lasso). The key condition is that the dimensionality $p_n$ can…

This work improves robustness guarantees for neural networks using low rank representations.

New insights into variable selection with different model assumptions.

We obtain the first positive results for bounded sample compression in the agnostic regression setting with the $\ell_p$ loss, where $p\in [1,\infty]$. We construct a generic approximate sample compression scheme for real-valued function classes exhibiting exponential size in the fat-shattering dimension but independen…

This study shows how optimizer choice affects adversarial robustness in neural networks.

Study analyzes perturbations in singular subspaces under random noise.

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $\|x'-x^*\|_\infty \leq \fracε{\sqrt{d}}\cdot \|Ax^*-b\|_2\cdot \|A^\dagger\|$ where $x^*=\arg\min_{x\in \mathbb{R}^d}\|Ax-b\|…

Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. Our aim is to understand the reasons underlying…

We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood, which involves solving a convex program for each node; for Ising models this is …

ScoreAG generates unrestricted adversarial images maintaining semantic integrity.

New bound on Rademacher complexity for vector functions.

The study generalizes cohomology results for hyperbolic groups.

This paper tackles the problem of defending a neural network against adversarial attacks crafted with different norms (in particular $\ell_\infty$ and $\ell_2$ bounded adversarial examples). It has been observed that defense mechanisms designed to protect against one type of attacks often offer poor performance against…

Owing to the susceptibility of deep learning systems to adversarial attacks, there has been a great deal of work in developing (both empirically and certifiably) robust classifiers. While most work has defended against a single type of attack, recent work has looked at defending against multiple perturbation models usi…

Adam's bias shifts from full-batch to max-margin of different norms for separable data.

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

This paper explores adversarial training limits and improves model robustness against norm-bounded perturbations.

We consider the problem of Graphical lasso with an additional $\ell_{\infty}$ element-wise norm constraint on the precision matrix. This problem has applications in high-dimensional covariance decomposition such as in \citep{Janzamin-12}. We propose an ADMM algorithm to solve this problem. We also use a continuation st…

Feature hashing and other random projection schemes are commonly used to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in $\mathbb{R}^n$ into a much lower-dimensional space $\mathbb{R}^m$, while approximately preserving Euclidean norm. These sc…

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal $\ell_{1,\infty}$-penalized recursive least squares (R…

The vanishing of reduced $\ell^2$-cohomology for amenable groups can be traced to the work of Cheeger & Gromov. The subject matter here is reduced $\ell^p$-cohomology for $p \in ]1,\infty[$, particularly its vanishing. Results showing its triviality are obtained, for example: when $p \in ]1,2]$ and $G$ is amenable; whe…

Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector $\ell_1$ norm, whic…

In this paper, we study the Lévy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional $\ell^p$-ball with the $\ell^q$-distance function for $1\leq p<q\leq +\infty$ is equivalent to the concentration to the…

This paper analyzes the Lipschitz constants of deep neural networks with random weights.

Extends randomized smoothing to certify robustness against various threat models and adversarial perturbations.