相关论文: Most ReLU Networks Suffer from $\ell^2$ Adversaria…

We consider the phenomenon of adversarial examples in ReLU networks with independent gaussian parameters. For networks of constant depth and with a large range of widths (for instance, it suffices if the width of each layer is polynomial in…

Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples. In this work we focus on two-layer neural networks trained using data which lie on a low…

The existence of adversarial examples is relatively understood for random fully connected neural networks, but much less so for convolutional neural networks (CNNs). The recent work [Daniely, 2025] establishes that adversarial examples can…

State-of-the-art machine learning models frequently misclassify inputs that have been perturbed in an adversarial manner. Adversarial perturbations generated for a given input and a specific classifier often seem to be effective on other…

This paper mathematically derives an analytic solution of the adversarial perturbation on a ReLU network, and theoretically explains the difficulty of adversarial training. Specifically, we formulate the dynamics of the adversarial…

Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under…

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the…

Despite a great deal of research, it is still unclear why neural networks are so susceptible to adversarial examples. In this work, we identify natural settings where depth-$2$ ReLU networks trained with gradient flow are provably…

Adversarial attacks add perturbations to the input features with the intent of changing the classification produced by a machine learning system. Small perturbations can yield adversarial examples which are misclassified despite being…

The existence of adversarial attacks on machine learning models imperceptible to a human is still quite a mystery from a theoretical perspective. In this work, we introduce two notions of adversarial attacks: natural or on-manifold attacks,…

We present empirical evidence that neural networks with ReLU and Absolute Value activations learn distance-based representations. We independently manipulate both distance and intensity properties of internal activations in trained models,…

Modern neural networks are highly non-robust against adversarial manipulation. A significant amount of work has been invested in techniques to compute lower bounds on robustness through formal guarantees and to build provably robust models.…

It is well-known that deep neural networks are vulnerable to adversarial attacks. Recent studies show that well-designed classification parts can lead to better robustness. However, there is still much space for improvement along this line.…

Deep neural networks are at the forefront of machine learning research. However, despite achieving impressive performance on complex tasks, they can be very sensitive: Small perturbations of inputs can be sufficient to induce incorrect…

A substantial body of empirical work documents the lack of robustness in deep learning models to adversarial examples. Recent theoretical work proved that adversarial examples are ubiquitous in two-layers networks with sub-exponential width…

Adversarial training is a widely used strategy for making neural networks resistant to adversarial perturbations. For a neural network of width $m$, $n$ input training data in $d$ dimension, it takes $\Omega(mnd)$ time cost per training…

Many machine learning models are vulnerable to adversarial attacks; for example, adding adversarial perturbations that are imperceptible to humans can often make machine learning models produce wrong predictions with high confidence.…

Deep neural networks are vulnerable to adversarial examples, i.e., carefully-perturbed inputs aimed to mislead classification. This work proposes a detection method based on combining non-linear dimensionality reduction and density…

In this paper, we initiate a rigorous study of the phenomenon of low-dimensional adversarial perturbations (LDAPs) in classification. Unlike the classical setting, these perturbations are limited to a subspace of dimension $k$ which is much…

Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…