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Main Authors: Cinà, Antonio Emanuele, Villani, Francesco, Pintor, Maura, Schönherr, Lea, Biggio, Battista, Pelillo, Marcello
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2402.01879
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author Cinà, Antonio Emanuele
Villani, Francesco
Pintor, Maura
Schönherr, Lea
Biggio, Battista
Pelillo, Marcello
author_facet Cinà, Antonio Emanuele
Villani, Francesco
Pintor, Maura
Schönherr, Lea
Biggio, Battista
Pelillo, Marcello
contents Evaluating the adversarial robustness of deep networks to gradient-based attacks is challenging. While most attacks consider $\ell_2$- and $\ell_\infty$-norm constraints to craft input perturbations, only a few investigate sparse $\ell_1$- and $\ell_0$-norm attacks. In particular, $\ell_0$-norm attacks remain the least studied due to the inherent complexity of optimizing over a non-convex and non-differentiable constraint. However, evaluating adversarial robustness under these attacks could reveal weaknesses otherwise left untested with more conventional $\ell_2$- and $\ell_\infty$-norm attacks. In this work, we propose a novel $\ell_0$-norm attack, called $σ$-zero, which leverages a differentiable approximation of the $\ell_0$ norm to facilitate gradient-based optimization, and an adaptive projection operator to dynamically adjust the trade-off between loss minimization and perturbation sparsity. Extensive evaluations using MNIST, CIFAR10, and ImageNet datasets, involving robust and non-robust models, show that $σ$\texttt{-zero} finds minimum $\ell_0$-norm adversarial examples without requiring any time-consuming hyperparameter tuning, and that it outperforms all competing sparse attacks in terms of success rate, perturbation size, and efficiency.
format Preprint
id arxiv_https___arxiv_org_abs_2402_01879
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle $σ$-zero: Gradient-based Optimization of $\ell_0$-norm Adversarial Examples
Cinà, Antonio Emanuele
Villani, Francesco
Pintor, Maura
Schönherr, Lea
Biggio, Battista
Pelillo, Marcello
Machine Learning
Cryptography and Security
Computer Vision and Pattern Recognition
Evaluating the adversarial robustness of deep networks to gradient-based attacks is challenging. While most attacks consider $\ell_2$- and $\ell_\infty$-norm constraints to craft input perturbations, only a few investigate sparse $\ell_1$- and $\ell_0$-norm attacks. In particular, $\ell_0$-norm attacks remain the least studied due to the inherent complexity of optimizing over a non-convex and non-differentiable constraint. However, evaluating adversarial robustness under these attacks could reveal weaknesses otherwise left untested with more conventional $\ell_2$- and $\ell_\infty$-norm attacks. In this work, we propose a novel $\ell_0$-norm attack, called $σ$-zero, which leverages a differentiable approximation of the $\ell_0$ norm to facilitate gradient-based optimization, and an adaptive projection operator to dynamically adjust the trade-off between loss minimization and perturbation sparsity. Extensive evaluations using MNIST, CIFAR10, and ImageNet datasets, involving robust and non-robust models, show that $σ$\texttt{-zero} finds minimum $\ell_0$-norm adversarial examples without requiring any time-consuming hyperparameter tuning, and that it outperforms all competing sparse attacks in terms of success rate, perturbation size, and efficiency.
title $σ$-zero: Gradient-based Optimization of $\ell_0$-norm Adversarial Examples
topic Machine Learning
Cryptography and Security
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2402.01879