Papers › Mind the box: l₁-APGD for sparse adversarial attacks on image classifiers

Mind the box: l₁-APGD for sparse adversarial attacks on image classifiers

1 Mar 2021arXiv:2103.01208archive 2025-07-28

Francesco Croce, Matthias Hein

We show that when taking into account also the image domain [0,1]ᵈ, established l₁-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the l₁-ball and [0,1]ᵈ. We study the expected sparsity of the steepest descent step for this effective threat model and show that the exact projection onto this set is computationally feasible and yields better performance. Moreover, we propose an adaptive form of PGD which is highly effective even with a small budget of iterations. Our resulting l₁-APGD is a strong white-box attack showing that prior works overestimated their l₁-robustness. Using l₁-APGD for adversarial training we get a robust classifier with SOTA l₁-robustness. Finally, we combine l₁-APGD and an adaptation of the Square Attack to l₁ into l₁-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of l₁-ball intersected with [0,1]ᵈ.

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