Papers › Computational Asymmetries in Robust Classification
Computational Asymmetries in Robust Classification
Samuele Marro, Michele Lombardi
In the context of adversarial robustness, we make three strongly related contributions. First, we prove that while attacking ReLU classifiers is 𝑁𝑃-hard, ensuring their robustness at training time is Σ²_P-hard (even on a single example). This asymmetry provides a rationale for the fact that robust classifications approaches are frequently fooled in the literature. Second, we show that inference-time robustness certificates are not affected by this asymmetry, by introducing a proof-of-concept approach named Counter-Attack (CA). Indeed, CA displays a reversed asymmetry: running the defense is 𝑁𝑃-hard, while attacking it is Σ₂ᴾ-hard. Finally, motivated by our previous result, we argue that adversarial attacks can be used in the context of robustness certification, and provide an empirical evaluation of their effectiveness. As a byproduct of this process, we also release UG100, a benchmark dataset for adversarial attacks.
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