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The adversarial vulnerability of Deep Neural Networks (DNNs) has beenwell-known and widely concerned, often under the context of learning top-$1$attacks (e.g., fooling a DNN to classify a cat image as dog). This paper showsthat the concern is much more serious by learning significantly more aggressiveordered top-$K$ clear-box~\footnote{ This is often referred to aswhite/black-box attacks in the literature. We choose to adopt neutralterminology, clear/opaque-box attacks in this paper, and omit the prefixclear-box for simplicity.} targeted attacks proposed in AdversarialDistillation. We propose a novel and rigorous quadratic programming (QP) methodof learning ordered top-$K$ attacks with low computing cost, dubbed as\textbf{QuadAttac$K$}. Our QuadAttac$K$ directly solves the QP to satisfy theattack constraint in the feature embedding space (i.e., the input space to thefinal linear classifier), which thus exploits the semantics of the featureembedding space (i.e., the principle of class coherence). With the optimizedfeature embedding vector perturbation, it then computes the adversarialperturbation in the data space via the vanilla one-step back-propagation. Inexperiments, the proposed QuadAttac$K$ is tested in the ImageNet-1kclassification using ResNet-50, DenseNet-121, and Vision Transformers (ViT-Band DEiT-S). It successfully pushes the boundary of successful ordered top-$K$attacks from $K=10$ up to $K=20$ at a cheap budget ($1\times 60$) and furtherimproves attack success rates for $K=5$ for all tested models, while retainingthe performance for $K=1$.

QuadAttack: A Quadratic Programming Approach to Ordered Top-K Attacks