Frame the adversary: a structure-aware attack methodology

Vicky Kouni, Stelios Perrakis, Francis Bach, Pascal Frossard, Yann Chevaleyre

Frequency-based adversarial attacks have recently grown popular by exploiting spectral sensitivities shared across neural architectures. Unlike spatial perturbations, frequency-based attacks expose deeper vulnerabilities, making them especially valuable for robust evaluation of safety-critical and security-sensitive applications. Yet, existing approaches are typically not derived as solutions to an optimization problem that explicitly captures transform-domain structure. In this paper, we propose a methodology for crafting principled frequency-based adversarial attacks, via a dedicated optimization framework. A cornerstone of our method hinges on the introduction of a perturbation constraint set, tied to highly structured non-orthogonal transforms, well-known for their flexible, non-predefined frequency handling. We prove that the attacks emerge as weighted $\ell_2$-projections onto this set, yielding a general and controlled attack generation mechanism. By this, we provide a clear geometric attack characterization, ensuring alignment between the optimization objective and the perturbation constraint. We assess our framework on standardized datasets, for pretrained and…