On the Effectiveness of Low Frequency Perturbations

Abstract: Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-of-the-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is particularly effective. Yet, it remains unclear whether this is due to generally constraining the attack search space or specifically removing high frequency components from consideration. By systematically controlling the frequency components of the perturbation, evaluating against the top-placing defense submissions in the NeurIPS 2017 competition, we empirically show that performance improvements in both the white-box and black-box transfer settings are yielded only when low frequency components are preserved. In fact, the defended models based on adversarial training are roughly as vulnerable to low frequency perturbations as undefended models, suggesting that the purported robustness of state-of-the-art ImageNet defenses is reliant upon adversarial perturbations being high frequency in nature. We do find that under $\ell_\infty$ $\epsilon=16/255$, the competition distortion bound, low frequency perturbations are indeed perceptible. This questions the use of the $\ell_\infty$-norm, in particular, as a distortion metric, and, in turn, suggests that explicitly considering the frequency space is promising for learning robust models which better align with human perception.