While convolutional neural networks (CNNs) have achieved success in computer vision tasks, it is vulnerable to backdoor attacks. Such attacks could mislead the victim model to make attacker-chosen prediction with a specific trigger pattern. Until now, the trigger injection of existing attacks is mainly limited to spatial domain. Recent works take advantage of perceptual properties of planting specific patterns in the frequency domain, which only reflect indistinguishable pixel-wise perturbations in pixel domain. However, in the black-box setup, the inaccessibility of training process often renders more complex trigger designs. Existing frequency attacks simply handcraft the magnitude of spectrum, introducing anomaly frequency disparities between clean and poisoned data and taking risks of being removed by image processing operations (such as lossy compression and filtering). In this paper, we propose a robust low-frequency black-box backdoor attack (LFBA), which minimally perturbs low-frequency components of frequency spectrum and maintains the perceptual similarity in spatial space simultaneously. The key insight of our attack restrict the search for the optimal trigger to low-frequency region that can achieve high attack effectiveness, robustness against image transformation defenses and stealthiness in dual space. We utilize simulated annealing (SA), a form of evolutionary algorithm, to optimize the properties of frequency trigger including the number of manipulated frequency bands and the perturbation of each frequency component, without relying on the knowledge from the victim classifier. Extensive experiments on real-world datasets verify the effectiveness and robustness of LFBA against image processing operations and the state-of-the-art backdoor defenses, as well as its inherent stealthiness in both spatial and frequency space, making it resilient against frequency inspection.

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