Deep Learning (DL) is increasingly used in safety-critical applications, raising concerns about its reliability. DL suffers from a well-known problem of lacking robustness, especially when faced with adversarial perturbations known as Adversarial Examples (AEs). Despite recent efforts to detect AEs using advanced attack and testing methods, these approaches often overlook the input distribution and perceptual quality of the perturbations. As a result, the detected AEs may not be relevant in practical applications or may appear unrealistic to human observers. This can waste testing resources on rare AEs that seldom occur during real-world use, limiting improvements in DL model dependability. In this paper, we propose a new robustness testing approach for detecting AEs that considers both the feature level distribution and the pixel level distribution, capturing the perceptual quality of adversarial perturbations. The two considerations are encoded by a novel hierarchical mechanism. First, we select test seeds based on the density of feature level distribution and the vulnerability of adversarial robustness. The vulnerability of test seeds are indicated by the auxiliary information, that are highly correlated with local robustness. Given a test seed, we then develop a novel genetic algorithm based local test case generation method, in which two fitness functions work alternatively to control the perceptual quality of detected AEs. Finally, extensive experiments confirm that our holistic approach considering hierarchical distributions is superior to the state-of-the-arts that either disregard any input distribution or only consider a single (non-hierarchical) distribution, in terms of not only detecting imperceptible AEs but also improving the overall robustness of the DL model under testing.

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