Hierarchical Distribution-Aware Testing of Deep Learning

With its growing use in safety/security-critical applications, Deep Learning (DL) has raised increasing concerns regarding its dependability. In particular, DL has a notorious problem of lacking robustness. Despite recent efforts made in detecting Adversarial Examples (AEs) via state-of-the-art attacking and testing methods, they are normally input distribution agnostic and/or disregard the perception quality of AEs. Consequently, the detected AEs are irrelevant inputs in the application context or unnatural/unrealistic that can be easily noticed by humans. This may lead to a limited effect on improving the DL model's dependability, as the testing budget is likely to be wasted on detecting AEs that are encountered very rarely in its real-life operations. In this paper, we propose a new robustness testing approach for detecting AEs that considers both the input distribution and the perceptual quality of inputs. The two considerations are encoded by a novel hierarchical mechanism. First, at the feature level, the input data distribution is extracted and approximated by data compression techniques and probability density estimators. Such quantified feature level distribution, together with indicators that are highly correlated with local robustness, are considered in selecting test seeds. Given a test seed, we then develop a two-step genetic algorithm for local test case generation at the pixel level, in which two fitness functions work alternatively to control the quality of detected AEs. Finally, extensive experiments confirm that our holistic approach considering hierarchical distributions at feature and pixel levels is superior to state-of-the-arts that either disregard any input distribution or only consider a single (non-hierarchical) distribution, in terms of not only the quality of detected AEs but also improving the overall robustness of the DL model under testing.