Decoding adversarial vulnerabilities via copula

Deep learning models have achieved outstanding performance in computer vision applications. However, their lack of interpretability and susceptibility to adversarial examples raise concerns. Adversarial perturbations, though imperceptible, can severely compromise model performance. While prior studies have provided theoretical perspectives on adversarial vulnerabilities, a concrete explanation at the feature level remains unexplored. In this paper, we employ copula structures to examine feature relationships in clean and adversarial examples. Copula-based analysis facilitates the separation of marginal distributions from dependency structures, offering a clear view of how adversarial perturbations distort feature relationships. We observe that clean samples maintain sparse dependency structures, while adversarial examples introduce unnatural dependencies absent in clean data. To counteract this, we propose COpula STructure Alignment (COSTA), a novel regularization approach that preserves clean feature dependencies in the latent space, thereby improving model robustness. Experimental evaluations on CIFAR-10 and CIFAR-100 confirm that COSTA enhances adversarial robustness, outperforming both standard and adversarially trained autoencoders. Our findings provide new insights into adversarial robustness through the lens of copula-based dependency modeling.