Attack-Free Adversarial Vulnerability Assessment via Second-Order Statistics of Predictive Probabilities

Deep neural networks are widely deployed in safety-critical applications such as medical image analysis and autonomous driving, where adversarial robustness is essential. Existing robustness evaluations primarily measure overall performance degradation under attack, offering limited insight into class-wise or directional vulnerability patterns. We propose a second-order statistical framework that treats class-wise softmax outputs as random variables and analyzes their conditional variance–covariance structure to characterize structural vulnerability. Using only clean validation data-without generating adversarial examples or relying on specific attack algorithms-the framework enables attack-agnostic evaluation while significantly reducing computational cost, serving as a practical pre-screening tool for rapid model assessment. The conditional variance of the correct-class probability quantifies relative class-wise adversarial vulnerability, while conditional covariance reveals directional misclassification tendencies. Experiments on standard benchmarks under diverse untargeted and targeted attack settings demonstrate strong alignment between the proposed metrics and class-wise attack success rates, suggesting that adversarial vulnerability can be effectively characterized without explicit attack generation.