Deep neural networks (DNNs) have achieved remarkable progress across various domains, yet they remain highly vulnerable to adversarial attacks, which significantly hinder their deployment in safety-critical applications. While stochastic defenses have shown promise, most existing approaches rely on fixed noise injection and fail to account for the geometric stability of the decision space. To address these limitations, we introduce a novel framework, which named as Dual Stochasticity and Geometric Normalization (DSGN). Specifically, DSGN incorporates learnable, input-dependent Gaussian noise into both the feature representation and classifier weights, creating a dual-path stochastic modeling mechanism that captures multi-level predictive uncertainty. To enhance decision consistency, both noisy components are projected onto a unit hypersphere via 𝓁2 normalization, constraining the logit space and promoting angular margin separation. This design stabilizes both the representation and decision geometry, leading to more stable decision boundaries and improved robustness. We evaluate the effectiveness of DSGN on several benchmark datasets and CNNs. Our results indicate that DSGN achieves a robust accuracy improvement of approximately 1% to 6% over the state-of-the-arts baseline model under PGD and 1% to 17% improvement under AutoAttack, demonstrating its effectiveness in enhancing adversarial robustness while maintaining high clean accuracy.
Wu et al. (Thu,) studied this question.