Minimal Cascade Gradient Smoothing for Fast Transferable Preemptive Adversarial Defense

Adversarial attacks persist as a major challenge in deep learning. While training- and test-time defenses are well-studied, they often reduce clean accuracy, incur high cost, or fail under adaptive threats. In contrast, preemptive defenses, which perturb media before release, offer a practical alternative but remain slow, model-coupled, and brittle. We propose the Minimal Sufficient Preemptive Defense (MSPD), a fast, transferable framework that defends against future attacks without access to the target model or gradients. MSPD is driven by Minimal Cascade Gradient Smoothing (MCGS), a two-epoch optimization paradigm executed on a surrogate backbone. This defines a minimal yet effective regime for robust generalization across unseen models and attacks. MSPD runs at 0.02s/image (CIFAR-10) and 0.26s/image (ImageNet), 28--1696x faster than prior preemptive methods, while improving robust accuracy by +5% and clean accuracy by +3.7% across 11 models and 7 attacks. To evaluate adaptive robustness, we introduce Preemptive Reversion, the first white-box diagnostic attack that cancels preemptive perturbations under full gradient access. Even in this setting, MSPD retains a +2.2% robustness margin over the baseline. In practice, when gradients are unavailable, MSPD remains reliable and efficient. MSPD, MCGS, and Preemptive Reversion are each supported by formal theoretical proofs. The implementation is available at https://github.com/azrealwang/MSPD.