Laplace-Bridged Randomized Smoothing for Fast Certified Robustness
For practitioners deploying certified classifiers on resource-constrained edge devices, LBS dramatically reduces certification cost while maintaining or improving robustness, addressing a key bottleneck in practical adoption.
Laplace-Bridged Smoothing (LBS) reformulates randomized smoothing to avoid noise-augmented training and reduce certification cost by replacing Monte Carlo sampling with analytic computations, achieving stronger certified robustness on CIFAR-10 and ImageNet while reducing per-sample cost by nearly an order of magnitude and up to 494× speedup on edge devices.
Randomized Smoothing (RS) offers formal $\ell_2$ guarantees for arbitrary base classifiers but faces two key practical bottlenecks: (i) it often relies on noise-augmented training to achieve nontrivial certificates, which increases training cost, can reduce clean accuracy, and weakens RS as a genuinely post-hoc defense; and (ii) certification is computationally expensive, typically requiring tens of thousands of noisy forward passes per input, which hinders deployment, especially on resource-constrained edge devices. To address both limitations, we propose Laplace-Bridged Smoothing (LBS), an analytic reformulation of RS that replaces high-dimensional input-space Monte Carlo (MC) sampling with efficient computations in a low-dimensional probability space. LBS preserves formal robustness guarantees without requiring noise-augmented training while substantially reducing certification burden. On CIFAR-10 and ImageNet, LBS attains stronger certified robustness than RS and reduces per-sample certification cost by nearly an order of magnitude. Notably, on NVIDIA Jetson Orin Nano and Raspberry Pi 4, LBS achieves speedups of up to $494\times$, enabling practical certified deployment on real-world edge devices. Finally, we provide theoretical justification for the analytic formulation and certificate validity of LBS.