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This paper introduces Laplace-Bridged Smoothing (LBS), a reformulation of Randomized Smoothing (RS) that replaces Monte Carlo sampling in the input space with efficient computations in a lower-dimensional probability space. LBS eliminates the need for noise-augmented training, a common requirement for RS, while maintaining formal robustness guarantees. Experiments on CIFAR-10 and ImageNet demonstrate that LBS achieves stronger certified robustness and reduces per-sample certification cost by nearly an order of magnitude, leading to significant speedups on edge devices.
Edge devices can now achieve up to 494x faster certified robustness with Laplace-Bridged Smoothing, making formally verified AI deployments practical in resource-constrained settings.
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.
