Laplace-Bridged Randomized Smoothing for Fast Certified Robustness

TL;DR

This paper introduces Laplace-Bridged Smoothing, an analytic method that enhances randomized smoothing for certified robustness, significantly reducing computational costs and enabling deployment on edge devices.

Contribution

We propose Laplace-Bridged Smoothing, an analytic reformulation that eliminates the need for noise-augmented training and reduces certification computation in randomized smoothing.

Findings

LBS achieves stronger certified robustness than traditional RS on CIFAR-10 and ImageNet.

LBS reduces certification cost per sample by nearly tenfold.

LBS enables practical deployment on resource-constrained edge devices with speedups up to 494×.

Abstract

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.