Laplace-Bridged Randomized Smoothing for Fast Certified Robustness

2026-04-27

AI Summary

This work addresses the limitations of randomized smoothing for ℓ₂ robustness certification, which suffers from degraded post-hoc defense properties due to noise-augmented training and high computational costs from Monte Carlo estimation, hindering deployment on edge devices. The authors propose Laplace-Bridged Smoothing (LBS), the first method to reformulate randomized smoothing into a closed-form solution that directly computes certified radii in a low-dimensional probability space without requiring noise-augmented training. LBS achieves stronger certified robustness on CIFAR-10 and ImageNet, accelerates per-sample certification by nearly an order of magnitude, and demonstrates up to 494× speedup on resource-constrained platforms such as the Jetson Orin Nano and Raspberry Pi 4, significantly advancing the practicality of certified defenses in edge computing scenarios.

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.

Problem

• Randomized Smoothing
• Certified Robustness
• Noise-Augmented Training
• Computational Cost
• Edge Devices

Innovation

• Randomized Smoothing
• Certified Robustness
• Laplace-Bridged Smoothing
• Edge Deployment
• Analytic Certification