提出LBS方法，让模型认证更快更省资源，无需训练时加噪声。
Laplace-Bridged Randomized Smoothing for Fast Certified Robustness
- 用低维概率空间替代高维采样，实现快速认证
- 在CIFAR-10和ImageNet上认证效果优于传统方法
- 边缘设备上提速最高达494倍，适合实际部署
随机平滑（RS）为任意基础分类器提供ℓ₂形式化保证，但存在两大实践瓶颈：(i) 通常依赖噪声增强训练以获得有效证书，这增加了训练成本，降低干净准确率，并削弱了其作为真正事后防御的能力；(ii) 认证计算开销大，每输入需数万次噪声前向传播，阻碍部署，尤其在资源受限的边缘设备上。为此，我们提出拉普拉斯桥接平滑（LBS），对RS进行解析重构，将高维输入空间蒙特卡洛采样替换为低维概率空间中的高效计算。LBS无需噪声增强训练即可保持形式化鲁棒性保证，显著降低认证负担。在CIFAR-10和ImageNet上，LBS获得比RS更强的认证鲁棒性，且单样本认证成本降低近一个数量级。特别地，在NVIDIA Jetson Orin Nano和Raspberry Pi 4上，速度提升最高达494倍，实现真实边缘设备上的实用认证部署。最后，我们提供了该解析形式与证书有效性的理论证明。
原文摘要 · Abstract (English)
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.
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