Incremental Randomized Smoothing Certification

TL;DR

This work tackles the high computational cost of randomized smoothing (RS) robustness certification for DNNs when models are subsequently approximated via quantization or pruning. It introduces Incremental Randomized Smoothing (IRS), which reuses certification guarantees from a base smoothed model to certify a modified smoothed model using substantially fewer samples, by leveraging a disparity bound $\zeta_x$ and a certification cache. The method combines $\underline{p_A}$ from RS with $\zeta_x$ to derive a new certified radius, and it efficiently estimates $\zeta_x$ using shared Gaussian seeds and Clopper–Pearson bounds to achieve speedups. Experiments on CIFAR-10 and ImageNet show IRS can deliver up to 4.1x faster certification while retaining strong robustness guarantees, enabling faster exploration of approximate networks for deployment on resource-constrained devices.

Abstract

Randomized smoothing-based certification is an effective approach for obtaining robustness certificates of deep neural networks (DNNs) against adversarial attacks. This method constructs a smoothed DNN model and certifies its robustness through statistical sampling, but it is computationally expensive, especially when certifying with a large number of samples. Furthermore, when the smoothed model is modified (e.g., quantized or pruned), certification guarantees may not hold for the modified DNN, and recertifying from scratch can be prohibitively expensive. We present the first approach for incremental robustness certification for randomized smoothing, IRS. We show how to reuse the certification guarantees for the original smoothed model to certify an approximated model with very few samples. IRS significantly reduces the computational cost of certifying modified DNNs while maintaining strong robustness guarantees. We experimentally demonstrate the effectiveness of our approach, showing up to 3x certification speedup over the certification that applies randomized smoothing of the approximate model from scratch.

Figures (12)

• Figure 1: Workflow of IRS from left to right. IRS takes the classifier $f$ and input $x$. IRS reuses the $\underline{p_A}$ and $\overline{p_B}$ estimates computed for $f$ on $x$ by RS. IRS estimate $\zeta_{x}$ from $f$ and $f^p$. For the smoothed classifier $g^p$ obtained from any of the approximate classifiers $f^p$ it computes the certified radius by combining $\underline{p_A}$ and $\overline{p_B}$ with $\zeta_{x}$.
• Figure 2: The number of samples for the Clopper-Pearson method to achieve a target error $\chi$ with confidence $(1 - \alpha)$.
• Figure 3: Total certification time versus ACR with $\sigma= 1.0$.
• Figure 4: The number of samples for the Agresti-Coull and Wilson method to achieve a target error $\chi$ with confidence $(1 - \alpha)$ where $\alpha = 0.01$. The plots show that the number of required samples for different methods peaks at 0.5 and decreases towards the boundaries.
• Figure 5: CIFAR10 ResNet-20 with $\sigma=1$, for $n_p \in \{5\%, 10\% \dots 80\%\}$ of $n$

Theorems & Definitions (10)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 4
• proof
• Theorem 4
• proof
• Theorem 4
• proof