Estimating the Robustness Radius for Randomized Smoothing with 100$\times$ Sample Efficiency

Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To understand if an RS-enabled DNN is effective in the sampled input domains, it is mandatory to sample data points within the operational design domain, acquire the point-wise certificate regarding robustness radius, and compare it with pre-defined acceptance criteria. Consequently, ensuring that a point-wise robustness certificate for any given data point is obtained relatively cost-effectively is crucial. This work demonstrates that reducing the number of samples by one or two orders of magnitude can still enable the computation of a slightly smaller robustness radius (commonly ~20% radius reduction) with the same confidence. We provide the mathematical foundation for explaining the phenomenon while experimentally showing promising results on the standard CIFAR-10 and ImageNet datasets.