# Certified Adversarial Robustness via Randomized Smoothing

8 Feb 2019  ·  , , ·

We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed recently in the literature, but existing guarantees are loose. We prove a tight robustness guarantee in $\ell_2$ norm for smoothing with Gaussian noise. We use randomized smoothing to obtain an ImageNet classifier with e.g. a certified top-1 accuracy of 49% under adversarial perturbations with $\ell_2$ norm less than 0.5 (=127/255). No certified defense has been shown feasible on ImageNet except for smoothing. On smaller-scale datasets where competing approaches to certified $\ell_2$ robustness are viable, smoothing delivers higher certified accuracies. Our strong empirical results suggest that randomized smoothing is a promising direction for future research into adversarially robust classification. Code and models are available at http://github.com/locuslab/smoothing.

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## Results from the Paper Edit

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Robust classification CIFAR-10 ResNet-110 w/ Randomized Smoothing Accuracy-Robustness Area 0.0065 # 3
Robust classification ImageNet ResNet-50 w/ Randomized Smoothing Accuracy-Robustness Area 0.0022 # 2