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Certified defense using randomized smoothing is a popular technique toprovide robustness guarantees for deep neural networks against l2 adversarialattacks. Existing works use this technique to provably secure a pretrainednon-robust model by training a custom denoiser network on entire training data.However, access to the training set may be restricted to a handful of datasamples due to constraints such as high transmission cost and the proprietarynature of the data. Thus, we formulate a novel problem of "how to certify therobustness of pretrained models using only a few training samples". We observethat training the custom denoiser directly using the existing techniques onlimited samples yields poor certification. To overcome this, our proposedapproach (DE-CROP) generates class-boundary and interpolated samplescorresponding to each training sample, ensuring high diversity in the featurespace of the pretrained classifier. We train the denoiser by maximizing thesimilarity between the denoised output of the generated sample and the originaltraining sample in the classifier's logit space. We also perform distributionlevel matching using domain discriminator and maximum mean discrepancy thatyields further benefit. In white box setup, we obtain significant improvementsover the baseline on multiple benchmark datasets and also report similarperformance under the challenging black box setup.

DE-CROP: Data-efficient Certified Robustness for Pretrained Classifiers