  Recent works have shown the effectiveness of randomized smoothing as a
scalable technique for building neural network-based classifiers that are
provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we
employ adversarial training to improve the performance of randomized smoothing.
We design an adapted attack for smoothed classifiers, and we show how this
attack can be used in an adversarial training setting to boost the provable
robustness of smoothed classifiers. We demonstrate through extensive
experimentation that our method consistently outperforms all existing provably
$\ell_2$-robust classifiers by a significant margin on ImageNet and CIFAR-10,
establishing the state-of-the-art for provable $\ell_2$-defenses. Moreover, we
find that pre-training and semi-supervised learning boost adversarially trained
smoothed classifiers even further. Our code and trained models are available at
http://github.com/Hadisalman/smoothing-adversarial .
