We empirically demonstrate that test-time adaptive batch normalization, which re-estimates the batch-normalization statistics during inference, can provide $ell_2$-certification as well as improve the commonly occurring corruption robustness of adversarially trained models while maintaining their state-of-the-art empirical robustness against adversarial attacks. Furthermore, we obtain similar $ell_2$-certification as the current state-of-the-art certification models for CIFAR-10 by learning our adversarially trained model using larger $ell_2$-bounded adversaries. Therefore our work is a step towards bridging the gap between the state-of-the-art certification and empirical robustness. Our results also indicate that improving the empirical adversarial robustness may be sufficient as we achieve certification and corruption robustness as a by-product using test-time adaptive batch normalization.
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