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Making neural networks robust against adversarial inputs has resulted in anarms race between new defenses and attacks. The most promising defenses,adversarially robust training and verifiably robust training, have limitationsthat restrict their practical applications. The adversarially robust trainingonly makes the networks robust against a subclass of attackers and we revealsuch weaknesses by developing a new attack based on interval gradients. Bycontrast, verifiably robust training provides protection against any L-pnorm-bounded attacker but incurs orders of magnitude more computational andmemory overhead than adversarially robust training.  We propose two novel techniques, stochastic robust approximation and dynamicmixed training, to drastically improve the efficiency of verifiably robusttraining without sacrificing verified robustness. We leverage two criticalinsights: (1) instead of over the entire training set, soundover-approximations over randomly subsampled training data points aresufficient for efficiently guiding the robust training process; and (2) Weobserve that the test accuracy and verifiable robustness often conflict aftercertain training epochs. Therefore, we use a dynamic loss function toadaptively balance them for each epoch.  We designed and implemented our techniques as part of MixTrain and evaluatedit on six networks trained on three popular datasets including MNIST, CIFAR,and ImageNet-200. Our evaluations show that MixTrain can achieve up to $95.2\%$verified robust accuracy against $L_\infty$ norm-bounded attackers while taking$15$ and $3$ times less training time than state-of-the-art verifiably robusttraining and adversarially robust training schemes, respectively. Furthermore,MixTrain easily scales to larger networks like the one trained on ImageNet-200,significantly outperforming the existing verifiably robust training methods.

MixTrain: Scalable Training of Verifiably Robust Neural Networks