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Recently, bound propagation based certified robust training methods have beenproposed for training neural networks with certifiable robustness guarantees.Despite that state-of-the-art (SOTA) methods including interval boundpropagation (IBP) and CROWN-IBP have per-batch training complexity similar tostandard neural network training, they usually use a long warmup schedule withhundreds or thousands epochs to reach SOTA performance and are thus stillcostly. In this paper, we identify two important issues in existing methods,namely exploded bounds at initialization, and the imbalance in ReLU activationstates and improve IBP training. These two issues make certified trainingdifficult and unstable, and thereby long warmup schedules were needed in priorworks. To mitigate these issues and conduct faster certified training withshorter warmup, we propose three improvements based on IBP training: 1) Wederive a new weight initialization method for IBP training; 2) We propose tofully add Batch Normalization (BN) to each layer in the model, since we find BNcan reduce the imbalance in ReLU activation states; 3) We also designregularization to explicitly tighten certified bounds and balance ReLUactivation states during wamrup. We are able to obtain 65.03% verified error onCIFAR-10 ($\epsilon=\frac{8}{255}$) and 82.36% verified error on TinyImageNet($\epsilon=\frac{1}{255}$) using very short training schedules (160 and 80total epochs, respectively), outperforming literature SOTA trained withhundreds or thousands epochs under the same network architecture. The code isavailable at https://github.com/shizhouxing/Fast-Certified-Robust-Training.

Fast Certified Robust Training with Short Warmup