Fast Certified Robust Training with Short Warmup

TL;DR

This paper introduces three improvements to IBP-based certified robust training, enabling significantly faster training with shorter warmup periods while maintaining state-of-the-art robustness guarantees.

Contribution

The authors propose a new weight initialization, full Batch Normalization, and a regularization technique to improve IBP training stability and speed, reducing warmup epochs needed for certification.

Findings

Achieved 65.03% verified error on CIFAR-10 with only 160 epochs.

Achieved 82.36% verified error on TinyImageNet with only 80 epochs.

Outperformed previous methods requiring hundreds or thousands of epochs.

Abstract

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