Safety
Towards Generalized Certified Robustness with Multi-Norm Training
arXiv:2410.03000v3 Announce Type: replace Abstract: Existing certified training methods can only train models to be robust against a certain perturbation type (e.g. l_infty or l_2). However, an l_inft
arXiv:2410.03000v3 Announce Type: replace Abstract: Existing certified training methods can only train models to be robust against a certain perturbation type (e.g. l_infty or l_2). However, an l_infty certifiably robust model may not be certifiably robust against l_2 perturbation (and vice versa) and also has low robustness against other perturbations (e.g. geometric and patch transformation). By constructing a theoretical framework to analyze and mitigate the tradeoff, we propose the first multi-norm certified training framework extbf{CURE}, consisting of several multi-norm certified training methods, to attain better union robustness when training from scratch or fine-tuning a pre-trained certified model. Inspired by our theoretical findings, we devise bound alignment and connect natural training with certified training for better union robustness. Compared with SOTA-certified training, extbf{CURE} improves union robustness to 32.0% on MNIST, 25.8% on CIFAR-10, and 10.6% on TinyImagenet across different epsilon values. It leads to better generalization on a diverse set of challenging unseen geometric and patch perturbations to 6.8% and 16.0% on CIFAR-10. Overall, our contributions pave a path towards extit{generalized certified robustness}.
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Source: arXiv cs.LG | 2026-04-15