Papers › Lipschitz-Certifiable Training with a Tight Outer Bound
Lipschitz-Certifiable Training with a Tight Outer Bound
Sungyoon Lee, Jaewook Lee, Saerom Park
Verifiable training is a promising research direction for training a robust network. However, most verifiable training methods are slow or lack scalability. In this study, we propose a fast and scalable certifiable training algorithm based on Lipschitz analysis and interval arithmetic. Our certifiable training algorithm provides a tight propagated outer bound by introducing the box constraint propagation (BCP), and it efficiently computes the worst logit over the outer bound. In the experiments, we show that BCP achieves a tighter outer bound than the global Lipschitz-based outer bound. Moreover, our certifiable training algorithm is over 12 times faster than the state-of-the-art dual relaxation-based method; however, it achieves comparable or better verification performance, improving natural accuracy. Our fast certifiable training algorithm with the tight outer bound can scale to Tiny ImageNet with verification accuracy of 20.1\% (ℓ₂-perturbation of ϵ=36/255). Our code is available at \url{https://github.com/sungyoon-lee/bcp}.
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