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Lipschitz-Certifiable Training with a Tight Outer Bound
Sungyoon Lee · Jaewook Lee · Saerom Park

Tue Dec 08 09:00 PM -- 11:00 PM (PST) @ Poster Session 2 #635
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\% ($\ell_2$-perturbation of $\epsilon=36/255$). Our code is available at \url{https://github.com/sungyoon-lee/bcp}.

Author Information

Sungyoon Lee (Seoul National University)
Jaewook Lee (Seoul National University)
Saerom Park (Sungshin Women's University)

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