Lipschitz-Certifiable Training with a Tight Outer Bound
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}.
Code (1)
Similar Papers 제목 키워드 기반
Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Bounds
Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschi…
Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxation
Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challen…
1-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustness
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community h…
Globally-Robust Neural Networks
The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness,…
1-Lipschitz Layers Compared: Memory Speed and Certifiable Robustness
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently the scientific communit…