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, which captures the operational properties of on-line local robustness certification while yielding a natural learning objective for robust training. We show that widely-used architectures can be easily adapted to this objective by incorporating efficient global Lipschitz bounds into the network, yielding certifiably-robust models by construction that achieve state-of-the-art verifiable and clean accuracy. Notably, this approach requires significantly less time and memory than recent certifiable training methods, and leads to negligible costs when certifying points on-line; for example, our evaluation shows that it is possible to train a large tiny-imagenet model in a matter of hours. We posit that this is possible using inexpensive global bounds -- despite prior suggestions that tighter local bounds are needed for good performance -- because these models are trained to achieve tighter global bounds. Namely, we prove that the maximum achievable verifiable accuracy for a given dataset is not improved by using a local bound.

通过在网络中加入全局Lipschitz边界，文中提出的方法可以快速训练大型强健的神经网络，实现了可证明的最先进的可验证准确性。同时，该方法比最近的可证方法需要的时间和内存少得多，并在在线认证时产生可忽略的成本。

全局鲁棒神经网络