  With the increment of interest in leveraging machine learning technology in
safety-critical systems, the robustness of neural networks under external
disturbance receives more and more concerns. Global robustness is a robustness
property defined on the entire input domain. And a certified globally robust
network can ensure its robustness on any possible network input. However, the
state-of-the-art global robustness certification algorithm can only certify
networks with at most several thousand neurons. In this paper, we propose the
GPU-supported global robustness certification framework GROCET, which is more
efficient than the previous optimization-based certification approach.
Moreover, GROCET provides differentiable global robustness, which is leveraged
in the training of globally robust neural networks.
