  A globally robust deep neural network resists perturbations on all meaningful
inputs. Current robustness certification methods emphasize local robustness,
struggling to scale and generalize. This paper presents a systematic and
efficient method to evaluate and verify global robustness for deep neural
networks, leveraging the PAC verification framework for solid guarantees on
verification results. We utilize probabilistic programs to characterize
meaningful input regions, setting a realistic standard for global robustness.
Additionally, we introduce the cumulative robustness curve as a criterion in
evaluating global robustness. We design a statistical method that combines
multi-level splitting and regression analysis for the estimation, significantly
reducing the execution time. Experimental results demonstrate the efficiency
and effectiveness of our verification method and its capability to find rare
and diversified counterexamples for adversarial training.
