Certifying Global Robustness for Deep Neural Networks

Abstract: 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.