The wide deployment of deep neural networks, though achieving great success in many domains, has severe safety and reliability concerns. Existing adversarial attack generation and automatic verification techniques cannot formally verify whether a network is globally robust, i.e., the absence or not of adversarial examples in the input space. To address this problem, we develop a global robustness verification framework with three components: 1) a novel rule-based ``back-propagation'' finding which input region is responsible for the class assignment by logic reasoning; 2) a new network architecture Sliding Door Network (SDN) enabling feasible rule-based ``back-propagation''; 3) a region-based global robustness verification (RGRV) approach. Moreover, we demonstrate the effectiveness of our approach on both synthetic and real datasets.
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