  The robustness of deep neural networks has received significant interest
recently, especially when being deployed in safety-critical systems, as it is
important to analyze how sensitive the model output is under input
perturbations. While most previous works focused on the local robustness
property around an input sample, the studies of the global robustness property,
which bounds the maximum output change under perturbations over the entire
input space, are still lacking. In this work, we formulate the global
robustness certification for neural networks with ReLU activation functions as
a mixed-integer linear programming (MILP) problem, and present an efficient
approach to address it. Our approach includes a novel interleaving twin-network
encoding scheme, where two copies of the neural network are encoded
side-by-side with extra interleaving dependencies added between them, and an
over-approximation algorithm leveraging relaxation and refinement techniques to
reduce complexity. Experiments demonstrate the timing efficiency of our work
when compared with previous global robustness certification methods and the
tightness of our over-approximation. A case study of closed-loop control safety
verification is conducted, and demonstrates the importance and practicality of
our approach for certifying the global robustness of neural networks in
safety-critical systems.
