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Neural networks have been widely used to solve complex real-world problems.Due to the complicate, nonlinear, non-convex nature of neural networks, formalsafety guarantees for the output behaviors of neural networks will be crucialfor their applications in safety-critical systems.In this paper, the outputreachable set computation and safety verification problems for a class ofneural networks consisting of Rectified Linear Unit (ReLU) activation functionsare addressed. A layer-by-layer approach is developed to compute outputreachable set. The computation is formulated in the form of a set ofmanipulations for a union of polyhedra, which can be efficiently applied withthe aid of polyhedron computation tools. Based on the output reachable setcomputation results, the safety verification for a ReLU neural network can beperformed by checking the intersections of unsafe regions and output reachableset described by a union of polyhedra. A numerical example of a randomlygenerated ReLU neural network is provided to show the effectiveness of theapproach developed in this paper.

Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations