Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations
This work addresses safety verification for neural networks in safety-critical systems, representing an incremental advance by applying polyhedron-based methods to ReLU networks.
The paper tackles the problem of computing output reachable sets and verifying safety for neural networks with ReLU activations, developing a layer-by-layer approach that formulates computations as manipulations on unions of polyhedra, and demonstrates effectiveness through a numerical example on a randomly generated network.
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed to compute output reachable set. The computation is formulated in the form of a set of manipulations for a union of polyhedra, which can be efficiently applied with the aid of polyhedron computation tools. Based on the output reachable set computation results, the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra. A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper.