Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems, which can be efficiently solved by using convex optimization tools. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.