Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks
This work addresses safety verification for neural networks in control systems, such as robotics, but appears incremental as it builds on existing methods for specific network types.
The paper tackles the problem of estimating output reachable sets and verifying safety for multi-layer perceptron neural networks, introducing maximum sensitivity and formulating reachable set estimation as optimization problems, with an application to a robotic arm model demonstrating effectiveness.
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. 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.