ReachNN: Reachability Analysis of Neural-Network Controlled Systems
This work addresses the safety verification problem for neural-network controlled systems, which is critical for applications like autonomous vehicles, but it is incremental as it extends existing methods to more general activation functions.
The paper tackles the challenge of verifying safety in neural-network controlled systems by proposing a reachability analysis approach based on Bernstein polynomials, which can handle a broader set of activation functions, including heterogeneous networks, and demonstrates effectiveness on various benchmarks.
Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for verifying neural network controlled systems are limited to a few specific activation functions. In this work, we propose a new reachability analysis approach based on Bernstein polynomials that can verify neural-network controlled systems with a more general form of activation functions, i.e., as long as they ensure that the neural networks are Lipschitz continuous. Specifically, we consider abstracting feedforward neural networks with Bernstein polynomials for a small subset of inputs. To quantify the error introduced by abstraction, we provide both theoretical error bound estimation based on the theory of Bernstein polynomials and more practical sampling based error bound estimation, following a tight Lipschitz constant estimation approach based on forward reachability analysis. Compared with previous methods, our approach addresses a much broader set of neural networks, including heterogeneous neural networks that contain multiple types of activation functions. Experiment results on a variety of benchmarks show the effectiveness of our approach.