2019/06/25 by Chao Huang, Jiameng Fan, Huang, Chao +7 · 1 citation
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Formal Methods in Verification #Machine Learning (cs.LG) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1906.10654
openalex publication_date 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.