Robustness Analysis of Neural Networks via Semidefinite Programming

Monday, October 21, 2019 - 4:00pm to Tuesday, October 22, 2019 - 4:55pm

Event Calendar Category

LIDS Seminar Series

Speaker Name

George Pappas


University of Pennsylvania

Building and Room Number



Deep neural networks have dramatically impacted machine learning problems in numerous fields. Despite these major advances, neural networks are not robust and hence not suitable for safety-critical applications. In this lecture, we will present a novel framework for analyzing the robustness of deep neural networks against norm-bounded nonlinearities. In particular, we develop a semidefinite programming (SDP) framework for safety verification and robustness analysis of neural networks with general activation functions. Our main idea is to abstract various properties of activation functions (e.g., monotonicity, bounded slope, bounded values, and repetition across layers) with the formalism of quadratic constraints. We then analyze the safety properties of the abstracted network via the S-procedure and semidefinite programming. Compared to other approaches proposed in the literature, our method is less conservative, especially for deep networks, with an order of magnitude reduction in computational complexity. Furthermore, our approach is applicable to any activation functions. Such bounds are very important in analyzing the safety of control systems regulated by neural networks.


George J. Pappas is the UPS Foundation Professor and Chair of the Department of Electrical and Systems Engineering at the University of Pennsylvania. He also holds a secondary appointment in the Departments of Computer and Information Sciences, and Mechanical Engineering and Applied Mechanics. He is a member of the GRASP Lab and the PRECISE Center. He has previously served as the Deputy Dean for Research in the School of Engineering and Applied Science. His research focuses on control theory and in particular, hybrid systems, embedded systems, hierarchical and distributed control systems, with applications to unmanned aerial vehicles, distributed robotics, green buildings, and biomolecular networks. He is a Fellow of IEEE, IFAC, and has received various awards such as the Antonio Ruberti Young Researcher Prize, the George S. Axelby Award, the O. Hugo Schuck Best Paper Award, the National Science Foundation PECASE, and the George H. Heilmeier Faculty Excellence Award.