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Certifying the safety or robustness of neural networks against inputuncertainties and adversarial attacks is an emerging challenge in the area ofsafe machine learning and control. To provide such a guarantee, one must beable to bound the output of neural networks when their input changes within abounded set. In this paper, we propose a semidefinite programming (SDP)framework to address this problem for feed-forward neural networks with generalactivation functions and input uncertainty sets. Our main idea is to abstractvarious properties of activation functions (e.g., monotonicity, bounded slope,bounded values, and repetition across layers) with the formalism of quadraticconstraints. We then analyze the safety properties of the abstracted networkvia the S-procedure and semidefinite programming. Our framework spans thetrade-off between conservatism and computational efficiency and applies toproblems beyond safety verification. We evaluate the performance of ourapproach via numerical problem instances of various sizes.

Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming