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

• 成果类型: Article
• 署名作者: Fazlyab, Mahyar; Morari, Manfred; Pappas, George J.
• 署名单位: University of Pennsylvania
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3046193
• 发表日期: 2022
• 页码: 1-15
• 关键词: Neural networks; safety; Robustness; Biological neural networks; programming; Perturbation methods; uncertainty; Convex Optimization; Deep Neural Networks; robustness analysis; safety verification; semidefinite programming (SDP)

摘要

Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the output of neural networks when their input changes within a bounded set. In this article, we propose a semidefinite programming (SDP) framework to address this problem for feed-forward neural networks with general activation functions and input uncertainty sets. 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 SDP. Our framework spans the tradeoff between conservatism and computational efficiency and applies to problems beyond safety verification. We evaluate the performance of our approach via numerical problem instances of various sizes.