Efficient Global Robustness Certification of Neural Networks via Interleaving Twin-Network Encoding
This work addresses the need for verifying neural network safety in critical systems, though it is incremental as it builds on existing global robustness certification methods.
The paper tackles the problem of certifying the global robustness of neural networks across the entire input space, presenting an efficient approach using a novel interleaving twin-network encoding scheme and over-approximation algorithm, with experiments showing improved timing efficiency and tightness compared to previous methods.
The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While most previous works focused on the local robustness property around an input sample, the studies of the global robustness property, which bounds the maximum output change under perturbations over the entire input space, are still lacking. In this work, we formulate the global robustness certification for neural networks with ReLU activation functions as a mixed-integer linear programming (MILP) problem, and present an efficient approach to address it. Our approach includes a novel interleaving twin-network encoding scheme, where two copies of the neural network are encoded side-by-side with extra interleaving dependencies added between them, and an over-approximation algorithm leveraging relaxation and refinement techniques to reduce complexity. Experiments demonstrate the timing efficiency of our work when compared with previous global robustness certification methods and the tightness of our over-approximation. A case study of closed-loop control safety verification is conducted, and demonstrates the importance and practicality of our approach for certifying the global robustness of neural networks in safety-critical systems.