Verification of Neural Network Robustness Against Weight Perturbations Using Star Sets

Neural network reliability is susceptible to perturbations in both inputs and model weights. While formal verification of neural network robustness against input perturbations is a hot topic, robustness analysis against weight perturbations remains an emergent area of research. Neural network weights are subject to hardware vulnerabilities and environmental changes, posing significant risks to system reliability in safety-critical applications such as autonomous driving and medical diagnostics. To address this issue, we introduce ‘ModelStar,’ a novel framework that utilizes reachability analysis to evaluate the robustness of deep neural networks (DNNs) against weight perturbations. ModelStar employs a linear set propagation technique to analyze the impact of an infinite family of parameter variations on DNN outputs. Our results demonstrate that ModelStar surpasses existing methods in analysing the impact of perturbations, verifying DNN robustness on up to 60% more samples in image classification tasks. Besides providing tighter robustness bounds than existing methods, ModelStar allows formal robustness verification against weight perturbations in any linear layer, a capability not supported by prior work, to our knowledge. This advancement marks a significant step towards the reliable use of DNN accelerators in safety-critical applications.