Verifying Robustness of Neural Networks with Abstract Features

The neural networks are vulnerable, as they are easily affected by small perturbations on the input. So, it is crucial to ensure stability and robustness in high-security scenarios. Many approaches aim to verify the robustness of neural networks by defining robust regions. However, these approaches do not fully represent the feature regions accurately, leading to imprecise robustness boundaries. In this paper, we propose a method to capture the abstract features based on abstract interpretation theory, and then to verify the robustness of the neural networks. Firstly, samples are divided into decision-making and non-decision-making states, the decision-making states correspond to real output classifications in the abstract output domain. Then, iterating from the abstract output domain to the input domain, to obtain the abstract features associated with the decision-making states. Experimental results demonstrate the effectiveness of the obtained abstract features, and more accuracy in verifying robustness boundaries compared to the strategy of defining robust regions.