1. Introduction
Recently, Deep Neural Networks (DNN) have been widely applied in various fields, such as computer vision [1], speech recognition [2], and natural language processing [3]. DNN is a multi-layer neural network model based on neurons. It learns the features and representations of data through multiple layers of nonlinear transformations and can continuously learn and train to improve its performance in processing large-scale and complex data. In some specific fields, the performance of DNN has even surpassed that of humans. However, like traditional software, DNNs also inevitably contain defects. In safety-critical fields such as autonomous driving systems, medical diagnosis, and malware detection, failures by defects of DNNs may cause disastrous consequences. For example, in the first robot-assisted heart valve surgery in UK, the mechanical arm of the robot collided with the hand of the surgeon, resulting in the aorta of patient being punctured [4]. In addition, several serious traffic accidents are caused by DNN defects in autonomous driving systems. For instance, in 2021, a Tesla vehicle equipped with autonomous driving software collided with a white cargo truck in Detroit, United States, as the autonomous driving software identified the cargo truck as the sky by mistake [5]. Similarly, in 2016 and 2019, two serious accidents occurred in Florida, United States, which also caused by erroneous behaviors of the car autonomous driving software [6], [7].