Neural Network Robustness Evaluation Based on Interval Analysis.

Neural networks are widely deployed in many scenarios and have reached or exceeded human-level performance in some tasks. However, the researchers found that existing neural networks are vulnerable to attacks. One of the cases is that the network outputs the wrong result in the presence of small perturbations in the input. It indicates that the neural network does not meet the robustness. Neural networks, which do not meet robustness, will limit their application in safety-critical systems such as automatic driving and wise medical. Hence, the research on the robustness of neural networks is significant. Interval analysis is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation and can be used to calculate the exact output range of a real-valued function. Based on the theoretical framework of interval analysis, we define the interval extension of neural networks and prove that it includes the inclusion isotonicity and Lipschitzian property. It illustrates the feasibility of using interval extension to compute the output range of a neural network corresponding to a given input range. In order to evaluate the robustness of the neural network, we further analyze the characteristics of the neural network interval extension and design a neural network robustness evaluation method based on the greedy strategy. Experiment results on the MNIST and ACAS Xu datasets show that the method can effectively evaluate the robustness of the neural network with good time performance.