Theoretical analysis of norm selection for robustness verification of neural networks
Saharat Saengsawang, Guoqiang Li · Physical Communication · 2023
In the robustness verification of neural network, Lp-norm is generally used to measure the distance between two different data. However, different kinds of Lp-norm examine the specific differences between each dimension of the data. Some Lp-norm computational methods magnify specific differences between datasets. To verify the robustness of the network, the usual method is to calculate the different robustness radii of the L∞-norm. But which Lp norm performs best under a given network is rarely considered. To better reflect the nature of the network, this paper proposes a theoretical analysis of the robustness of the network that can be verified by choosing any norm type, and the relationship between the size of Lp-ball corresponding to different robust radii is proved. We conducted experiments on different classification networks and obtained a general norm selection method. As a result, a specific norm can be considered first for network robustness without computing all the different Lp-norm.