A major barrier recognized by the whole community is that the loss surfaces of deep neural networks are extremely nonconvex and nonsmooth. Such nonconvexity and nonsmoothness make the analysis of the optimization and generalization properties of such networks prohibitively difficult. An intuitive approach is to bypass these geometrical properties to seek a theoretical explanation. However, some papers argue that these “intimidating” geometrical properties themselves are the major factors shaping the properties of deep neural networks and the key to explaining deep learning.