In the first part of this presentation we will introduce the notion of an active strict saddle and will show that this notion is generic in the class of semi-algebraic functions.
In the second part, we will show that the stochastic subgradient descent  (SGD) on a weakly convex function avoids active strict saddles with probability one. As a consequence, ''generically'' on a weakly convex, semialgebraic function, the SGD converges to a local minimum.