If you want to know the details, you should read the article more thoroughly. There is no back-propagation (or any training) involved, as this article is about

If you want to know the details, you should read the article more thoroughly. There is no back-propagation (or any training) involved, as this article is about what kinds of things neural networks can do in principle. I.e. how we can be sure that neural networks can in theory solve some problem we have. In practice, you have to actually find a network (by training) that solves your problem with a reasonable amount of resources, using the data you have, and that's a whole other issue (in fact, an entire research field!).