First, I will review neural networks and deep learning that lie behind the recent rise of AI. It is rather easy to explain the main ideas of this, but the questions how and why it works so well is a mystery. This black-box aspect is an important reason for many of the troubles AI is facing and the risks with this technology. In an attempt to understand deep learning better, I will introduce metrics in the neural networks and discuss tools in ergodic theory that then will be applicable, coming from a joint work with Benny Avelin. This concerns random products of transformations, which occurs in deep learning, in fact in several ways (random initialization, stochastic gradient descent and the drop-out procedure). Thanks to the basic nature of compositions of random maps, the second part of my talk could be of potential interest to some other non-ML topics of the program.