I am quite happy to see this paper with @NunoGalo and @jlperla in print. We emphasize that deep learning works because it automatically learns useful state-space representations. Transforming the state space is an old technique in economics. For example, we have been solving models in logs instead of levels for decades. The problem is that, in general, it is difficult to find the best representations: why logs and not another transformation? Deep learning finds these transformations by using an approximation class that has enough expressiveness. While I am very happy with the paper, I believe I can dig deeper into this idea, and I am already well advanced with a follow-up paper, where I am using geometry to clarify many further ideas in ways I find very transparent. Stay tuned!