I found your article very helpful and enlightening, as I was not familiar with hyperbolic geometry before. I learned that hyperbolic geometry has many applications in physics, such as special relativity, general relativity, and astrophysics. I also learned that there are different ways of representing hyperbolic space in a Euclidean space, such as the Poincaré ball model, which is a disk where the distance between points increases as they approach the boundary. I also learned that there are various methods and challenges for developing hyperbolic deep neural networks, which are neural networks that operate in hyperbolic space.

I think your article is very relevant and timely, as hyperbolic geometry and machine learning are both active and important fields of research. I appreciate your effort to make this topic accessible and understandable to a general audience. I would recommend your article to anyone who is interested in learning more about hyperbolic geometry and machine learning.