# Hyperbolic Geometry and Poincaré Embeddings

This post is finally going to get back to some ML related topics. In fact, the original reason I took that whole math-y detour in the previous posts was to more deeply understand this topic. It turns out trying to under tensor calculus and differential geometry (even to a basic level) takes a while! Who knew? In any case, we're getting back to our regularly scheduled program.

In this post, I'm going to explain one of the applications of an abstract area of mathematics called hyperbolic geometry. The reason why this area is of interest is because there has been a surge of research showing its application in various fields, chief among them is a paper by Facebook researchers [1] in which they discuss how to utilize a model of hyperbolic geometry to represent hierarchical relationships. I'll cover some of the math weighting more towards intuition, show some of their results, and also show some sample code from Gensim. Don't worry, this time I'll try much harder not going to go down the rabbit hole of trying to explain all the math (no promises though).

(Note: If you're unfamiliar with tensors or manifolds, I suggest getting a quick overview with my previous two posts: Tensors, Tensors, Tensors and Manifolds: A Gentle Introduction)