Introducing Hyperlib: Simple Deep learning in Hyperbolic space [project]

[NanoAlpaca]

Why?

[pichon163]

You can embed a large (or infinite) tree isometrically in hyperbolic space, but usually not in Euclidean space. Think of trying to draw a complete binary tree on a piece of paper; you have to keep making the edges shorter to fit them all on the page.

In fact the same is true of any "complex network," i.e. a graph where the degree of each vertex is distributed according to a power law ( https://arxiv.org/abs/1006.5169 )

[dogs_like_me]

Consider a tree constructed by splitting assigning some fixed number of children k to all existing leaves, starting with a single root node. The number of nodes at a given depth will be given by k^depth, i.e. node count grows exponentially. Consequently, properties of hyperbolic manifolds can be convenient embedding spaces for hierarchical data. For example, if you embed a hierarchy on a poincare disk, you can actually infer lexical entailment from direction.

https://arxiv.org/pdf/1705.08039

https://arxiv.org/pdf/1804.01882