Poincaré Embeddings for Learning Hierarchical Representations

These exotic (non linear algebra based) embedding representations are often slow to take off unless they have an obvious use case. The other one that I've always been curious of is Poincarré Embeddings [1] - where the embedding also has a hierarchical representation of the space. There's issues with these becoming popular: 1. Querying the embeddings requires more math knowledge than just "lol cosine similarity". This also requires to write code for the query 2. You can often easily match the performance with regular embeddings by just adding dimensions and training more. So the advantage of exotic embeddings has to be with the information in the more complex mathematical abstraction. So they need a killer usecase to become popular, it's hard to move the needle. [1]: https://arxiv.org/abs/1705.08039

that's funny, I was just reading on "Hyperbolic geometry of the olfactory space", it maps nicely to hierarchical knowledge representation: https://advances.sciencemag.org/content/4/8/eaaq1458 also see Tatyana Sharpee' argument for hyperbolic geometry in neural circuits: https://www.sciencedirect.com/science/article/abs/pii/S09594... the paper from 2010 that popularized its applications: "Hyperbolic Geometry of Complex Networks": https://arxiv.org/abs/1006.5169 A related work "Poincare embeddings for learning hierarchical representations" from 2017 is well known in "graph embeddings" space: https://arxiv.org/abs/1705.08039

Equations wrong in the original Poincare embeddings paper https://arxiv.org/abs/1705.08039 ? Do you recall which? And thanks for sharing your Lorentz implementation!

Authors learn embeddings in a Poincaré space rather than Euclidean, better for hierarchical relationships. The reference paper is a good read: Nickel & Kiela '17 "Poincaré Embeddings for Learning Hierarchical Representations", https://arxiv.org/abs/1705.08039