Neural Information Processing Systems http://nips.cc/

Hyperbolic embeddings achieve excellent performance when embedding hierarchical data structures like synonym or type hierarchies, but they can be limited by numerical error when ordinary floating-point numbers are used to represent points in hyperbolic space. Standard models such as the Poincar{\'e} disk and the Lorentz model have unbounded numerical error as points get far from the origin. To address this, we propose a new model which uses an integer-based tiling to represent \emph{any} point in hyperbolic space with provably bounded numerical error. This allows us to learn high-precision embeddings without using BigFloats, and enables us to store the resulting embeddings with fewer bits. We evaluate our tiling-based model empirically, and show that it can both compress hyperbolic embeddings (down to 2\% of a Poincar{\'e} embedding on WordNet Nouns) and learn more accurate embeddings on real-world datasets.

The paper touches an issue that is very important and most likely the reason why hyperbolic embeddings have not been adopted widely. From my experience, hyperbolic embeddings sometimes have catastrophic results compared with competing methods. This is because of numerical instabilities. The paper is very well written with a lot of theoretical and empirical results. The solutions the authors provide is theoretically proven and very well documented.

Hyperbolic embeddings achieve excellent performance when embedding hierarchical data structures like synonym or type hierarchies, but they can be limited by numerical error when ordinary floating-point numbers are used to represent points in hyperbolic space. Standard models such as the Poincar{\'e} disk and the Lorentz model have unbounded numerical error as points get far from the origin. To address this, we propose a new model which uses an integer-based tiling to represent \emph{any} point in hyperbolic space with provably bounded numerical error. This allows us to learn high-precision embeddings without using BigFloats, and enables us to store the resulting embeddings with fewer bits. We evaluate our tiling-based model empirically, and show that it can both compress hyperbolic embeddings (down to 2\% of a Poincar{\'e} embedding on WordNet Nouns) and learn more accurate embeddings on real-world datasets.

Hyperbolic embeddings achieve excellent performance when embedding hierarchical data structures like synonym or type hierarchies, but they can be limited by numerical error when ordinary floating-point numbers are used to represent points in hyperbolic space. Standard models such as the Poincar{\'e} disk and the Lorentz model have unbounded numerical error as points get far from the origin. To address this, we propose a new model which uses an integer-based tiling to represent \emph{any} point in hyperbolic space with provably bounded numerical error. This allows us to learn high-precision embeddings without using BigFloats, and enables us to store the resulting embeddings with fewer bits. We evaluate our tiling-based model empirically, and show that it can both compress hyperbolic embeddings (down to $2\%$ of a Poincar{\'e} embedding on WordNet Nouns) and learn more accurate embeddings on real-world datasets.