Poincaré Embedding

A Region-Based Representation (Nickel & Kiela, NIPS 2017, Poincaré Embeddings for Learning Hierarchical Representations) that embeds objects in hyperbolic space (the Poincaré ball) instead of Euclidean space. Hyperbolic geometry expands exponentially toward its boundary, so it can embed tree-like hierarchies with low distortion in very few dimensions — general concepts sit near the origin, specific ones near the boundary, capturing hierarchy and overlapping meanings naturally.

It is a contemporary alternative to Gaussian Embedding and a precursor to Box Embedding in the search for representations that go beyond points. Trade-off versus boxes: hyperbolic distance computations are more involved than the cheap min/max intersection of axis-aligned boxes.

Related Concepts

• Region-Based Representation — the family this belongs to
• Box Embedding — Euclidean box alternative with cheap overlap
• Gaussian Embedding — Gaussian alternative
• Embeddings — point-vector baseline

Articles

• Express Words in a Box - Understanding Box Embedding from the Basics — Shun Tsukagoshi; introduces Poincaré Embedding as a region-representation precursor to boxes