Region-Based Representation
A family of embedding methods that represent an object as a region of space — a shape with volume — rather than a single point. Because a region has extent, it can express things a point cannot: the spread of a concept’s meaning, containment (hierarchy / hypernymy), and overlap (relatedness, set-theoretic relations).
Motivation: point embeddings (Word2Vec, BERT) encode similarity as distance/direction, but a point has no volume, so “animal” cannot be shown to contain “dog” and “cat”. Region representations restore that asymmetry.
The Main Variants
| Variant | Shape | Captures | Note |
|---|---|---|---|
| Gaussian Embedding | Gaussian distribution | Spread via variance; uncertainty | Vilnis & McCallum, ICLR 2015 |
| Poincaré Embedding | Point in hyperbolic space | Tree-like hierarchy with few dims | Nickel & Kiela, NIPS 2017 |
| Box Embedding | Axis-aligned box | Containment, intersection, volume | Cheapest exact overlap calculation |
Boxes are the most widely applied of the three precisely because intersection and volume are trivial to compute (per-dimension min/max), whereas Gaussian overlap and hyperbolic distances are costlier.
Related Concepts
- Box Embedding — region as a box
- Gaussian Embedding — region as a Gaussian
- Poincaré Embedding — region/hierarchy in hyperbolic space
- Set-Theoretic Embeddings — the relations regions make expressible
- Compositional Embeddings — composing regions via set operations
- Embeddings — point-representation baseline this family extends
Articles
- Express Words in a Box - Understanding Box Embedding from the Basics — Shun Tsukagoshi; surveys the region-representation family before focusing on boxes