Module hyperbolic 

Hyperbolic embeddings using the Poincaré ball model.

The Poincaré ball model embeds hierarchical data (trees, taxonomies, ontologies) in hyperbolic space where distances naturally encode hierarchical relationships. Nodes close to the root are near the origin; leaf nodes are near the boundary.

Use cases in Oxios:

• Persona hierarchy (parent → child relationships)
• Skill graph (prerequisite chains)
• Memory category taxonomy

Reference: “Poincaré Embeddings for Learning Hierarchical Representations” (Nickel & Kiela, 2017)

Structs

HyperbolicConfig

Configuration for hyperbolic operations.

HyperbolicEmbedding

Hyperbolic embedding manager for hierarchical data.

Functions

batch_euclidean_to_poincare

Batch-convert Euclidean vectors to Poincaré ball points.

euclidean_to_poincare

Convert a Euclidean vector to a point on the Poincaré ball.

hyperbolic_distance

Compute the hyperbolic distance between two points on the Poincaré ball.

mobius_add

Möbius addition: the hyperbolic analog of vector addition.

mobius_scalar_mul

Möbius scalar multiplication: scaling in hyperbolic space.