Module product_manifold 

Product Manifolds: Mixed-Curvature Geometry

Real-world data often combines multiple structural types:

• Hierarchical: Trees, taxonomies → Hyperbolic space (H^n)
• Flat/Grid: General embeddings → Euclidean space (E^n)
• Cyclical: Periodic patterns → Spherical space (S^n)

Product manifolds combine these: M = H^h × E^e × S^s

Benefits

• 20x memory reduction on taxonomy data vs pure Euclidean
• Better hierarchy preservation through hyperbolic components
• Natural cyclical modeling through spherical components

References

• Gu et al. (2019): Learning Mixed-Curvature Representations in Product Spaces
• Skopek et al. (2020): Mixed-Curvature VAEs

Structs

ProductManifold

Product manifold: M = E^e × H^h × S^s

ProductManifoldConfig

Configuration for a product manifold

Enums

CurvatureType

Type of curvature for a manifold component