Mathematical Background¶
Mathematical foundations of hyperbolic geometry and Riemannian optimization.
Work in Progress
This page is under construction.
Topics to Cover¶
Manifold Theory¶
- Tangent spaces
- Exponential and logarithmic maps
- Parallel transport
- Riemannian metrics
Hyperbolic Geometry¶
- Models of hyperbolic space (Poincaré, Hyperboloid)
- Geodesics
- Curvature
Riemannian Optimization¶
- Riemannian gradients
- Exponential map updates
- Momentum on manifolds
References¶
Key papers implemented in Hyperbolix:
- Ganea et al. (2018): "Hyperbolic Neural Networks"
- Bécigneul & Ganea (2019): "Riemannian Adaptive Optimization Methods"
- Bdeir et al. (2023): "Fully Hyperbolic Convolutional Neural Networks"
[Detailed content coming soon]