hyptorch 0.1.3

Suite of hyperbolic neural networks in PyTorch

A suite of hyperbolic neural networks in PyTorch, primarily focused on the Poincaré ball model of hyperbolic geometry.

Overview

HypTorch provides tools for working with neural networks in hyperbolic space, including:

• Poincaré ball model operations
• Hyperbolic layers and modules
• Distance calculations in hyperbolic space
• Mappings between models (Poincaré to Klein and vice versa)
• Manifold abstractions for geometric operations

Installation

pip install hyptorch

Mathematical Background

Poincaré Ball Model

The Poincaré ball model is a model of hyperbolic geometry where the entire hyperbolic space is mapped to the interior of a Euclidean unit ball. The Poincaré ball has a negative curvature, which is represented by the parameter curvature in this library.

Some key operations include:

• Möbius addition: The equivalent of "adding" two points in hyperbolic space
• Exponential map: Mapping from the tangent space to the manifold
• Logarithmic map: Mapping from the manifold to the tangent space
• Parallel transport: Moving tangent vectors along geodesics

Applications

Hyperbolic neural networks are particularly effective for:

• Hierarchical data structures
• Tree-like data
• Network/graph embedding
• Natural language processing
• Any data with inherent hierarchical structure