Reproduce “Klein Model for Hyperbolic Neural Networks” on OpenResearch

About this paper

Yidan Mao, Jing Gu, Marcus C. Werner, Dongmian Zou

This paper introduces a comprehensive framework for implementing neural networks in the Klein model of hyperbolic space, complete with compact formulations for core operations. It formally connects Klein model geometry to Einstein gyrovector spaces and demonstrates that Klein Hyperbolic Neural Networks achieve comparable performance to existing Poincaré ball and hyperboloid models on graph node classification tasks.

Key insights

• The Klein model's straight-line geodesics simplify specific geometric operations, particularly the Einstein midpoint construction, which is beneficial for aggregation in neural networks.
• Formal equivalence exists between "tangent space constructions" in the Klein model and operations in Einstein gyrovector spaces, providing a theoretical foundation and enabling efficient computations.
• The Klein model provides a viable alternative to the more commonly used Poincaré and hyperboloid models, expanding the available options for hyperbolic deep learning applications.
• A comprehensive framework for implementing neural operations in the Klein model, especially for aggregation, was lacking in existing hyperbolic neural networks (HNNs).

Summary by alphaXiv.