Hyperbolic Neural Networks++
This work addresses the challenge of capturing hierarchical structures in data for machine learning applications, representing an incremental improvement with a unified hyperbolic approach.
The authors tackled the problem of embedding hierarchical data by generalizing neural network components to hyperbolic geometry, specifically the Poincaré ball model, resulting in superior parameter efficiency and performance over Euclidean methods.
Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this study, we generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincaré ball model. This novel methodology constructs a multinomial logistic regression, fully-connected layers, convolutional layers, and attention mechanisms under a unified mathematical interpretation, without increasing the parameters. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.