# Hyperbolic Neural Networks++

arXiv: https://arxiv.org/abs/2006.08210 · HTML: https://mlsanity.com/paper/2006.08210/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Hyperbolic Chamfer Distance for Point Cloud Completion and Beyond](https://mlsanity.com/paper/2412.17951/) (2024)
- [On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks](https://mlsanity.com/paper/2411.10128/) (2024)
- [The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective](https://mlsanity.com/paper/2610.07131/) (2026)

## Abstract (arXiv)

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 Poincar'e 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.