2020/06/15 by Ryohei Shimizu, Shimizu, Ryohei, Yusuke Mukuta +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Graph Neural Networks #Applied mathematics #Artificial intelligence #Artificial neural network #Ball (mathematics) #Bandwidth (computing) #Computer science #Convolutional neural network #Distortion (music) #Euclidean geometry #Exponential stability #FOS: Computer and information sciences #Geometry #Hyperbolic geometry #Interpretation (philosophy) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Multinomial distribution #Multinomial logistic regression #Nonlinear system #Pure mathematics #Stability (learning theory) #Statistics #Topological and Geometric Data Analysis #Tree (set theory) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2006.08210
published in arXiv (Cornell University) (Cornell University) · The Ninth International Conference on Learning Representations (ICLR 2021)
openalex publication_date 2020/06/15 · openalex created_date 2020/06/19 · arxiv created 2021/03/17 · arxiv updated 2021/03/18 · openalex updated_date 2026/08/06
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.