Year: 2019
Type: preprint
Abstract: Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic Gaussian}, a Gaussian-like distribution on hyperbolic space whose density can be evaluated analytically and differentiated with respect to the parameters. Our distribution enables the gradient-based learning of the probabilistic models on hyperbolic space that could never have been considered before. Also, we can sample from this hyperbolic probability distribution without resorting to auxiliary means like rejection sampling. As applications of our distribution, we develop a hyperbolic-analog of variational autoencoder and a method of probabilistic word embedding on hyperbolic space. We demonstrate the efficacy of our distribution on various datasets including MNIST, Atari 2600 Breakout, and WordNet.
Source: arXiv (Cornell University)
Authors: Nagano, Yoshihiro, Yamaguchi, Shoichiro, Fujita, Yasuhiro, Koyama, Masanori
Institutions: The University of Tokyo, Preferred Networks (Japan)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Masason Foundation
OpenAlex ID: W2944617599