Hyperbolic VAE via Latent Gaussian Distributions

Seunghyuk Cho, Juyong Lee, Dongwoo Kim

Keywords: Hyperbolic space, VAE, Distribution on hyperbolic space, RL, Hierarchical representation learning

TL;DR: We propose a hyperbolic VAE whose latent space consists of Gaussian distributions and provides strong numerical stability, addressing a common limitation reported in previous hyperbolic-VAEs.

Abstract: We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space consists of a set of Gaussian distributions. It is known that the set of the univariate Gaussian distributions with the Fisher information metric form a hyperbolic space, which we call a Gaussian manifold. To learn the VAE endowed with the Gaussian manifolds, we propose a pseudo-Gaussian manifold normal distribution based on the Kullback-Leibler divergence, a local approximation of the squared Fisher-Rao distance, to define a density over the latent space. In experiments, we demonstrate the efficacy of GM-VAE on two different tasks: density estimation of image datasets and environment modeling in model-based reinforcement learning. GM-VAE outperforms the other variants of hyperbolic- and Euclidean-VAEs on density estimation tasks and shows competitive performance in model-based reinforcement learning. We observe that our model provides strong numerical stability, addressing a common limitation reported in previous hyperbolic-VAEs.

Type Of Submission: Extended Abstract (4 pages, non-archival)

Submission Number: 85