Hyperbolic VAE via Latent Gaussian Distributions

• URL: http://arxiv.org/abs/2209.15217v3
• Date: Sun, 29 Oct 2023 06:18:12 GMT
• Title: Hyperbolic VAE via Latent Gaussian Distributions
• Authors: Seunghyuk Cho, Juyong Lee, Dongwoo Kim
• Abstract summary: We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space consists of a set of Gaussian distributions. 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.
• Score: 7.258394470200572
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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