论文标题
双曲线通过潜在高斯分布
Hyperbolic VAE via Latent Gaussian Distributions
论文作者
论文摘要
我们提出了一个高斯流动性自动编码器（GM-VAE），其潜在空间由一组高斯分布组成。众所周知，带有Fisher Information指标的单变量高斯分布的集合形成双曲线空间，我们称之为高斯歧管。为了学习具有高斯流形的VAE，我们提出了基于kullback-leibler Divergence（平方Fisher-rao距离的局部近似）的伪高斯歧管正态分布，以在潜在空间上定义一个密度。在实验中，我们证明了GM-VAE对两个不同任务的功效：基于模型的增强学习中图像数据集的密度估计和环境建模。 GM-VAE在密度估计任务上优于双曲线和欧几里得 - 视频的其他变体，并在基于模型的强化学习中表现出竞争性能。我们观察到我们的模型提供了强大的数值稳定性，并解决了以前的双曲线vaes中报告的共同限制。
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.
