We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space consists of a set of diagonal Gaussian distributions. It is known that the set of the diagonal Gaussian distributions with the Fisher information metric forms a product hyperbolic space, which we call a Gaussian manifold. To learn the VAE endowed with the Gaussian manifold, we first 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. With the newly proposed distribution, we introduce geometric transformations at the last and the first of the encoder and the decoder of VAE, respectively to help the transition between the Euclidean and Gaussian manifolds. Through the empirical experiments, we show competitive generalization performance of GM-VAE against other variants of hyperbolic- and Euclidean-VAEs. Our model achieves strong numerical stability, which is a common limitation reported with previous hyperbolic-VAEs.

通过使用高斯流形变分自编码器(GM-VAE)来提高图像数据集的密度估计和基于模型的强化学习下的环境建模。GM-VAE在估计密度任务上优于其他变量的双曲线和欧几里得VAEs，并在基于模型的强化学习中展现出竞争性的性能。

利用潜在高斯分布的双曲线VAE