Deep generative models have demonstrated successful applications in learning
non-linear data distributions through a number of latent variables and these
models use a nonlinear function (generator) to map latent samples into the data
space. On the other hand, the nonlinearity of the generator implies that the
latent space shows an unsatisfactory projection of the data space, which
results in poor representation learning. This weak projection, however, can be
addressed by a Riemannian metric, and we show that geodesics computation and
accurate interpolations between data samples on the Riemannian manifold can
substantially improve the performance of deep generative models. In this paper,
a Variational spatial-Transformer AutoEncoder (VTAE) is proposed to minimize
geodesics on a Riemannian manifold and improve representation learning. In
particular, we carefully design the variational autoencoder with an encoded
spatial-Transformer to explicitly expand the latent variable model to data on a
Riemannian manifold, and obtain global context modelling. Moreover, to have
smooth and plausible interpolations while traversing between two different
objects' latent representations, we propose a geodesic interpolation network
different from the existing models that use linear interpolation with inferior
performance. Experiments on benchmarks show that our proposed model can improve
predictive accuracy and versatility over a range of computer vision tasks,
including image interpolations, and reconstructions.

提出了一种变分空间转换自编码器（VTAE），通过在 Riemann 流形上最小化测地线来改善表征学习，并提高计算机视觉任务的预测准确性和适用性，包括图像插值和重构。

VTAE: 变分转换自编码器与流形学习

VTAE: Variational Transformer Autoencoder with Manifolds Learning

We present a neural network architecture based upon the Autoencoder (AE) and
Generative Adversarial Network (GAN) that promotes a convex latent distribution
by training adversarially on latent space interpolations. By using an AE as
both the generator and discriminator of a GAN, we pass a pixel-wise error
function across the discriminator, yielding an AE which produces non-blurry
samples that match both high- and low-level features of the original images.
Interpolations between images in this space remain within the latent-space
distribution of real images as trained by the discriminator, and therfore
preserve realistic resemblances to the network inputs. Code available at
this https URL

本论文提出了一种基于 Autoencoder 和生成对抗网络的神经网络结构，通过在潜在空间插值的对抗训练，促进了一个凸的潜在分布。该模型的生成器和辨别器均使用了 AE，能够生成不模糊的样本，并且具有与原始图像相匹配的高低级特征，样本间的插值也能保持真实图像的潜在空间分布，因此保留了对输入图像的逼真相似性。