We present a framework for learning disentangled and interpretable jointly continuous and discrete representations in an unsupervised manner. By augmenting the continuous latent distribution of variational autoencoders with a relaxed discrete distribution and controlling the amount of information encoded in each latent unit, we show how continuous and categorical factors of variation can be discovered automatically from data. The learned model also contains an inference network which can infer quantities such as angle and width of objects from image data in a completely unsupervised manner. Our experiments show that the framework disentangles continuous and discrete generative factors on various datasets, including disentangling digit type from stroke thickness, angle and width on MNIST, chair type from azimuth and width on the Chairs dataset and age from azimuth on CelebA.

本文提出了一种框架来无监督地学习清晰而可解释的连续和离散化的表示形式，通过增加变分自动编码机的连续潜在分布，并控制每个潜在单元中编码的信息量，展示了如何自动地从数据中发现连续和分类变化因素。实验结果显示，该框架在各种数据集上对连续和离散的生成因素进行了区分，并在离散生成因素突出时优于当前的 disentangling 方法。

学习分离的联合连续和离散表征