RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior

Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key idea of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, called RG-Flow, which can separate different scale information of images with disentangle representations at each scale. We demonstrate our method mainly on the CelebA dataset and show that the disentangled representation at different scales enables semantic manipulation and style mixing of the images. To visualize the latent representation, we introduce the receptive fields for flow-based models and find receptive fields learned by RG-Flow are similar to convolutional neural networks. In addition, we replace the widely adopted Gaussian prior distribution by sparse prior distributions to further enhance the disentanglement of representations. One of the most important unsupervised learning tasks is to learn the data distribution and build generative models. Over the past few years, various types of generative models have been proposed. Yet the latent variables are on equal footing and mixed globally. Here, we propose a new flow-based model, RG-Flow, which is inspired by the idea of renormalization group in statistical physics. RG-Flow imposes locality and hierarchical structure in bijective transformations. It allows us to access different scale information in original images by latent variables at different locations, which offers better explainability.