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

TL;DR

RG-Flow is a hierarchical, explainable flow-based generative model that leverages renormalization group ideas and sparse priors to disentangle image features at multiple scales, enabling semantic manipulation and efficient inpainting.

Contribution

It introduces a novel hierarchical flow model combining RG concepts and sparse priors, improving disentanglement, interpretability, and computational complexity over previous models.

Findings

Disentangled representations enable semantic image manipulation.

Receptive fields of RG-Flow resemble those of CNNs.

The model achieves $O( ext{log }L)$ complexity for inpainting tasks.

Abstract

Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further enhance the disentanglement of representations. From a theoretical perspective, our proposed method has $O(\log L)$ complexity for inpainting of an image with edge length $L$, compared to previous generative models with $O(L^2)$ complexity.