Atlas flow : compatible local structures on the manifold
This work addresses the challenge of understanding complex data manifolds, such as those in generative models like StyleGAN2, by providing a method to integrate local structures into a coherent global framework, which is incremental in nature.
The paper tackles the problem of analyzing global manifold structure by ensuring compatibility between overlapping local regions, proposing Atlas flow, a generative model that reattaches these regions and demonstrates good performance on synthetic datasets with noise.
In this paper, we focus on the intersections of a manifold's local structures to analyze the global structure of a manifold. We obtain local regions on data manifolds such as the latent space of StyleGAN2, using Mapper, a tool from topological data analysis. We impose gluing compatibility conditions on overlapping local regions, which guarantee that the local structures can be glued together to the global structure of a manifold. We propose a novel generative flow model called Atlas flow that uses compatibility to reattach the local regions. Our model shows that the generating processes perform well on synthetic dataset samples of well-known manifolds with noise. Furthermore, we investigate the style vector manifold of StyleGAN2 using our model.