Nonlinear Isometric Manifold Learning for Injective Normalizing Flows
This work addresses data modeling challenges for researchers in machine learning, but it is incremental as it builds on prior injective normalizing flow techniques.
The paper tackled the problem of modeling manifold data with normalizing flows by using isometric autoencoders to create embeddings with explicit inverses that preserve probability distributions, resulting in high-quality data generation on flat manifolds and simplified model selection compared to existing methods.
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.