Simple, Fast and Efficient Injective Manifold Density Estimation with Random Projections
This provides a principled and efficient baseline for generative modeling, bridging random projection theory with normalizing flows, though it appears incremental as it builds on existing flow-based methods.
The paper tackles the problem of injective manifold density estimation by introducing Random Projection Flows (RPFs), a framework that uses random semi-orthogonal matrices to project data into lower-dimensional latent spaces, resulting in a plug-and-play, efficient method with closed-form expressions for volume correction.
We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn from Haar-distributed orthogonal ensembles via QR decomposition of Gaussian matrices, to project data into lower-dimensional latent spaces for the base distribution. Unlike PCA-based flows or learned injective maps, RPFs are plug-and-play, efficient, and yield closed-form expressions for the Riemannian volume correction term. We demonstrate that RPFs are both theoretically grounded and practically effective, providing a strong baseline for generative modeling and a bridge between random projection theory and normalizing flows.