Random Projection Flows for Efficient Manifold Density Estimation

תקציר מקורי באנגליתarXiv:2509.25228v3 Announce Type: replace Abstract: Accurate density estimation is crucial for understanding complex high-dimensional data, but it becomes challenging when the data lies on or near low-dimensional manifolds. Random projections provide a natural way to reduce dimensionality while approximately preserving geometric structure, enabling effective density estimation in these settings. We introduce \emph{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 dist