CoreFlow: Low-Rank Matrix Generative Models

TL;DR

CoreFlow introduces a low-rank flow model that efficiently learns matrix distributions by capturing shared subspaces, improving generation quality especially in high-dimensional, limited-sample, and incomplete data scenarios.

Contribution

It proposes a novel geometry-preserving low-rank flow framework that separates shared matrix structure from sample-specific variation, enhancing efficiency and handling incomplete data.

Findings

Significantly improves spectral and moment-level generation quality in few-sample regimes.

Maintains competitive performance in data-rich settings.

Effective even with 9% of ambient dimension and 40% missing entries.

Abstract

Learning matrix-valued distributions from high-dimensional and possibly incomplete training data is challenging: ambient-space generative modeling is computationally expensive and statistically fragile when the matrix dimension is large but the sample size is limited. We propose CoreFlow, a geometry-preserving low-rank flow model that learns shared row/column subspaces across the matrix distribution, and then trains a continuous normalizing flow only on the induced low-dimensional core. CoreFlow is designed for settings where shared low-rank matrix geometry is present, especially in high-dimensional limited-sample regimes. This separates shared matrix geometry from sample-specific variation, preserves matrix structure, and substantially improves training efficiency. The same framework also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, CoreFlow substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even under compression to 9% of the ambient dimension and with up to 40% missing training entries.