CoreFlow: Low-Rank Matrix Generative Models

2026-04-27

AI Summary

Modeling high-dimensional matrix distributions under limited samples and missing data remains challenging due to high computational costs and statistical instability. This work proposes CoreFlow, the first approach integrating low-rank geometric priors with continuous normalizing flows. By learning shared row and column subspaces and constructing the flow model solely on a low-dimensional core tensor, CoreFlow effectively disentangles shared geometric structure from sample-specific variations. The method enables masked Riemannian optimization and iterative imputation, substantially improving generation quality. Experimental results demonstrate that, even under extreme conditions—retaining only 9% of the original dimensions with 40% missing entries—CoreFlow outperforms existing methods in both spectral and moment-based metrics, with particularly pronounced advantages in small-sample regimes.

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.

Problem

• matrix-valued distributions
• high-dimensional data
• limited-sample regime
• incomplete data
• low-rank structure

Innovation

• low-rank matrix generative models
• continuous normalizing flow
• shared subspace learning
• masked Riemannian updates
• matrix completion