CoreFlow用低秩流模型高效生成高维不完整矩阵数据。
CoreFlow: Low-Rank Matrix Generative Models
- 通过共享行/列子空间，将矩阵生成压缩到低维核心空间。
- 在样本少、缺失40%数据时仍保持高质量生成，压缩至9%维度仍有效。
- 适合高维小样本或含缺失值的矩阵生成任务，如生物、金融数据。
从高维且可能不完整的训练数据中学习矩阵值分布极具挑战：当矩阵维度高而样本量有限时，环境空间生成模型计算成本高且统计性能脆弱。我们提出CoreFlow，一种保持几何结构的低秩流模型，该模型学习矩阵分布中的共享行/列子空间，并仅在诱导的低维核心上训练连续归一化流。CoreFlow适用于存在共享低秩矩阵几何的场景，尤其在高维小样本情形下。该方法将共享矩阵几何与样本特异性变化分离，保持矩阵结构，显著提升训练效率。同一框架通过掩码黎曼更新和迭代补全处理不完整训练矩阵。在真实与合成基准测试中，CoreFlow在少样本条件下大幅提升了谱级和矩级生成质量，即使在压缩至9%环境维度、训练数据缺失高达40%的情况下仍保持竞争力。
原文摘要 · Abstract (English)
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.
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