首次证明IRLS可全局收敛到低维子空间，理论突破。
Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
- 用动态平滑正则化改进IRLS，实现从任意初值收敛
- 线性收敛至真实子空间，且适用于仿射子空间场景
- 为神经网络低维训练提供新思路，适合做理论研究者
鲁棒子空间估计在机器学习与数据分析中至关重要。迭代加权最小二乘法（IRLS）是一种优雅且实证有效的方案，但其理论性质长期不明。本文在确定性条件下，证明一种带有动态平滑正则化的IRLS变体，能从任意初始化出发线性收敛至底层子空间。该结果扩展至仿射子空间估计，这是此前缺乏恢复理论的设置。此外，通过低维神经网络训练的应用展示了IRLS的实际优势。本工作首次为鲁棒子空间恢复中的IRLS提供了全局收敛保证，并更广泛地为黎曼流形上的非凸IRLS提供了理论支持。
原文摘要 · Abstract (English)
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain poorly understood. This paper establishes that, under deterministic conditions, a variant of IRLS with dynamic smoothing regularization converges linearly to the underlying subspace from any initialization. We extend these guarantees to affine subspace estimation, a setting that lacks prior recovery theory. Additionally, we illustrate the practical benefits of IRLS through an application to low-dimensional neural network training. Our results provide the first global convergence guarantees for IRLS in robust subspace recovery and, more broadly, for nonconvex IRLS on a Riemannian manifold.
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