# Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery

arXiv: https://arxiv.org/abs/2506.20533 · HTML: https://mlsanity.com/paper/2506.20533/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2025.

## Built on by (most cited first, 3 of 3)

- [Robust Moment-Based Estimation via Spectral Gradient Reweighting](https://mlsanity.com/paper/2605.27718/) (2026)
- [A Smoothing Newton Method for Rank-one Matrix Recovery](https://mlsanity.com/paper/2507.23017/) (2025)
- [Tight Majorizations and Convergence Rates of Nuclear Norm Minimization IRLS](https://mlsanity.com/paper/2608.23765/) (2026)

## Abstract (arXiv)

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.