# Global convergence of gradient descent for phase retrieval

arXiv: https://arxiv.org/abs/2410.09990 · HTML: https://mlsanity.com/paper/2410.09990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 13 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [A Geometric Analysis of Phase Retrieval](https://mlsanity.com/paper/1602.06664/) (2016)
- [Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval](https://mlsanity.com/paper/1803.07726/) (2018)
- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [Phase Retrieval using Alternating Minimization](https://mlsanity.com/paper/1306.0160/) (2013)
- [Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems](https://mlsanity.com/paper/1505.05114/) (2015)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [PhaseMax: Convex Phase Retrieval via Basis Pursuit](https://mlsanity.com/paper/1610.07531/) (2016)
- [Phase retrieval with random Gaussian sensing vectors by alternating projections](https://mlsanity.com/paper/1609.03088/) (2016)
- [Solving phase retrieval with random initial guess is nearly as good as by spectral initialization](https://mlsanity.com/paper/2101.03540/) (2021)
- [Global convergence of the gradient method for functions definable in o-minimal structures](https://mlsanity.com/paper/2303.03534/) (2023)
- [Concentration of Non-Isotropic Random Tensors with Applications to Learning and Empirical Risk Minimization](https://mlsanity.com/paper/2102.04259/) (2021)
- [The Local Landscape of Phase Retrieval Under Limited Samples](https://mlsanity.com/paper/2311.15221/) (2023)

## Abstract (arXiv)

We propose a tensor-based criterion for benign landscape in phase retrieval and establish boundedness of gradient trajectories. This implies that gradient descent will converge to a global minimum for almost every initial point.