# Global Convergence of Four-Layer Matrix Factorization under Random Initialization

arXiv: https://arxiv.org/abs/2511.09925 · HTML: https://mlsanity.com/paper/2511.09925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2025.

## Abstract (arXiv)

Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theory for two-layer matrix factorization is well-established, no global convergence guarantee for general deep matrix factorization under random initialization has been established to date. To address this gap, we provide a polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization, given certain conditions on the target matrix and a standard balanced regularization term. Our analysis employs new techniques to show saddle-avoidance properties of gradient decent dynamics, and extends previous theories to characterize the change in eigenvalues of layer weights.