{"ID":2842039,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.09925","arxiv_id":"2511.09925","title":"Global Convergence of Four-Layer Matrix Factorization under Random Initialization","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2511.09925","url_pdf":"https://arxiv.org/pdf/2511.09925v2","authors":"[\"Minrui Luo\",\"Weihang Xu\",\"Xiang Gao\",\"Maryam Fazel\",\"Simon Shaolei Du\"]","published":"2025-11-13T03:40:10Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}