Feb. 13, 2024, 5:41 a.m. | Jianhao Ma Salar Fattahi

cs.LG updates on arXiv.org arxiv.org

We study the problem of symmetric matrix completion, where the goal is to reconstruct a positive semidefinite matrix $\rm{X}^\star \in \mathbb{R}^{d\times d}$ of rank-$r$, parameterized by $\rm{U}\rm{U}^{\top}$, from only a subset of its observed entries. We show that the vanilla gradient descent (GD) with small initialization provably converges to the ground truth $\rm{X}^\star$ without requiring any explicit regularization. This convergence result holds true even in the over-parameterized scenario, where the true rank $r$ is unknown and conservatively over-estimated by a …

convergence cs.lg gradient math.oc matrix positive show small star stat.ml study

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