Geometric Analysis of Noisy Low-rank Matrix Recovery in the Exact Parameterized and the Overparameterized Regimes

Abstract

We study noisy matrix sensing in both exact-parametrization and overparametrization regimes. The analysis quantifies how the restricted-isometry property shapes the non-convex landscape, bounds the distance of local minimizers from the ground truth, and proves a strict-saddle property that yields global convergence of perturbed gradient descent.