Implicit Regularization in Perturbed Deep Matrix Factorization: Spectral Conditions and Stability

ArXi:2605.28613v1 Announce Type: cross This paper studies the stability of low-rank implicit regularization in perturbed deep matrix factorization, where the target matrix is corrupted by a noise matrix. We first derive sufficient spectral conditions under which gradient descent exhibits a low-rank phase in the noiseless setting. These conditions show how the target spectrum, initialization, and step size jointly determine the existence of a nonempty low-rank interval.