The rapid recent progress in machine learning (ML) has raised a number of scientific
questions that challenge the longstanding dogma of the field. One of the most important …

Abstract We propose $\textsf {ScaledGD ($\lambda $)} $, a preconditioned gradient descent
method to tackle the low-rank matrix sensing problem when the true rank is unknown, and …

In practical instances of nonconvex matrix factorization, the rank of the true solution $
r^{\star} $ is often unknown, so the rank $ r $ of the model can be over-specified as $ r> …

In this work, we study the performance of sub-gradient method (SubGM) on a natural
nonconvex and nonsmooth formulation of low-rank matrix recovery with ℓ1-loss, where the …

We study the asymmetric matrix factorization problem under a natural nonconvex
formulation with arbitrary overparametrization. The model-free setting is considered, with …

We consider minimizing a twice-differentiable, L-smooth, and\(\mu\)-strongly convex
objective\(\phi\) over an\(n\times n\) positive semidefinite matrix\(M\succeq 0\), under the …

Tensor-on-tensor regression: Riemannian optimization, over-parameterization, statistical-computational
gap and their interplay Page 1 The Annals of Statistics 2024, Vol. 52, No. 6, 2583–2612 …

We consider using gradient descent to minimize the nonconvex function f (X)= ϕ (XX T) over
an n× r factor matrix X, in which ϕ is an underlying smooth convex cost function defined over …

We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted
Gaussian measurements, with no prior knowledge on the intrinsic rank. We consider the …

Gradient descent (GD) is crucial for generalization in machine learning models, as it induces
implicit regularization, promoting compact representations. In this work, we examine the role …