Substantial progress has been made recently on developing provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

We consider the problem of recovering a complete (ie, square and invertible) matrix A 0,
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …

Single-index models are a class of functions given by an unknown univariate``link''function
applied to an unknown one-dimensional projection of the input. These models are …

When training deep neural networks for classification tasks, an intriguing empirical
phenomenon has been widely observed in the last-layer classifiers and features, where (i) …

We provide the first global optimization landscape analysis of Neural Collapse--an intriguing
empirical phenomenon that arises in the last-layer classifiers and features of neural …

We lower bound the complexity of finding ϵ-stationary points (with gradient norm at most ϵ)
using stochastic first-order methods. In a well-studied model where algorithms access …

This paper shows that a perturbed form of gradient descent converges to a second-order
stationary point in a number iterations which depends only poly-logarithmically on …

Over past several years, machine learning, or more generally artificial intelligence, has
generated overwhelming research interest and attracted unprecedented public attention. As …

Recent applications that arise in machine learning have surged significant interest in solving
min-max saddle point games. This problem has been extensively studied in the convex …

Owing to their connection with generative adversarial networks (GANs), saddle-point
problems have recently attracted considerable interest in machine learning and beyond. By …