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 …

Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

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 …

Minimax optimization has found extensive applications in modern machine learning, in
settings such as generative adversarial networks (GANs), adversarial training and multi …

Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

We provide new theoretical insights on why over-parametrization is effective in learning
neural networks. For a $ k $ hidden node shallow network with quadratic activation and $ n …

Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

We prove lower bounds on the complexity of finding ϵ ϵ-stationary points (points x such that
‖ ∇ f (x) ‖ ≤ ϵ‖∇ f (x)‖≤ ϵ) of smooth, high-dimensional, and potentially non-convex …

Many important geometric estimation problems naturally take the form of synchronization
over the special Euclidean group: estimate the values of a set of unknown group elements x …