A random m× n matrix S is an oblivious subspace embedding (OSE) with parameters є> 0,
δ∈(0, 1/3) and d≤ m≤ n, if for any d-dimensional subspace W⊆ R n, P (∀ x∈ W (1+ є)− 1 …

We give a stochastic optimization algorithm that solves a dense n× n real-valued linear
system Ax= b, returning x such that|| A x− b||≤ є|| b|| in time: Õ ((n 2+ nk ω− 1) log1/є), where …

We take a random matrix theory approach to random sketching and show an asymptotic first-
order equivalence of the regularized sketched pseudoinverse of a positive semidefinite …

Superposition--when a neural network represents more``features''than it has dimensions--
seems to pose a serious challenge to mechanistically interpreting current AI systems …

Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear
functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas …

The Dynamic Mode Decomposition (DMD) is a versatile and increasingly popular method for
data driven analysis of dynamical systems that arise in a variety of applications in, eg …

We employ random matrix theory to establish consistency of generalized cross validation
(GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling …

Parker and Lê introduced random butterfly transforms (RBTs) as a preprocessing technique
to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure …

The Dynamic Mode Decomposition (DMD) is a method for computational analysis of
nonlinear dynamical systems in data driven scenarios. Based on high fidelity numerical …

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This
class of problems appears widely in a variety of applications in machine learning and …