Randomized numerical linear algebra-RandNLA, for short-concerns the use of
randomization as a resource to develop improved algorithms for large-scale linear algebra …

This paper explores challenges in training Physics-Informed Neural Networks (PINNs),
emphasizing the role of the loss landscape in the training process. We examine difficulties in …

Large matrices arise in many machine learning and data analysis applications, including as
representations of datasets, graphs, model weights, and first and second-order derivatives …

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 …

Ill-conditioned problems are ubiquitous in large-scale machine learning: as a data set grows
to include more and more features correlated with the labels, the condition number …

The essential difficulty of gradient-based bilevel optimization using implicit differentiation is
to estimate the inverse Hessian vector product with respect to neural network parameters …

This paper develops a scalable new algorithm, called NysADMM, to minimize a smooth
convex loss function with a convex regularizer. NysADMM accelerates the inexact …

Gaussian process (GP) is a Bayesian model which provides several advantages for
regression tasks in machine learning such as reliable quantitation of uncertainty and …

This work is concerned with computing low-rank approximations of a matrix function for a
large symmetric positive semidefinite matrix, a task that arises in, eg, statistical learning and …

We present a new class of preconditioned iterative methods for solving linear systems of the
form Ax= b. Our methods are based on constructing a low-rank Nyström approximation to A …