Related papers: Potential Hessian Ascent: The Sherrington-Kirkpatr…
The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…
Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…
We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution…
We present a randomized algorithm for producing a quasi-optimal hierarchically semi-separable (HSS) approximation to an $N\times N$ matrix $A$ using only matrix-vector products with $A$ and $A^T$. We prove that, using $O(k \log(N/k))$…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of…
Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z,…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
A common practice in obtaining a semiparametric efficient estimate is through iteratively maximizing the (penalized) log-likelihood w.r.t. its Euclidean parameter and functional nuisance parameter via Newton-Raphson algorithm. The purpose…
We study a class of nonlinear eigenvalue problems of Schr\"{o}dinger type, where the potential is singular on a set of points. Such problems are widely present in physics and chemistry, and their analysis is of both theoretical and…
We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…