相关论文: Non-intrusive Data-driven ADI-based Low-rank Balan…

In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…

This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…

For the purpose of effective suppression of the cycle-skipping phenomenon in full waveform inversion (FWI), we developed a Deep Neural Network (DNN) approach to predict the absent low-frequency components by exploiting the implicit relation…

Parameter inference is essential when interpreting observational data using mathematical models. Standard inference methods for differential equation models typically rely on obtaining repeated numerical solutions of the differential…

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…

Large Language Models (LLMs) have achieved great success in solving difficult tasks across many domains, but such success comes with a high computation cost, and inference latency. As developers and third parties customize these models, the…

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on…

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

Emerging technologies such as Reconfigurable Intelligent Surfaces (RIS) make it possible to optimize some parameters of wireless channels. Conventional approaches require relating the channel and its programmable parameters via a simple…

In this paper we address the issue of pruning (i.e., shortening) a given interleaver via truncation of the transposition vector of the mother permutation and study its impact on the structural properties of the permutation. This method of…

We consider the problem of learning an $\varepsilon$-optimal policy in controlled dynamical systems with low-rank latent structure. For this problem, we present LoRa-PI (Low-Rank Policy Iteration), a model-free learning algorithm…

We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…

We consider the problem of estimating missing values in trajectories of linear parameter-varying (LPV) systems. We solve this interpolation problem for the class of shifted-affine LPV systems. Conditions for the existence and uniqueness of…

Diffusion models have been achieving state-of-the-art results across various generation tasks. However, a notable drawback is their sequential generation process, requiring long-sequence step-by-step generation. Existing methods, such as…

Despite all recent progress, it is still challenging to edit and manipulate natural images with modern generative models. When using Generative Adversarial Network (GAN), one major hurdle is in the inversion process mapping a real image to…

The Lagrange multiplier method has proven highly effective for mitigating the ill-conditioning of full waveform inversion (FWI), enabling robust and computationally efficient algorithms that converge to accurate velocity models even from…

We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…