Related papers: Generalizing Reduced Rank Extrapolation to Low-Ran…
In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
Document-level relation extraction (RE) aims to extract the relations between entities from the input document that usually containing many difficultly-predicted entity pairs whose relations can only be predicted through relational…
Domain-specific intelligence demands specialized knowledge and sophisticated reasoning for problem-solving, posing significant challenges for large language models (LLMs) that struggle with knowledge hallucination and inadequate reasoning…
Recent breakthroughs in large language models (LLMs) have fundamentally shifted recommender systems from discriminative to generative paradigms, where user behavior modeling is achieved by generating target items conditioned on historical…
Retrieval Augmented Generation (RAG) is a common method for integrating external knowledge into pretrained Large Language Models (LLMs) to enhance accuracy and relevancy in question answering (QA) tasks. However, prompt engineering and…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Reinforcement learning with verifiable rewards (RLVR) has proven effective in eliciting complex reasoning in large language models (LLMs). However, standard RLVR training often leads to excessively verbose processes (in reasoning tasks) and…
In many applications, it is necessary to retrieve pairs of vertices with the path between them satisfying certain constraints, since regular expression is a powerful tool to describe patterns of a sequence. To meet such requirements, in…
Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS)…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…