相关论文: Zolotarev Quadrature Rules and Load Balancing for …

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…

Self-training (ST) is a simple yet effective semi-supervised learning method. However, why and how ST improves generalization performance by using potentially erroneous pseudo-labels is still not well understood. To deepen the understanding…

Sparse attention methods exploit the inherent sparsity in attention to speed up the prefilling phase of long-context inference, mitigating the quadratic complexity of full attention computation. While existing sparse attention methods rely…

The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

Despite considerable progress in neural relevance ranking techniques, search engines still struggle to process complex queries effectively - both in terms of precision and recall. Sparse and dense Pseudo-Relevance Feedback (PRF) approaches…

Parameter-Efficient Fine-Tuning (PEFT) effectively adapts pre-trained transformers to downstream tasks. However, the optimization of tasks performance often comes at the cost of generalizability in fine-tuned models. To address this issue,…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…

We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

Table retrieval is the task of retrieving the most relevant tables from large-scale corpora given natural language queries. However, structural and semantic discrepancies between unstructured text and structured tables make embedding…

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…

For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their…

A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…

Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmooth Riemannian optimization problem associated with the…

In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…