Related papers: An efficient and memory free algorithm for subdiff…
The discretization of convection-diffusion equations by implicit or semi-implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as GMRES. Many techniques bearing the name of \emph{recycling…
Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
Present day computational fluid dynamics simulations generate extremely large amounts of data, sometimes on the order of TB/s. Often, a significant fraction of this data is discarded because current storage systems are unable to keep pace.…
Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Federated learning (FL) is emerging as a privacy-aware alternative to classical cloud-based machine learning. In FL, the sensitive data remains in data silos and only aggregated parameters are exchanged. Hospitals and research institutions…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…
This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the…
Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…
Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced…
Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…
This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…
From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods…
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…
Federated learning paradigm to utilize datasets across multiple data providers. In FL, cross-silo data providers often hesitate to share their high-quality dataset unless their data value can be fairly assessed. Shapley value (SV) has been…