Related papers: On the Optimality of CVOD-based Column Selection

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…

In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we proposed an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD) of a set of…

The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this…

Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…

We derive error bounds for CUR matrix approximation using determinant-based methods that relate local projection errors to global approximation quality. For general matrices, we establish determinant identities for bordered Gramian matrices…

We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called…

Pillar-based 3D object detection has gained traction in self-driving technology due to its speed and accuracy facilitated by the artificial densification of pillars for GPU-friendly processing. However, dense pillar processing fundamentally…

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified…

As Deep Neural Networks are becoming more popular, much of the attention is being devoted to Computer Vision problems that used to be solved with more traditional approaches. Video frame interpolation is one of such challenges that has seen…

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy…

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

The recently developed interpolative separable density fitting (ISDF) decomposition is a powerful way for compressing the redundant information in the set of orbital pairs, and has been used to accelerate quantum chemistry calculations in a…

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…