Related papers: An Improved Incremental Singular Value Decompositi…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we…
We study mixed finite element/Crank--Nicolson discretizations of a nonlinear Oldroyd problem with general nonsingular and weakly singular memory kernels. Direct evaluation of the history term requires storing all previous velocity…
We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe…
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…
Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…
Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes…
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…
In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…
Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…
There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems…
Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular…
This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…
Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…
Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…
The randomized singular value decomposition (RSVD) is by now a well established technique for efficiently computing an approximate singular value decomposition of a matrix. Building on the ideas that underpin the RSVD, the recently proposed…
This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…