Related papers: Beyond Uniform SVD:Dual-Level Optimization across …
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…
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…
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…
Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
Accurate and early diagnosis of pneumonia through X-ray imaging is essential for effective treatment and improved patient outcomes. Recent advancements in machine learning have enabled automated diagnostic tools that assist radiologists in…
This paper evaluates Tucker decomposition and Singular Value Decomposition (SVD) for compressing neuroimaging data. Tucker decomposition preserves multi-dimensional relationships, achieving superior reconstruction fidelity and perceptual…
The randomized singular value decomposition proposed in [27] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of…
While the capabilities of generative foundational models have advanced rapidly in recent years, methods to prevent harmful and unsafe behaviors remain underdeveloped. Among the pressing challenges in AI safety, machine unlearning (MU) has…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
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…
The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
Low-rank and sparse composite approximation is a natural idea to compress Large Language Models (LLMs). However, such an idea faces two primary challenges that adversely affect the performance of existing methods. The first challenge…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…
Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study presents an innovative integration of High-Order Singular Value Decomposition (HOSVD) with Long…
Class-incremental learning aims to continuously acquire new knowledge while preserving previously learned information, thereby mitigating catastrophic forgetting. Existing methods primarily restrict parameter updates but often overlook…