Related papers: Pass-Efficient Randomized LU Algorithms for Comput…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…
The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the…
Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV)…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
While Convolutional Neural Networks (CNNs) excel at learning complex latent-space representations, their over-parameterization can lead to overfitting and reduced performance, particularly with limited data. This, alongside their high…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Gaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…
Post-training KV-Cache compression methods typically either sample a subset of effectual tokens or quantize the data into lower numerical bit width. However, these methods cannot exploit redundancy in the hidden dimension of the KV tensors.…
CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…
Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and…
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…
Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…
Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…