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Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To…

Fine-tuning LLMs is both computationally and memory-intensive. While parameter-efficient fine-tuning methods, such as QLoRA and DoRA, reduce the number of trainable parameters and lower memory usage, they do not decrease computational cost.…

Tagging is nowadays the most prevalent and practical way to make images searchable. However, in reality many manually-assigned tags are irrelevant to image content and hence are not reliable for applications. A lot of recent efforts have…

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant…

The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…

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…

In the field of large language model (LLM) compression, singular value decomposition (SVD) is a widely studied and adopted low-rank decomposition technique. Since SVD operates exclusively on linear modules, and these modules in LLMs are…

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

We present the first provable Least-Squares Value Iteration (LSVI) algorithms that have runtime complexity sublinear in the number of actions. We formulate the value function estimation procedure in value iteration as an approximate maximum…

Supervised fine-tuning (SFT) is a standard approach to adapting large language models (LLMs) to new domains. In this work, we improve the statistical efficiency of SFT by selecting an informative subset of training examples. Specifically,…

Computation of singular value decomposition (SVD) has been a topic of concern by many numerical linear algebra researchers. Fast SVD has been a very effective tool in computer vision in a number of aspects, such as: face recognition, eye…

This paper addresses the search for a fast and meaningful image segmentation in the context of $k$-means clustering. The proposed method builds on a widely-used local version of Lloyd's algorithm, called Simple Linear Iterative Clustering…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

Supervised fine-tuning (SFT) on visual instruction data often improves perceptual capabilities in vision-language models (VLMs) while degrading reasoning performance, creating a persistent reasoning tax during post-training. We investigate…

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by…

An enhanced Kogbetliantz method for the singular value decomposition (SVD) of general matrices of order two is proposed. The method consists of three phases: an almost exact prescaling, that can be beneficial to the LAPACK's xLASV2 routine…

Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…