Related papers: Superfast Low Rank Approximation
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…
Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer,…
Low-rank adaptation (LoRA) has been prominently employed for parameter-efficient fine-tuning of large language models (LLMs). However, the limited expressive capacity of LoRA, stemming from the low-rank constraint, has been recognized as a…
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
We study the $\ell_0$-Low Rank Approximation Problem, where the goal is, given an $m \times n$ matrix $A$, to output a rank-$k$ matrix $A'$ for which $\|A'-A\|_0$ is minimized. Here, for a matrix $B$, $\|B\|_0$ denotes the number of its…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…
Although the advancements of pre-trained Large Language Models have significantly accelerated recent progress in NLP, their ever-increasing size poses significant challenges for conventional fine-tuning, especially in memory-intensive…
Low-rank adaptations (LoRAs) have revolutionized the finetuning of large foundation models, enabling efficient adaptation even with limited computational resources. The resulting proliferation of LoRAs presents exciting opportunities for…
Fine-tuning large language models (LLMs) is crucial for improving their performance on downstream tasks, but full-parameter fine-tuning (Full-FT) is computationally expensive and memory-intensive. Parameter-efficient fine-tuning (PEFT)…
Low-rank Adaptation (LoRA) has emerged as a powerful method for fine-tuning large-scale foundation models. Despite its popularity, the theoretical understanding of LoRA has remained limited. This paper presents a theoretical analysis of…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
Low-Rank Adaptation (LoRA) is a widely adopted parameter-efficient fine-tuning (PEFT) method for Large Language Models (LLMs), but it still incurs notable overhead and suffers from parameter interference in complex datasets. While recent…