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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…
Robust Principal Component Analysis (RPCA) and its associated non-convex relaxation methods constitute a significant component of matrix completion problems, wherein matrix factorization strategies effectively reduce dimensionality and…
Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning (PEFT) method that learns weight updates $\Delta W = AB$ for pretrained weights $W$ through low-rank adapters $A$ and $B$. While LoRA ensures hardware efficiency,…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
The low-rank matrix approximation problem with respect to the component-wise $\ell_1$-norm ($\ell_1$-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine…
Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…
Low-rank factorization is a popular model compression technique that minimizes the error $\delta$ between approximated and original weight matrices. Despite achieving performances close to the original models when $\delta$ is optimized, a…
Low-Rank Adaptation (LoRA) has proven effective in reducing computational costs while maintaining performance comparable to fully fine-tuned foundation models across various tasks. However, its fixed low-rank structure restricts its…
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…
In this work, we propose norm-bounded low-rank adaptation (NB-LoRA) for parameter-efficient fine tuning. NB-LoRA is a novel parameterization of low-rank weight adaptations that admits explicit bounds on each singular value of the adaptation…
Low-Rank Adaptation (LoRA) is a widely used Parameter-Efficient Fine-Tuning (PEFT) method that updates an initial weight matrix $W_0$ with a delta matrix $\Delta W$ consisted by two low-rank matrices $A$ and $B$. A previous study suggested…
From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises…
In this paper we generalize and extend an idea of low-rank adaptation (LoRA) of large language models (LLMs) based on Transformer architecture. Widely used LoRA-like methods of fine-tuning LLMs are based on matrix factorization of gradient…
We primarily study a special a weighted low-rank approximation of matrices and then apply it to solve the background modeling problem. We propose two algorithms for this purpose: one operates in the batch mode on the entire data and the…
Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matrices can be performed at sublinear cost -- by using much…
As large language models (LLMs) continue to scale in size, the computational overhead has become a major bottleneck for task-specific fine-tuning. While low-rank adaptation (LoRA) effectively curtails this cost by confining the weight…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
Transformer models have achieved remarkable results in various natural language tasks, but they are often prohibitively large, requiring massive memories and computational resources. To reduce the size and complexity of these models, we…