Related papers: CUR Low Rank Approximation at Deterministic Sublin…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
Low-rank adaptation is a popular parameter-efficient fine-tuning method for large language models. In this paper, we analyze the impact of low-rank updating, as implemented in LoRA. Our findings suggest that the low-rank updating mechanism…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
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…
Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory…
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…
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…
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…
The Automatic Amortized Resource Analysis (AARA) derives program-execution cost bounds using types. To do so, AARA often makes use of cost-free types, which are critical for the composition of types and cost bounds. However, inferring…
Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally…
Low-rank Adaptation (LoRA) has gained popularity as a fine-tuning approach for Large Language Models (LLMs) due to its low resource requirements and good performance. While a plethora of work has investigated improving LoRA serving…
Fine-tuning large language models (LLMs) is computationally expensive, and Low-Rank Adaptation (LoRA) provides a cost-effective solution by approximating weight updates through low-rank matrices. In real-world scenarios, LLMs are fine-tuned…
A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…
We introduce and study the problem of consistent low-rank approximation, in which rows of an input matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ arrive sequentially and the goal is to provide a sequence of subspaces that well-approximate the…
We study the computational limits of Low-Rank Adaptation (LoRA) for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient…
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…
Retrieval-augmented generation (RAG) with large language models (LLMs) is especially valuable in specialized domains, where precision is critical. To more specialize the LLMs into a target domain, domain-specific RAG has recently been…
In fine-tuning large language models (LLMs), conserving computational resources while maintaining effectiveness and improving outcomes within the same computational constraints is crucial. The Low-Rank Adaptation (LoRA) strategy balances…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…