Related papers: CUR Low Rank Approximation at Deterministic Sublin…

Low-Rank Adaptation (LoRA) is a widely-used parameter-efficient finetuning method for large language models. LoRA saves memory by training only low rank perturbations to selected weight matrices. In this work, we compare the performance of…

Continual learning in Neural Machine Translation (NMT) faces the dual challenges of catastrophic forgetting and the high computational cost of retraining. This study establishes Low-Rank Adaptation (LoRA) as a parameter-efficient framework…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

The selection of hyper-parameters is critical in Deep Learning. Because of the long training time of complex models and the availability of compute resources in the cloud, "one-shot" optimization schemes - where the sets of hyper-parameters…

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not…

We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

In this work, we present randomized compression algorithms for flat rank-structured matrices with shared bases, termed uniform Block Low-Rank (BLR) matrices. Our main contribution is a technique called tagging, which improves upon the…

Recent large language models (LLMs) employ billions of parameters to enable broad problem-solving capabilities. Such language models also tend to be memory-bound because of the dominance of matrix-vector and matrix-matrix multiplications…

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…

Matrix completion is a ubiquitous tool in machine learning and data analysis. Most work in this area has focused on the number of observations necessary to obtain an accurate low-rank approximation. In practice, however, the cost of…

In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…

In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…

Long-range tasks demand reasoning over long inputs. However, existing solutions are limited, e.g., long-context models require large compute budgets, parameter-efficient fine-tuning (PEFT) needs training data, and retrieval-augmented…

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac-Frenkel…

Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face several challenges, including the need for rank adaptivity,…

Adapting large language models (LLMs) to downstream tasks via full fine-tuning is increasingly impractical due to its computational and memory demands. Parameter-efficient fine-tuning (PEFT) approaches such as Low-Rank Adaptation (LoRA)…

Low-Rank Adaptation (LoRA) dominates parameter-efficient fine-tuning (PEFT). However, it faces a ``linear ceiling'': increasing the rank yields diminishing returns in expressive capacity due to intrinsic linear constraints. We introduce…

In multi-core systems, various factors like inter-process communication, dependency, resource sharing and scheduling, level of parallelism, synchronization, number of available cores etc. influence the extent of possible High Performance…