Related papers: How Does the Low-Rank Matrix Decomposition Help In…

Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…

Most efforts in interpretability in deep learning have focused on (1) extracting explanations of a specific downstream task in relation to the input features and (2) imposing constraints on the model, often at the expense of predictive…

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

Recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. We…

Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the…

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…

The latest advancements in neural image compression show great potential in surpassing the rate-distortion performance of conventional standard codecs. Nevertheless, there exists an indelible domain gap between the datasets utilized 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…

In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the…

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.…

Deep learning has significantly advanced medical imaging analysis, yet variations in image resolution remain an overlooked challenge. Most methods address this by resampling images, leading to either information loss or computational…

We present a new framework for self-supervised representation learning by formulating it as a ranking problem in an image retrieval context on a large number of random views (augmentations) obtained from images. Our work is based on two…

This work tackles the problem of semi-supervised learning of image classifiers. Our main insight is that the field of semi-supervised learning can benefit from the quickly advancing field of self-supervised visual representation learning.…

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…

Deep learning methods for super-resolution of a remote sensing scene from multiple unregistered low-resolution images have recently gained attention thanks to a challenge proposed by the European Space Agency. This paper presents an…

This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix…