Related papers: Decentralized Singular Value Decomposition for Lar…

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…

In usual (non-stochastic) tensor network calculations, the truncated singular value decomposition (SVD) is often used for approximating a tensor, and it causes systematic errors. By introducing stochastic noise in the approximation,…

The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…

In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch…

We propose a new hypermatrix singular value decomposition based upon the spectral decomposition of the symmetric products of transposes.

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of…

A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…

Distributed machine learning has been widely studied in the literature to scale up machine learning model training in the presence of an ever-increasing amount of data. We study distributed machine learning from another perspective, where…

This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…

With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value…

In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…

Despite the groundbreaking success of diffusion models in generating high-fidelity images, their latent space remains relatively under-explored, even though it holds significant promise for enabling versatile and interpretable image editing…

This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value…

Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

Decentralized control of mobile robotic sensor networks is a fundamental problem in robotics that has attracted intensive research in recent decades. Most of the existing works dealt with two-dimensional spaces. This report is concerned…