Related papers: An SVD-like Decomposition of Bounded-Input Bounded…

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…

A central objective in computer vision is to design models with appropriate 2-D inductive bias. Desiderata for 2D inductive bias include two-dimensional position awareness, dynamic spatial locality, and translation and permutation…

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…

Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this work, we present a new construction where the regularization…

The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on…

The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…

The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…

An important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors…

There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…

Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…

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…

In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an…

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…

In this job we have introduced a filtered adaptive technique that allows highlighting selective seismic events according to its polarization. This technique consists in the implementation of a polarizing filter based on the Single Value…

The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with…

Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…

This paper describes the singular value decomposition (SVD) of the Poisson kernel for the Dirichlet problem for the Laplacian on bounded regions in R^N, N >=2. This operator is a compact linear transformation from L^2 of the boundary to L^2…

A main object of our study is multiset functions -- that is, permutation-invariant functions over inputs of varying sizes. Deep Sets, proposed by \cite{zaheer2017deep}, provides a \emph{universal representation} for continuous multiset…

Representation learning and exploration are among the key challenges for any deep reinforcement learning agent. In this work, we provide a singular value decomposition based method that can be used to obtain representations that preserve…

We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe…