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A good visual representation is an inference map from observations (images) to features (vectors) that faithfully reflects the hidden modularized generative factors (semantics). In this paper, we formulate the notion of "good"…
Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…
We propose a dual system for unsupervised object segmentation in video, which brings together two modules with complementary properties: a space-time graph that discovers objects in videos and a deep network that learns powerful object…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
Although QR iterations dominate in eigenvalue computations, there are several important cases when alternative LR-type algorithms may be preferable. In particular, in the symmetric tridiagonal case where differential qd algorithm with…
In this paper, we describe a new algorithm that approximates the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi eigenvalue method for symmetric matrices…
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value ecomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning,…
Extracting informative representations from videos is fundamental for effectively learning various downstream tasks. We present a novel approach for unsupervised learning of meaningful representations from videos, leveraging the concept of…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…
In this paper, we study the convergence properties of an iterative algorithm for fast nonlinear model predictive control of quasi-linear parameter-varying systems without inequality constraints. Compared to previous works considering this…
Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most…
Iterative graph algorithms often compute intermediate values and update them as computation progresses. Updated output values are used as inputs for computations in current or subsequent iterations; hence the number of iterations required…