Related papers: A Reexamination of the COnfLUX 2.5D LU Factorizati…

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is…

The Factored Frontier (FF) algorithm is a simple approximate inferencealgorithm for Dynamic Bayesian Networks (DBNs). It is very similar tothe fully factorized version of the Boyen-Koller (BK) algorithm, butinstead of doing an exact update…

The components underpinning PLMs -- large weight matrices -- were shown to bear considerable redundancy. Matrix factorization, a well-established technique from matrix theory, has been utilized to reduce the number of parameters in PLM.…

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…

Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new…

We consider Guth's approach to the Fourier restriction problem via polynomial partitioning. By writing out his induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms, we…

Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…

We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…

Endpoint divergences in the convolution integrals appearing in next-to-leading-power factorization theorems prevent a straightforward application of standard methods to resum large logarithmic power-suppressed corrections in collider…

Collaborative filtering models based on matrix factorization and learned similarities using Artificial Neural Networks (ANNs) have gained significant attention in recent years. This is, in part, because ANNs have demonstrated good results…

This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…

Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges…

In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…

Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…

We propose a novel factorization algorithm that leverages the theory underlying the SQUFOF method, including reduced quadratic forms, infrastructural distance, and Gauss composition. We also present an analysis of our method, which has a…

Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is…

On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…

Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the…