Related papers: Factoring with Hints
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…
We consider a version of the continuum armed bandit where an action induces a filtered realisation of a non-homogeneous Poisson process. Point data in the filtered sample are then revealed to the decision-maker, whose reward is the total…
The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the…
We consider approximation of diameter of a set $S$ of $n$ points in dimension $m$. E$\tilde{g}$ecio$\tilde{g}$lu and Kalantari \cite{kal} have shown that given any $p \in S$, by computing its farthest in $S$, say $q$, and in turn the…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
We have implemented a new way of computing three-point correlation functions. It is based on a factorization of the entire correlation function into two parts which are evaluated with open spin- (and to some extent flavor-) indices. This…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problem into many separate…
In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…