Related papers: Integer Factorisation, Fermat & Machine Learning o…
We revisit Schnorr's lattice-based integer factorization algorithm, now with an effective point of view. We present effective versions of Theorem 2 of Schnorr's "Factoring integers and computing discrete logarithms via diophantine…
The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We…
Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…
We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…
The problem of factorising positive integer $N$ into two integer factors $x$ and $y$ is first reformulated as an optimisation problem over the positive integer domain of either of the Diophantine polynomials $Q_N(x,y)=N^2(N-xy)^2 +…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…
Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for…
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($k\geq 3$) terms to quadratic terms…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…