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Random reshuffling techniques are prevalent in large-scale applications, such as training neural networks. While the convergence and acceleration effects of random reshuffling-type methods are fairly well understood in the smooth setting,…
In standard generative adversarial network (SGAN), the discriminator estimates the probability that the input data is real. The generator is trained to increase the probability that fake data is real. We argue that it should also…
Traditional quantum random number generators can produce only one type of random number, while the optimal distribution of random numbers for different applications is usually distinct. The typical solution to this challenge is either using…
Heterogeneous Graph Neural Networks (HGNNs) are powerful tools for deep learning on heterogeneous graphs. Typical HGNNs require repetitive message passing during training, limiting efficiency for large-scale real-world graphs. Recent…
Back-propagation is a popular machine learning algorithm that uses gradient descent in training neural networks for supervised learning, but can be very slow. A number of algorithms have been developed to speed up convergence and improve…
Cryptographic random number generation is critical for any quantum safe encryption. Based on the natural uncertainty of some quantum processes, variety of quantum random number generators or QRNGs have been created with physical quantum…
We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs). Denote $n$ and $w$ as the length and the width of a ROBP. We have the following results. For standard ROBPs, we give an…
Random numbers are an essential resource to many applications, including cryptography and Monte Carlo simulations. Quantum random number generators (QRNGs) represent the ultimate source of randomness, as the numbers are obtained by sampling…
Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[…
The article presents and evaluates a scalable FRaGenLP algorithm for generating random linear programming problems of large dimension $n$ on cluster computing systems. To ensure the consistency of the problem and the boundedness of the…
We discuss the current state of the art of Quantum Random Number Generators (QRNG) and their possible applications in the search for quantum advantages. To this aim, we first discuss a possible way of benchmarking QRNG by applying them to…
This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…
The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random…
We propose a rejection sampling scheme using the discriminator of a GAN to approximately correct errors in the GAN generator distribution. We show that under quite strict assumptions, this will allow us to recover the data distribution…
In simulations, probabilistic algorithms and statistical tests, we often generate random integers in an interval (e.g., [0,s)). For example, random integers in an interval are essential to the Fisher-Yates random shuffle. Consequently,…
Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for…
The Recoil Growth algorithm, proposed in 1999 by Consta et al., is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding…
Delay differential equations (DDE) can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator (RNG) might be…
In this article, we propose a new counter-based implementation of John von Neumann's middle-square random number generator (RNG). Several rounds of squaring are applied to a counter to produce a random output. We discovered that four rounds…
For globally connected devices like smart phones, personal computers and Internet-of-things devices, the ability to generate random numbers is essential for execution of cryptographic protocols responsible for information security.…