Related papers: Entropy of Pseudo Random Number Generators
Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying…
A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is…
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some…
Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these…
We report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating. The error, manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to the interplay…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
This is a comment on the article "Probabilistic Integration: A Role in Statistical Computation?" by F.-X. Briol, C. J. Oates, M. Girolami, M. A. Osborne and D. Sejdinovic to appear in Statistical Science. There is a role for statistical…
In the quantum Monte Carlo (QMC) method, the Pseudo-Random Number Generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the…
Pulsars exhibit signals with precise inter-arrival times that are on the order of milliseconds to seconds, depending on the individual pulsar. There are subtle variations in the timing of pulsar signals. We show that these variations can…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
In a Monte-Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones.…
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present…
The security of many cryptographic constructions depends on random number generators for providing unpredictable keys, nonces, initialization vectors and other parameters. Modern operating systems implement cryptographic pseudo-random…
This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
Pseudorandom number generators (PRNGs) are ubiquitous in stochastic simulations and machine learning (ML), where they drive sampling, parameter initialization, regularization, and data shuffling. While widely used, the potential impact of…
The problem of constructing pseudorandom generators that fool halfspaces has been studied intensively in recent times. For fooling halfspaces over the hypercube with polynomially small error, the best construction known requires seed-length…
Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations…