Related papers: Random Variate Generation with Formal Guarantees

This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…

Random numbers are essential for our modern information based society e.g. in cryptography. Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms but rather on a physical…

A random number generator is proposed based on a theorem about existence of chaos in fixed point iteration of x= cot2(x). Digital computer simulation of this function iteration exhibits random behavior. A method is proposed to extract…

Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For…

We describe a methodology and standard of proof for experimental claims of quantum random number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations,…

An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

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,…

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…

Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy.…

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…

We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with…

We study the problem of generating a random variate $X$ from a finite discrete probability distribution $P$ using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number…

Random numbers are commonly used in many different fields, ranging from simulations in fundamental science to security applications. In some critical cases, as Bell's tests and cryptography, the random numbers are required to be both secure…

As large language models (LLMs) are increasingly used across various applications, there is a growing need to control text generation to satisfy specific constraints or requirements. This raises a crucial question: Is it possible to…

This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the…

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm…

A C library for random number generation, Randompack, is presented. The library implements several modern random number generators (engines), including xoshiro256, PCG64, Philox, ranlux++, and sfc64; 14 continuous distributions including…