相关论文: A Small PRG for Polynomial Threshold Functions of …

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…

Generating high-quality random numbers with a Gaussian probability distribution function is an important and resource consuming computational task for many applications in the fields of machine learning and Monte Carlo algorithms. Recently,…

This work considers the deployment of pseudo-random number generators (PRNGs) on graphics processing units (GPUs), developing an approach based on the xorgens generator to rapidly produce pseudo-random numbers of high statistical quality.…

This paper presents an algorithm for generating pseudorandom numbers using quasigroups. Random numbers have several applications in the area of secure communication. The proposed algorithm uses a matrix of size n x n which is pre-generated…

In this work, we study the mean-field flow for learning subspace-sparse polynomials using stochastic gradient descent and two-layer neural networks, where the input distribution is standard Gaussian and the output only depends on the…

Let X be randomly chosen from {-1,1}^n, and let Y be randomly chosen from the standard spherical Gaussian on R^n. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr [X belongs to P] - Pr [Y…

This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…

We study whether a uniformly random Boolean function $f : \{-1,1\}^p \to \{-1,1\}$ is determined by its Walsh--Fourier coefficients of degree at most $d$. We show that the threshold lies at $p/2$ up to an $O(\sqrt{p \log p})$ window: if \[…

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…

A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued…

We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of polynomial threshold functions. More specifically, for a Boolean function f on n variables equal to the sign of a real, multivariate polynomial…

We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a uniform TC^0 algorithm (a uniform…

We revisit Nisan's classical pseudorandom generator (PRG) for space-bounded computation (STOC 1990) and its applications in streaming algorithms. We describe a new generator, HashPRG, that can be thought of as a symmetric version of Nisan's…

Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…

We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…

The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…

Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator…

We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states…

Assume that for every derandomization result for logspace algorithms, there is a pseudorandom generator strong enough to nearly recover the derandomization by iterating over all seeds and taking a majority vote. We prove under a precise…

We study the arithmetic complexity of hitting set generators, which are pseudorandom objects used for derandomization of the polynomial identity testing problem. We give new explicit constructions of hitting set generators whose outputs are…