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

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…

We introduce the Collatz-Weyl Generators, a family of uniform pseudorandom number generators (PRNGs) which are based on generalized Collatz mappings, derived from the Collatz conjecture and Weyl sequences. The high-quality statistical…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Empirical tests for pseudorandom number generators based on the use of processes or physical models have been successfuly used and are considered as complementary to theoretical test of randomness. In this work a statistical methodology for…

The hardness vs.~randomness paradigm aims to explicitly construct pseudorandom generators $G:\{0,1\}^r \rightarrow \{0,1\}^m$ that fool circuits of size $m$, assuming the existence of explicit hard functions. A ``high-end PRG'' with seed…

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…

The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

How many operations do we need on the average to compute an approximate root of a random Gaussian polynomial system? Beyond Smale's 17th problem that asked whether a polynomial bound is possible, we prove a quasi-optimal bound $\text{(input…

This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a…

We prove a new bound on the average sensitivity of polynomial threshold functions. In particular we show that a polynomial threshold function of degree $d$ in at most $n$ variables has average sensitivity at most…

In this work, we continue the line of research on the complexity of distributions (Viola, Journal of Computing 2012), and study samplers defined by low degree polynomials. An $n$-tuple $P = (P_1,\dots, P_n)$ of functions $P_i \colon…

We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…

We propose a new generator for the generalized inverse Gaussian (GIG) distribution by decomposing the density of GIG into two components. The first component is a truncated inverse Gamma density, in order to sample from which we improve the…

In the random graph $G(n,p)$ with $pn$ bounded, the degrees of the vertices are almost i.i.d Poisson random variables with mean $\gl:= p(n-1)$. Motivated by this fact, we introduce the Poisson cloning model $G_{PC} (n,p)$ for random graphs…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

We present a new secret sharing algorithm that provides the storage efficiency of an Information Dispersal Algorithm (IDA) while providing perfect secret sharing. We achieve this by mixing the input message with random bytes generated using…

We present a simple formula for the generating function for the polynomials in the $d$--dimensional semiclassical wave packets. We then use this formula to prove the associated Rodrigues formula.

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

Expander graphs are among the most useful combinatorial objects in theoretical computer science. A line of work studies random walks on expander graphs for their pseudorandomness against various classes of test functions, including…