Related papers: Fractional Pseudorandom Generators from Any Fourie…

Pseudo-random number generators (PRNGs) are widely used in modern computing and are expected to exhibit excellent statistical performance and repeatability. This study evaluates and compares modern PRNGs used in high performance computing…

One of the key results in Robertson and Seymour's seminal work on graph minors is the Grid-Minor Theorem (also called the Excluded Grid Theorem). The theorem states that for every grid $H$, every graph whose treewidth is large enough…

We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative…

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square site percolation model. A generator suitable for high precision calculations is identified from an application specific…

We study the problem of strongly refuting semirandom $k$-LIN$(\mathbb{F})$ instances: systems of $k$-sparse inhomogeneous linear equations over a finite field $\mathbb{F}$. For the case of $\mathbb{F} = \mathbb{F}_2$, this is the…

Machine learning is a rapidly advancing field with diverse applications across various domains. One prominent area of research is the utilization of deep learning techniques for solving partial differential equations(PDEs). In this work, we…

Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interesting aspects of stochastic optimizers by using heavy-tailed…

We analyze a random walk strategy on undirected regular networks involving power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a `simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks' with…

In a high dimensional multiple testing framework, we present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. The coverage probability holds simultaneously over all subsets S, which means that…

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…

Trustworthiness of generative language models (GLMs) is crucial in their deployment to critical decision making systems. Hence, certified risk control methods such as selective prediction and conformal prediction have been applied to…

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on rational sublattice which coincides with the Galois field. The period of the trajectories increases as a function of lattice size and…

In this paper, we are concerned with mean hitting time $\langle\mathcal{H}\rangle$ for random walks on recursive growth tree networks that are built based on an arbitrary tree as the seed via implementing various primitive graphic…

We study the problem of obtaining lower bounds for polynomial calculus (PC) and polynomial calculus resolution (PCR) on proof degree, and hence by [Impagliazzo et al. '99] also on proof size. [Alekhnovich and Razborov '03] established that…

Polynomial identity testing and arithmetic circuit lower bounds are two central questions in algebraic complexity theory. It is an intriguing fact that these questions are actually related. One of the authors of the present paper has…

In the first part of this paper, we enumerate exactly walks on the square lattice that start from the origin, but otherwise avoid the non positive horizontal half-axis. We call them "walks on the slit plane". We count them by their length,…

Given a matrix $A\in \mathrm{GL}_d(\mathbb{Z})$. We study the pseudorandomness of vectors $\mathbf{u}_n$ generated by a linear recurrent relation of the form $$ \mathbf{u}_{n+1} \equiv A \mathbf{u}_n \pmod {p^t}, \qquad n = 0, 1, \ldots, $$…

Pseudo-random number generators (PRNGs) are essential in a wide range of applications, from cryptography to statistical simulations and optimization algorithms. While uniform randomness is crucial for security-critical areas like…

Recent generative models based on score matching and flow matching have significantly advanced generation tasks, but their potential in discriminative tasks remains underexplored. Previous approaches, such as generative classifiers, have…