Related papers: On Hardness Assumptions Needed for "Extreme High-E…

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A…

A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…

Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…

We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form psi(P(x)), where P is a low-degree polynomial and psi is a function with small Lipschitz…

We present an explicit pseudorandom generator for oblivious, read-once, width-$3$ branching programs, which can read their input bits in any order. The generator has seed length $\tilde{O}( \log^3 n ).$ The previously best known seed length…

In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…

These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…

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…

The hardcore model on a graph $G$ with parameter $\lambda>0$ is a probability measure on the collection of all independent sets of $G$, that assigns to each independent set $I$ a probability proportional to $\lambda^{|I|}$. In this paper we…

Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is…

As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…

High quality random numbers are necessary in the modern world. Ranging from encryption keys in cyber security to models and simulations for scientific use: it's important that these random numbers are of high quality and quickly attainable.…

We establish that a large, flexible class of long, high redundancy error correcting codes can be efficiently and accurately decoded with guessing random additive noise decoding (GRAND). Performance evaluation demonstrates that it is…

We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…

The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a…

A weight-$t$ halfspace is a Boolean function $f(x)=$sign$(w_1 x_1 + \cdots + w_n x_n - \theta)$ where each $w_i$ is an integer in $\{-t,\dots,t\}.$ We give an explicit pseudorandom generator that $\delta$-fools any intersection of $k$…

Pseudorandom codes (PRCs), introduced by Christ and Gunn (CRYPTO '2024), are error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings, while still being decodable by someone holding the key.…

Generating secure random numbers is vital to the security and privacy infrastructures we rely on today. Having a computer system generate a secure random number is not a trivial problem due to the deterministic nature of computer systems.…