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Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

Logic in Computer Science · Computer Science 2025-03-19 Olivier Zeyen , Maxime Cordy , Martin Gubri , Gilles Perrouin , Mathieu Acher

In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product…

Data Structures and Algorithms · Computer Science 2022-03-07 Clément L. Canonne , Gautam Kamath , Audra McMillan , Jonathan Ullman , Lydia Zakynthinou

Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…

Discrete Mathematics · Computer Science 2024-11-15 Yiqiao Bao , Sampath Kannan , Erik Waingarten

We consider generalized solutions of the Perona-Malik equation in dimension one, defined as all possible limits of solutions to the semi-discrete approximation in which derivatives with respect to the space variable are replaced by…

Analysis of PDEs · Mathematics 2023-04-11 Massimo Gobbino , Nicola Picenni

This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…

Information Theory · Computer Science 2025-06-18 Hadi Kazemi , Ankit Pensia , Varun Jog

The level of distribution of a complex valued sequence $b$ measures "how well $b$ behaves" on arithmetic progressions $nd+a$. Determining whether $\theta$ is a level of distribution for $b$ involves summing a certain error over $d\leq D$,…

Number Theory · Mathematics 2021-03-30 Lukas Spiegelhofer

Motivated by applications to monotonicity testing, Lehman and Ron (JCTA, 2001) proved the existence of a collection of vertex disjoint paths between comparable sub-level sets in the directed hypercube. The main technical contribution of…

Discrete Mathematics · Computer Science 2024-12-05 Deeparnab Chakrabarty , C. Seshadhri

We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…

Machine Learning · Computer Science 2025-08-07 Puqian Wang , Nikos Zarifis , Ilias Diakonikolas , Jelena Diakonikolas

The problem of testing monotonicity of a Boolean function $f:\{0,1\}^n \to \{0,1\}$ has received much attention recently. Denoting the proximity parameter by $\varepsilon$, the best tester is the non-adaptive…

Data Structures and Algorithms · Computer Science 2018-01-10 Deeparnab Chakrabarty , C. Seshadhri

We study the uniform query reliability problem, which asks, for a fixed Boolean query Q, given an instance I, how many subinstances of I satisfy Q. Equivalently, this is a restricted case of Boolean query evaluation on tuple-independent…

Databases · Computer Science 2023-01-18 Antoine Amarilli

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Recent work has shown that the hidden states of large language models contain signals useful for uncertainty estimation and hallucination detection, motivating a growing interest in efficient probe-based approaches. Yet it remains unclear…

Computation and Language · Computer Science 2026-04-14 Joe Stacey , Hadas Orgad , Kentaro Inui , Benjamin Heinzerling , Nafise Sadat Moosavi

This report presents a neurosymbolic framework for safety verification and control synthesis in high-dimensional monotone dynamical systems without relying on explicit models or conservative Lipschitz bounds. The approach combines the…

Systems and Control · Electrical Eng. & Systems 2026-01-28 Saber Jafarpour , Alireza Nadali , Ashutosh Trivedi , Majid Zamani

Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE…

Statistics Theory · Mathematics 2025-07-01 William Gay , William He , Nicholas Kocurek , Ryan O'Donnell

To ensure reliable causal conclusions from observational (i.e., non-randomized) studies, researchers routinely conduct sensitivity analysis to assess robustness to hidden bias due to unmeasured confounding. In matched observational studies…

Methodology · Statistics 2025-11-11 Siyu Heng , Elaine K. Chiu , Hyunseung Kang

We consider a family of prior probability distributions of particular interest, all being defined on the three-dimensional convex set of two-level quantum systems. Each distribution is, following recent work of Petz and Sudar, taken to be…

Quantum Physics · Physics 2009-10-30 Paul B. Slater

All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a…

Quantum Physics · Physics 2020-09-29 Mohammad A. Alhejji , Graeme Smith

Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and…

Computational Complexity · Computer Science 2019-10-29 Sivaramakrishnan Natarajan Ramamoorthy , Cyrus Rashtchian

We provide an optimization-based argument for the monotonicity of the multiplicative algorithm (MA) for a class of optimal experimental design problems considered in Yu (2010). Our proof avoids introducing auxiliary variables (or problems)…

Optimization and Control · Mathematics 2025-08-12 Renbo Zhao

We investigate concentration properties of functions of random vectors with values in the discrete cube, satisfying the stochastic covering property (SCP) or the strong Rayleigh property (SRP). Our result for SCP measures include…

Probability · Mathematics 2021-08-31 Radosław Adamczak , Bartłomiej Polaczyk