Related papers: Second Moment Method on k-SAT: a General Framework
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
This technical report presents implementation of two symbolic model checking algorithms that use SAT/SMT Solvers, namely interpolation based model checking and k-induction based model checking. We also do a comparative analysis of these two…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
In this paper, we present a general response-time analysis and schedulability-test framework, called k2Q (k to Q). It provides automatic constructions of closed-form quadratic bounds or utilization bounds for a wide range of applications in…
Recent advancements in machine learning have accelerated its widespread adoption across various real-world applications. However, in safety-critical domains, the deployment of machine learning models is riddled with challenges due to their…
This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
We develop a generalized method of moments (GMM) approach for fast parameter estimation in a new class of Dirichlet latent variable models with mixed data types. Parameter estimation via GMM has been demonstrated to have computational and…
We study the task of learning latent-variable models. A common algorithmic technique for this task is the method of moments. Unfortunately, moment-based approaches are hampered by the fact that the moment tensors of super-constant degree…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data. We call an input…
Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in…
Let $\phi$ be a fixed Hecke--Maass form for $\mathrm{SL}_3 (\mathbb{Z})$ and $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\mathrm{SL}_2 (\mathbb{Z}) $. Let $1/4+t_j^2$ be the Laplace eigenvalue of $u_j $. In this paper,…
This paper studies moment and tensor recovery problems whose decomposing vectors are contained in some given semialgebraic sets. We propose Moment-SOS relaxations with generic objectives for recovering moments and tensors, whose…
Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results…
We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…
Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the…