相关论文: Rounding Meets Approximate Model Counting

The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of…

What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…

Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…

Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…

Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…

We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

Linear constraints are one of the most fundamental constraints in fields such as computer science, operations research and optimization. Many applications reduce to the task of model counting over integer linear constraints (MCILC). In this…

Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy…

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower…

Fast distributed algorithms that output a feasible solution for constraint satisfaction problems, such as maximal independent sets, have been heavily studied. There has been much less research on distributed sampling problems, where one…

Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problem into many separate…

We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler (2020). The task is to distinguish whether an input set $x\subseteq [n]$ has size either $k$ or…

Accurate predictions of the abundance and clustering of dark matter haloes play a key role in testing the standard cosmological model. Here, we investigate the accuracy of one of the leading methods of connecting the simulated dark matter…

Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle…

Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often…

We study the counting version of the Boolean satisfiability problem #SAT using the ZH-calculus, a graphical language originally introduced to reason about quantum circuits. Using this, we generalize #SAT to a weighted variant we call…

A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…