Related papers: Fast Witness Counting
The goal of this paper is to improve the generality and accuracy of open-vocabulary object counting in images. To improve the generality, we repurpose an open-vocabulary detection foundation model (GroundingDINO) for the counting task, and…
We study the problem of learning vector-valued linear predictors: these are prediction rules parameterized by a matrix that maps an $m$-dimensional feature vector to a $k$-dimensional target. We focus on the fundamental case with a convex…
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its…
In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…
It is widely acknowledged that the convergence proof of the error in the $l_{\infty}$ norm of the high-order finite difference method (FDM) and finite element method (FEM) in 2D is challenging. In this paper, we derive the sixth-order…
The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a…
In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all…
We present algorithms for the $(1+\epsilon)$-approximate version of the closest vector problem for certain norms. The currently fastest algorithm (Dadush and Kun 2016) for general norms has running time of $2^{O(n)} (1/\epsilon)^n$. We…
Speaker verification is to judge the similarity between two unknown voices in an open set, where the ideal speaker embedding should be able to condense discriminant information into a compact utterance-level representation that has small…
Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical…
The problem of model counting, also known as #SAT, is to compute the number of models or satisfying assignments of a given Boolean formula $F$. Model counting is a fundamental problem in computer science with a wide range of applications.…
Here we consider a class of $2\otimes2\otimes d$ chessboard density matrices starting with three-qubit ones which have positive partial transposes with respect to all subsystems. To investigate the entanglement of these density matrices, we…
This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…
A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector…
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…