相关论文: Hitting-sets for low-distance multilinear depth-3

In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…

As we push the boundaries of performance in various vision tasks, the models grow in size correspondingly. To keep up with this growth, we need very aggressive pruning techniques for efficient inference and deployment on edge devices.…

In modern multilabel classification problems, each data instance belongs to a small number of classes from a large set of classes. In other words, these problems involve learning very sparse binary label vectors. Moreover, in large-scale…

Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…

We give a shorter proof of a slightly weaker version of a theorem of Nets Katz and the author. We prove that if a set of $L$ lines in $\mathbb{R}^3$ contains at most $L^{1/2}$ lines in any low degree algebraic surface, then the number of…

Given a polygonal workspace $W$, a depth sensor placed at point $p=(x,y)$ inside $W$ and oriented in direction $\theta$ measures the distance $d=h(x,y,\theta)$ between $p$ and the closest point on the boundary of $W$ along a ray emanating…

Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…

In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on…

In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…

We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…

3D object detection is an essential task in autonomous driving. Recent techniques excel with highly accurate detection rates, provided the 3D input data is obtained from precise but expensive LiDAR technology. Approaches based on cheaper…

Given a set $P$ of $n$ points and a set $S$ of $m$ disks in the plane, the disk hitting set problem asks for a smallest subset of $P$ such that every disk of $S$ contains at least one point in the subset. The problem is NP-hard. In this…

The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…

For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…

We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…

$\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\eps}{\varepsilon} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}} \newcommand{\IntRange}[1]{[ #1 ]}…

Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…

Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…

A set $P = H \cup \{w\}$ of $n+1$ points in general position in the plane is called a wheel set if all points but $w$ are extreme. We show that for the purpose of counting crossing-free geometric graphs on such a set $P$, it suffices to…