Related papers: Hitting-sets for low-distance multilinear depth-3

In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…

In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation…

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…

This paper presents HITNet, a novel neural network architecture for real-time stereo matching. Contrary to many recent neural network approaches that operate on a full cost volume and rely on 3D convolutions, our approach does not…

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable…

This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…

We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…

We consider the problem of finding a near ground state of a $p$-spin model with Rademacher couplings by means of a low-depth circuit. As a direct extension of the authors' recent work [Gamarnik, Jagannath, Wein 2020], we establish that any…

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…

We consider a class of $0$-$1$ polynomial programming termed multiple choice polynomial programming (MCPP) where the constraint requires exact one component per subset of the partition to be $1$ after all the entries are partitioned.…

High-dimensional feature vectors are likely to contain sets of measurements that are approximate replicates of one another. In complex applications, or automated data collection, these feature sets are not known a priori, and need to be…

Deep learning-based techniques have proven effective in polyp segmentation tasks when provided with sufficient pixel-wise labeled data. However, the high cost of manual annotation has created a bottleneck for model generalization. To…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity…

We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…

A distance matrix $A \in \mathbb R^{n \times m}$ represents all pairwise distances, $A_{ij}=\mathrm{d}(x_i,y_j)$, between two point sets $x_1,...,x_n$ and $y_1,...,y_m$ in an arbitrary metric space $(\mathcal Z, \mathrm{d})$. Such matrices…

In this paper, we aim to learn a mapping (or embedding) from images to a compact binary space in which Hamming distances correspond to a ranking measure for the image retrieval task. We make use of a triplet loss because this has been shown…

Let $C$ be a depth-3 arithmetic circuit of size at most $s$, computing a polynomial $ f \in \mathbb{F}[x_1,\ldots, x_n] $ (where $\mathbb{F}$ = $\mathbb{Q}$ or $\mathbb{C}$) and the fan-in of the product gates of $C$ is bounded by $d$. We…

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…

This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimizer will take the aircraft's controlled…