相关论文: The weighted difference substitutions and Nonnegat…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines,…
The distinguished weights form a subset of the weight lattice and are closely tied to the notion of $p$-cells. These weights are defined via iterations of the Lusztig-Vogan bijection. We prove that all distinguished weights exhibit an…
The problem of identifying statistically significant inferences about the structure of the graphical model is considered, along with the related task of constructing a confidence set for a graphical model. It has been proven that the…
Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative…
A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…
We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
We introduce a framework for automatic differentiation with weighted finite-state transducers (WFSTs) allowing them to be used dynamically at training time. Through the separation of graphs from operations on graphs, this framework enables…
The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible…
Machine learning models usually assume that a set of feature values used to obtain an output is fixed in advance. However, in many real-world problems, a cost is associated with measuring these features. To address the issue of reducing…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
We prove effective versions of Oppenheim's conjecture for generic inhomogeneous forms in the S-arithmetic setting. We prove an effective result for fixed rational shifts and generic forms and we also prove a result where both the quadratic…
Self-supervised learning has recently shown great potential in vision tasks through contrastive learning, which aims to discriminate each image, or instance, in the dataset. However, such instance-level learning ignores the semantic…
Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies.…