Related papers: Chinese Remainder Theorem Approach to Montgomery-T…
The Householder algorithm for the QR factorization of a tall thin n x p full-rank matrix X has the added bonus of producing a matrix M with orthonormal columns that are a basis for the orthocomplement of the column space of X. We give a…
Accurately solving the Schr\"odinger equation for intricate systems remains a prominent challenge in physical sciences. A paradigm-shifting approach to address this challenge involves the application of artificial intelligence techniques.…
Machine reading comprehension (MRC) is a crucial task in natural language processing and has achieved remarkable advancements. However, most of the neural MRC models are still far from robust and fail to generalize well in real-world…
In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first…
Chinese character decomposition has been used as a feature to enhance Machine Translation (MT) models, combining radicals into character and word level models. Recent work has investigated ideograph or stroke level embedding. However,…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
We propose a coalgebraic model for constructing and reasoning about state-based protocols that implement efficient reductions among random processes. We provide basic tools that allow efficient protocols to be constructed in a compositional…
Based on rectangle theory of formal concept and set covering theory, the concept reduction preserving binary relations is investigated in this paper. It is known that there are three types of formal concepts: core concepts, relative…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step…
Many learning-to-rank (LtR) algorithms focus on query-independent model, in which query and document do not lie in the same feature space, and the rankers rely on the feature ensemble about query-document pair instead of the similarity…
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Implementations of known reductions of the Strong Real Jacobian Conjecture (SRJC), to the case of an identity map plus cubic homogeneous or cubic linear terms, and to the case of gradient maps, are shown to preserve significant algebraic…
While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically,…