Related papers: Matrix Ordering through Spectral and Nilpotent Str…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, raise in the quantum computation, bin-packing and matrix analysis. We find the…
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
Shape-morphing soft materials can enable diverse target morphologies through voxel-level material distribution design, offering significant potential for various applications. Despite progress in basic shape-morphing design with simple…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…
We study the approximation of the spectrum of a second-order elliptic differential operator by the Hybrid High-Order (HHO) method. The HHO method is formulated using cell and face unknowns which are polynomials of some degree $k\geq0$. The…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same…
The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice of an orthonormal basis depends on a number of desirable…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix…