Related papers: Optimized on-line computation of PageRank algorith…
Process optimization in chemical engineering may be hindered by the limited availability of reliable thermodynamic data for fluid mixtures. Remarkable progress is being made in predicting thermodynamic mixture properties by machine learning…
We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible…
The evaluation of mathematical results plays a central role in assessing researchers' contributions and shaping the direction of the field. Currently, such evaluations rely primarily on human judgment, whether through journal peer review or…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
Analysing how information flows along the layers of a multilayer perceptron is a topic of paramount importance in the field of artificial neural networks. After framing the problem from the point of view of information theory, in this…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…
Efficient inference is a critical challenge in deep generative modeling, particularly as diffusion models grow in capacity and complexity. While increased complexity often improves accuracy, it raises compute costs, latency, and memory…
Thanks to its versatility, its simplicity, and its fast convergence, ADMM is among the most widely used approaches for solving a convex problem in distributed form. However, making it running efficiently is an art that requires a fine…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Node influence metrics have been applied to many applications, including ranking web pages on internet, or locations on spatial networks. PageRank is a popular and effective algorithm for estimating node influence. However, conventional…
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which…
The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization…
In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of…
With the rapid growth of Internet services, recommendation systems play a central role in delivering personalized content. Faced with massive user requests and complex model architectures, the key challenge for real-time recommendation…
Higher-order networks are efficient representations of sequential data. Unlike the classic first-order network approach, they capture indirect dependencies between items composing the input sequences by the use of \textit{memory-nodes}. We…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
In this paper, we consider a problem of learning supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank algorithm. Due to huge hidden dimension of the…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…