Related papers: Learning Algebraic Multigrid Using Graph Neural Ne…

Graph Neural Networks (GNNs) have greatly advanced the semi-supervised node classification task on graphs. The majority of existing GNNs are trained in an end-to-end manner that can be viewed as tackling a bi-level optimization problem.…

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity…

Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…

We define a novel type of ensemble Graph Convolutional Network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its…

Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…

Deep neural networks often suffer from poor generalization due to complex and non-convex loss landscapes. Sharpness-Aware Minimization (SAM) is a popular solution that smooths the loss landscape by minimizing the maximized change of…

We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We derive a baseline algorithm called LinBreg, an accelerated…

The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…

In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named \emph{coarsening based on compatible weighted matching},…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

This paper studies joint spectrum allocation and user association in large heterogeneous cellular networks. The objective is to maximize some network utility function based on given traffic statistics collected over a slow timescale,…

Graph neural networks have been successful for machine learning, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing graph…

This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…

The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few…

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…

Automatic modulation recognition (AMR) is a promising technology for intelligent communication receivers to detect signal modulation schemes. Recently, the emerging deep learning (DL) research has facilitated high-performance DL-AMR…

Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…

This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where…

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…