Related papers: Lean Algebraic Multigrid (LAMG): Fast Graph Laplac…

We study distributed algorithms built around minor-based vertex sparsifiers, and give the first algorithm in the CONGEST model for solving linear systems in graph Laplacian matrices to high accuracy. Our Laplacian solver has a round…

This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying…

A symmetric matrix is called a Laplacian if it has nonpositive off-diagonal entries and zero row sums. Since the seminal work of Spielman and Teng (2004) on solving Laplacian linear systems in nearly linear time, several algorithms have…

In federated graph learning (FGL), a complete graph is divided into multiple subgraphs stored in each client due to privacy concerns, and all clients jointly train a global graph model by only transmitting model parameters. A pain point of…

Convolutional neural networks are nowadays witnessing a major success in different pattern recognition problems. These learning models were basically designed to handle vectorial data such as images but their extension to non-vectorial and…

The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…

The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…

We propose representation of configurational physical quantities and microscopic structures for multicomponent system on lattice, by extending a concept of generalized Ising model (GIM) to graph theory. We construct graph Laplacian (and…

Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…

Multi-relational graph clustering has demonstrated remarkable success in uncovering underlying patterns in complex networks. Representative methods manage to align different views motivated by advances in contrastive learning. Our empirical…

Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…

Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the…

Large language models (LLMs) often suffer from hallucination, generating factually incorrect statements when handling questions beyond their knowledge and perception. Retrieval-augmented generation (RAG) addresses this by retrieving…

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…

We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares…

Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…