Related papers: Lean Algebraic Multigrid (LAMG): Fast Graph Laplac…
Dynamic and temporal graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion…
Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
Semantic Knowledge Graphs (SKG) face challenges with scalability, flexibility, contextual understanding, and handling unstructured or ambiguous information. However, they offer formal and structured knowledge enabling highly interpretable…
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…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
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…
Graph Neural Networks (GNNs) have empowered the advance in graph-structured data analysis. Recently, the rise of Large Language Models (LLMs) like GPT-4 has heralded a new era in deep learning. However, their application to graph data poses…
This research explores the application of the auxiliary space multigrid method (ASMG) that is based on additive Schur complement approximation (ASCA) to graph Laplacian matrices arising from general graphs. A major predicament when…
This paper targets solving distributed machine learning problems such as federated learning in a communication-efficient fashion. A class of new stochastic gradient descent (SGD) approaches have been developed, which can be viewed as the…
Large Language Models (LLMs) have demonstrated substantial efficacy in advancing graph-structured data analysis. Prevailing LLM-based graph methods excel in adapting LLMs to text-rich graphs, wherein node attributes are text descriptions.…
We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…
The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation…
Dynamic graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion…
The structural properties of naturally arising social graphs are extensively studied to understand their evolution. Prior approaches for modeling network dynamics typically rely on rule-based models, which lack realism and generalizability,…
In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…
An increasing number of machine learning tasks require dealing with large graph datasets, which capture rich and complex relationship among potentially billions of elements. Graph Neural Network (GNN) becomes an effective way to address the…
GraphRAG integrates (knowledge) graphs with large language models (LLMs) to improve reasoning accuracy and contextual relevance. Despite its promising applications and strong relevance to multiple research communities, such as databases and…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
Table reasoning, a task to answer questions by reasoning over data presented in tables, is an important topic due to the prevalence of knowledge stored in tabular formats. Recent solutions use Large Language Models (LLMs), exploiting the…