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

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…

Matrices associated with graphs, such as the Laplacian, lead to numerous interesting graph problems expressed as linear systems. One field where Laplacian linear systems play a role is network analysis, e. g. for certain centrality measures…

Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…

We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Semantic parsing is the task of producing a structured meaning representation for natural language utterances or questions. Recent research has pointed out that the commonly-used sequence-to-sequence (seq2seq) semantic parsers struggle to…

Large language models (LLMs) often struggle with knowledge-intensive tasks due to hallucinations and outdated parametric knowledge. While Retrieval-Augmented Generation (RAG) addresses this by integrating external corpora, its effectiveness…

Large language models (LLMs) are rapidly transforming various domains, including biomedicine and healthcare, and demonstrate remarkable potential from scientific research to new drug discovery. Graph-based retrieval-augmented generation…

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear…

Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of…

Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…

This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…

Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…

We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…

Large language models (LLMs) have demonstrated remarkable capabilities in a wide range of tasks, yet their application to specialized domains remains challenging due to the need for deep expertise. Retrieval-Augmented generation (RAG) has…

The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…

Recently, Retrieval-Augmented Generation (RAG) has achieved remarkable success in addressing the challenges of Large Language Models (LLMs) without necessitating retraining. By referencing an external knowledge base, RAG refines LLM…

Agglomeration-based strategies are important both within adaptive refinement algorithms and to construct scalable multilevel algebraic solvers. In order to automatically perform agglomeration of polygonal grids, we propose the use of…

A multi-view attributed graph (MVAG) G captures the diverse relationships and properties of real-world entities through multiple graph views and attribute views. Effectively utilizing all views in G is essential for MVAG clustering and…

A linear graph is a graph whose vertices are totally ordered. Biological and linguistic sequences with interactions among symbols are naturally represented as linear graphs. Examples include protein contact maps, RNA secondary structures…