Related papers: ALX: Large Scale Matrix Factorization on TPUs

Previous studies have reported that common dense linear algebra operations do not achieve speed up by using multiple geographical sites of a computational grid. Because such operations are the building blocks of most scientific…

Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However,…

There is a growing need for distributed graph processing systems that are capable of gracefully scaling to very large graph datasets. Unfortunately, this challenge has not been easily met due to the intense memory pressure imposed by…

Efficiently finding subgraph embeddings in large graphs is crucial for many application areas like biology and social network analysis. Set intersections are the predominant and most challenging aspect of current join-based subgraph query…

High-level applications, such as machine learning, are evolving from simple models based on multilayer perceptrons for simple image recognition to much deeper and more complex neural networks for self-driving vehicle control systems.The…

The integration of tabular data from diverse sources is often hindered by inconsistencies in formatting and representation, posing significant challenges for data analysts and personal digital assistants. Existing methods for automating…

Small distributed systems are limited by their main memory to generate massively large graphs. Trivial extension to current graph generators to utilize external memory leads to large amount of random I/O hence do not scale with size. In…

The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…

LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…

Complex networks are relational data sets commonly represented as graphs. The analysis of their intricate structure is relevant to many areas of science and commerce, and data sets may reach sizes that require distributed storage and…

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

Graph processing systems are essential for analyzing large-scale data with complex relationships, yet most existing frameworks rely on statically provisioned clusters, resulting in poor elasticity and inefficient resource utilization under…

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…

Transformers and large language models (LLMs), powered by the attention mechanism, have transformed numerous AI applications, driving the need for specialized hardware accelerators. A major challenge in these accelerators is efficiently…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…

PageRank is a well-known algorithm whose robustness helps set a standard benchmark when processing graphs and analytical problems. The PageRank algorithm serves as a standard for many graph analytics and a foundation for extracting graph…

Interconnection is crucial for computing systems. However, the current interconnection performance between processors and devices, such as memory devices and accelerators, significantly lags behind their computing performance, severely…

Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…