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Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspective, the exact Cholesky factorization introduces a clique in…
Subgraph matching is a basic operation widely used in many applications. However, due to its NP-hardness and the explosive growth of graph data, it is challenging to compute subgraph matching, especially in large graphs. In this paper, we…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…
While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring…
Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
Sparse attention is a core building block in many leading neural network models, from graph-structured learning to sparse sequence modeling. It can be decomposed into a sequence of three sparse matrix operations (3S): sampled dense-dense…
This work introduces Structured Linear Controlled Differential Equations (SLiCEs), a unifying framework for sequence models with structured, input-dependent state-transition matrices that retain the maximal expressivity of dense matrices…
When training large machine learning models with many variables or parameters, a single machine is often inadequate since the model may be too large to fit in memory, while training can take a long time even with stochastic updates. A…
We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search,…
We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…
Graph analytics are vital in fields such as social networks, biomedical research, and graph neural networks (GNNs). However, traditional CPUs and GPUs struggle with the memory bottlenecks caused by large graph datasets and their…
The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…
Sparse, irregular graphs show up in various applications like linear algebra, machine learning, engineering simulations, robotic control, etc. These graphs have a high degree of parallelism, but their execution on parallel threads of modern…
Sparse General Matrix-Matrix Multiplication (SpGEMM) is a fundamental operation in numerous scientific computing and data analytics applications, often bottlenecked by irregular memory access patterns. This paper presents Hash based…
Machine Learning (ML) models execute several parallel computations including Generalized Matrix Multiplication, Convolution, Dropout, etc. These computations are commonly executed on Graphics Processing Units (GPUs), by dividing the…
Exploiting sparsity enables hardware systems to run neural networks faster and more energy-efficiently. However, most prior sparsity-centric optimization techniques only accelerate the forward pass of neural networks and usually require an…
Sparse matrix-matrix multiplication (SpGEMM) is a critical operation in numerous fields, including scientific computing, graph analytics, and deep learning. These applications exploit the sparsity of matrices to reduce storage and…