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Graph convolutional networks (GCNs) are fundamental in various scientific applications, ranging from biomedical protein-protein interactions (PPI) to large-scale recommendation systems. An essential component for modeling graph structures…

A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…

Peak breaking Matrix Multiplication is a promising technique to improve the performance of DL, especially in LLM training and inference. We present FalconGEMM, a cross-platform framework that automates the deployment, optimization, and…

Emerging machine learning (ML) models (e.g., transformers) involve memory pin bandwidth-bound matrix-vector (MV) computation in inference. By avoiding pin crossings, processing in memory (PIM) can improve performance and energy for…

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…

The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…

Graph neural networks (GNNs) are widely used for learning on graph datasets derived from various real-world scenarios. Learning from extremely large graphs requires distributed training, and mini-batching with sampling is a popular approach…

The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…

Multiplication of a sparse matrix to a dense matrix (SpDM) is widely used in many areas like scientific computing and machine learning. However, existing works under-look the performance optimization of SpDM on modern many-core…

Applying machine learning techniques to the quickly growing data in science and industry requires highly-scalable algorithms. Large datasets are most commonly processed "data parallel" distributed across many nodes. Each node's contribution…

Deep learning demonstrates effectiveness across a wide range of tasks. However, the dense and over-parameterized nature of these models results in significant resource consumption during deployment. In response to this issue, weight…

Owing to the diverse scales and varying distributions of sparse matrices arising from practical problems, a multitude of choices are present in the design and implementation of sparse matrix-vector multiplication (SpMV). Researchers have…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…

Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…

Sparse matrix-vector multiplication (SpMV) is a fundamental operation in machine learning, scientific computing, and graph algorithms. In this paper, we investigate the space, time, and energy efficiency of SpMV using various compressed…

Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…

Sparse triangular solve (SpTRSV) is an extensively studied computational kernel. An important obstacle in parallel SpTRSV implementations is that in some parts of a sparse matrix the computation is serial. By transforming the dependency…

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…