Related papers: A Framework for General Sparse Matrix-Matrix Multi…

The material point method (MPM) is a hybrid particle-grid method widely used for simulating large deformation with history-dependent behavior. Standard MPM often relies on a dense background grid, which can be highly inefficient when…

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…

Sparse-Matrix Dense-Matrix multiplication (SpMM) is the key operator for a wide range of applications, including scientific computing, graph processing, and deep learning. Architecting accelerators for SpMM is faced with three challenges -…

With the fast growth of parameter size, it becomes increasingly challenging to deploy large generative models as they typically require large GPU memory consumption and massive computation. Unstructured model pruning has been a common…

Matrix Factorization (MF) on large scale data takes substantial time on a Central Processing Unit (CPU). While Graphical Processing Unit (GPU)s could expedite the computation of MF, the available memory on a GPU is finite. Leveraging GPUs…

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The…

We study exact sparse linear regression with an $\ell_0-\ell_2$ penalty and develop a branch-and-bound (BnB) algorithm explicitly designed for GPU execution. Starting from a perspective reformulation, we derive an interval relaxation that…

Structured Cartesian grids are a fundamental component in numerical simulations. Although these grids facilitate straightforward discretization schemes, their na\"{i}ve use in sparse domains leads to excessive memory overhead and…

We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…

We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…

Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…

Many recent GPUs feature matrix multiplication engines (aka Tensor Core Units or TCUs) that perform small fixed-size matrix-matrix products at very high throughput. They have been used very effectively to speed up dense matrix-matrix…

Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…

Fully homomorphic encryption (FHE) has recently attracted significant attention as both a cryptographic primitive and a systems challenge. Given the latest advances in accelerated computing, FHE presents a promising opportunity for…

To operate effectively in the real world, agents should be able to act from high-dimensional raw sensory input such as images and achieve diverse goals across long time-horizons. Current deep reinforcement and imitation learning methods can…

In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large sparse systems of linear equations…

Achieving high efficiency with numerical kernels for sparse matrices is of utmost importance, since they are part of many simulation codes and tend to use most of the available compute time and resources. In addition, especially in large…