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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…

B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…

Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient…

Fueled by the ability to mine real-world graph data, GNN applications have experienced phenomenal growth. Sparse Matrix-Matrix Multiplication (SpMM) is a critical operator in GNNs. However, existing SpMM designs for GNNs struggle to adapt…

Basic Linear Algebra Subprograms (BLAS) are a set of low level linear algebra kernels widely adopted by applications involved with the deep learning and scientific computing. The massive and economic computing power brought forth by the…

In this paper, we focus on three sparse matrix operations that are relevant for machine learning applications, namely, the sparse-dense matrix multiplication (SPMM), the sampled dense-dense matrix multiplication (SDDMM), and the composition…

This report presents some early results on code generation targeting tensor cores on NVIDIA GPUs using the MLIR compiler infrastructure. The state-of-the-art in high-performance deep learning today is primarily driven by manually optimized…

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…

Sparse matrix-vector multiplication (SpMV) is an essential linear algebra operation that dominates the computing cost in many scientific applications. Due to providing massive parallelism and high memory bandwidth, GPUs are commonly used to…

Most, if not all the modern scientific simulation packages utilize matrix algebra operations. Among the operation of the linear algebra, one of the most important kernels is the multiplication of matrices, dense and sparse. Examples of…

Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is…

To prepare images for better segmentation, we need preprocessing applications, such as smoothing, to reduce noise. In this paper, we present an enhanced computation method for smoothing 2D object in binary case. Unlike existing approaches,…

As inference on Large Language Models (LLMs) emerges as an important workload in machine learning applications, weight quantization has become a standard technique for efficient GPU deployment. Quantization not only reduces model size, but…

Sparse matrix multiplication operators (i.e., SpMM and SDDMM) are widely used in deep learning and scientific computing. Modern accelerators are commonly equipped with Tensor Core Units (TCUs) and CUDA cores to accelerate sparse operators.…

Sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication beyond memory capacity by implementing sparse…

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

In computational science and data analytics, many workloads involve irregular and sparse computations that are inherently difficult to optimize for modern hardware. A key kernel is Sparse General Matrix-Matrix Multiplication (SpGEMM), which…

Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs…