Related papers: Kokkos Kernels: Performance Portable Sparse/Dense …
Symmetric and sparse tensors arise naturally in many domains including linear algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors are equal to their transposes, so in the $n$-dimensional case we can save up to a…
Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…
Portable GPU frameworks such as Kokkos and RAJA reduce the burden of cross-architecture development but typically incur measurable overhead on fundamental parallel primitives relative to vendor-optimized libraries. We present…
This paper shows how to generate code that efficiently converts sparse tensors between disparate storage formats (data layouts) such as CSR, DIA, ELL, and many others. We decompose sparse tensor conversion into three logical phases:…
Current climate change has posed a grand challenge in the field of numerical modeling due to its complex, multiscale dynamics. In hydrological modeling, the increasing demand for high-resolution, real-time simulations has led to the…
Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel across scientific computing and machine learning. While prior work accelerates SpMM using Tensor Cores, no existing sparse kernel exploits the asynchronous features of…
Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
Existing 3D algorithms for distributed-memory sparse kernels suffer from limited scalability due to reliance on bulk sparsity-agnostic communication. While easier to use, sparsity-agnostic communication leads to unnecessary bandwidth and…
Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…
Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…
Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block…
Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…
As AI accelerators gain prominence, their potential for traditional scientific computing workloads remains unclear. This paper explores Tenstorrent's Wormhole architecture, a spatial computing platform designed for neural network…
Recent years have seen considerable work on compiling sparse tensor algebra expressions. This paper addresses a shortcoming in that work, namely how to generate efficient code (in time and space) that scatters values into a sparse result…
The Liquid Argon Time Projection Chamber (LArTPC) technology is widely used in high energy physics experiments, including the upcoming Deep Underground Neutrino Experiment (DUNE). Accurately simulating LArTPC detector responses is essential…
The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently…
The rapidly evolving landscape of AI and machine learning workloads has widened the gap between high-level domain operations and efficient hardware utilization. Achieving near-peak performance still demands deep hardware expertise-experts…