Related papers: Tackling the Matrix Multiplication Micro-kernel Ge…
Sparse general matrix-matrix multiplication (SpGEMM) is a critical operation in many applications. Current multithreaded implementations are based on Gustavson's algorithm and often perform poorly on large matrices due to limited cache…
The widespread adoption of large language models such as ChatGPT and Bard has led to unprecedented demand for these technologies. The burgeoning cost of inference for ever-increasing model sizes coupled with hardware shortages has limited…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art vendor libraries tune tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory…
Modern GPGPUs provide massive arithmetic throughput, yet many scientific kernels remain limited by memory bandwidth. In particular, repeatedly loading precomputed auxiliary data wastes abundant compute resources while stressing the memory…
Fourier Neural Operators (FNO) are widely used for learning partial differential equation solution operators. However, FNO lacks architecture-aware optimizations,with its Fourier layers executing FFT, filtering, GEMM, zero padding, and iFFT…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
This study was aimed at simultaneously achieving sufficient accuracy and high performance for general matrix multiplications. Recent architectures, such as NVIDIA GPUs, feature high-performance units designed for low-precision matrix…
General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…
Among ML operators today, GEneralMatrix Multiplication (GEMM)-based operators are known to be key operators that build the main backbone of ML models. As their computational overhead dominates the overall execution time (e.g., 42.8% - 96.6%…
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…
Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a…
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of…
Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox…
Data movement is the dominating factor affecting performance and energy in modern computing systems. Consequently, many algorithms have been developed to minimize the number of I/O operations for common computing patterns. Matrix…
Tile-based many-Processing Element (PE) accelerators can achieve competitive performance on General Matrix Multiplication (GEMM), but they are extremely hard to program, as their optimal software mapping is deeply coupled with hardware…
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…
In biological data, it is often the case that observed data are available only for a subset of samples. When a kernel matrix is derived from such data, we have to leave the entries for unavailable samples as missing. In this paper, we make…
Big data and the Internet of Things era continue to challenge computational systems. Several technology solutions such as NoSQL databases have been developed to deal with this challenge. In order to generate meaningful results from large…
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,…