Related papers: Generating Families of Practical Fast Matrix Multi…
Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$…
General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
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…
General Matrix Multiplication (GEMM) has a wide range of applications in scientific simulation and artificial intelligence. Although traditional libraries can achieve high performance on large regular-shaped GEMMs, they often behave not…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…
We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS and OpenBLAS, in order to obtain…
Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
The generic matrix-matrix multiplication (GEMM) is arguably the most popular computational kernel of the 20th century. Yet, surprisingly, no common methodology for evaluating GEMM performance has been established over the many decades of…
General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application…
We dispel with "street wisdom" regarding the practical implementation of Strassen's algorithm for matrix-matrix multiplication (DGEMM). Conventional wisdom: it is only practical for very large matrices. Our implementation is practical for…
The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…
GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
General matrix/matrix multiplication (GEMM) is crucial for scientific computing and machine learning. However, the increased scale of the computing platforms raises concerns about hardware and software reliability. In this poster, we…
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level…
Matrix libraries often focus on achieving high performance for problems considered to be either "small" or "large", as these two scenarios tend to respond best to different optimization strategies. We propose a unified technique for…
One of the most important and commonly used operations in many linear algebra functions is matrix-matrix multiplication (GEMM), which is also a key component in obtaining high performance of many scientific codes. It is a computationally…
General Matrix Multiplication (GEMM) is a critical kernel in high-performance computing and deep learning. While modern architectures like ARM's Scalable Matrix Extension (SME) introduce dedicated hardware for matrix operations, existing…