Related papers: Fast Matrix Multiplication via Compiler-only Layer…
Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls result in…
KBLAS is a new open source high performance library that provides optimized kernels for a subset of Level 2 BLAS functionalities on CUDA-enabled GPUs. Since performance of dense matrix-vector multiplication is hindered by the overhead of…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
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…
Power ISA(TM) Version 3.1 has introduced a new family of matrix math instructions, collectively known as the Matrix-Multiply Assist (MMA) facility. The instructions in this facility implement numerical linear algebra operations on small…
Basic Linear Algebra Subprograms (BLAS) is a core library in scientific computing and machine learning. This paper presents FT-BLAS, a new implementation of BLAS routines that not only tolerates soft errors on the fly, but also provides…
Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…
Matrix-multiply-accumulate (MMA) units, or tensor cores, are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a…
Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15…
The introduction of the Basic Linear Algebra Subroutine (BLAS) in the 1970s paved the way for different libraries to solve the same problem with an improved approach and hardware. The new BLAS implementation led to High-Performance…
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…
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…
Transformer-based large language models (LLMs) rely heavily on intensive matrix multiplications for attention and feed-forward layers, with the Q, K, and V linear projections in the Multi-Head Self-Attention (MHA) module constituting a…
Model merging has recently emerged as a lightweight alternative to ensembling, combining multiple fine-tuned models into a single set of parameters with no additional training overhead. Yet, existing merging methods fall short of matching…
Model quantization represents both parameters (weights) and intermediate values (activations) in a more compact format, thereby directly reducing both computational and memory cost in hardware. The quantization of recent large language…
Matrix multiplication is fundamental in the backpropagation algorithm used to train deep neural network models. Libraries like Intel's MKL or NVIDIA's cuBLAS implemented new and optimized matrix multiplication techniques that increase…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
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…
To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure…
General matrix-matrix multiplications with double-precision real and complex entries (DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimized for square matrices but often show bad performance for tall & skinny matrices, which…