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We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
Neuromorphic computing describes the use of VLSI systems to mimic neuro-biological architectures and is also looked at as a promising alternative to the traditional von Neumann architecture. Any new computing architecture would need a…
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…
Numerical features of matrix multiplier hardware units in NVIDIA and AMD data centre GPUs have recently been studied. Features such as rounding, normalisation, and internal precision of the accumulators are of interest. In this paper, we…
In this work, we propose an architecture and methodology to design hardware/software systems for high-performance embedded computing on FPGA. The hardware side is based on a many-core architecture whose design is generated automatically…
Generalized Sparse Matrix-Matrix Multiplication (SpGEMM) is a ubiquitous task in various engineering and scientific applications. However, inner product based SpGENN introduces redundant input fetches for mismatched nonzero operands, while…
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…
As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
We explore optimization options for the Stream-K algorithm, a work-centric parallelization of matrix multiplication (GEMM). In our study, we investigated differences between the theoretical and practical implementations, particularly noting…
Fine-grained workload and resource balancing is the key to high performance for regular and irregular computations on the GPUs. In this dissertation, we conduct an extensive survey of existing load-balancing techniques to build an…
Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…
Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have…
Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
We approach the problem of implementing mixed-datatype support within the general matrix multiplication (GEMM) operation of the BLIS framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or…
Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the…
Small animal PET scanners require high spatial resolution and good sensitivity. To reconstruct high-resolution images in 3D-PET, iterative methods, such as OSEM, are superior to analytical reconstruction algorithms, although their high…