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General-purpose Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel in scientific computing and deep learning. The emergence of new matrix computation units such as Tensor Cores (TCs) brings more opportunities for SpMM…
Matrix engines or units, in different forms and affinities, are becoming a reality in modern processors; CPUs and otherwise. The current and dominant algorithmic approach to Deep Learning merits the commercial investments in these units,…
We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024].…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
The Tsetlin Machine (TM) offers high-speed inference on resource-constrained devices such as CPUs. Its logic-driven operations naturally lend themselves to parallel execution on modern CPU architectures. Motivated by this, we propose an…
In-memory computing hardware accelerators allow more than 10x improvements in peak efficiency and performance for matrix-vector multiplications (MVM) compared to conventional digital designs. For this, they have gained great interest for…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
We describe an efficient FPGA implementation for the exponentiation of large matrices. The research is related to an algorithm for constructing uniformly distributed linear recurring sequences. The design utilizes the special properties of…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
Modern Neural Network (NN) architectures heavily rely on vast numbers of multiply-accumulate arithmetic operations, constituting the predominant computational cost. Therefore, this paper proposes a high-throughput, scalable and energy…
The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of…
Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…
Recent architectures integrate high-performance and power-efficient matrix engines. These engines demonstrate remarkable performance in low-precision matrix multiplication, which is crucial in deep learning. Several techniques have been…
This paper proposes a novel set of trigonometric implementations which are 5x faster than the inbuilt C++ functions. The proposed implementation is also highly memory efficient requiring no precomputations of any kind. Benchmark comparisons…
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…
This paper presents an extension to an existing instruction set architecture, which gains considerable reduction in power consumption. The reduction in power consumption is achieved through coding of the most commonly executed instructions…
This article presents new properties of the mesh array for matrix multiplication. In contrast to the standard array that requires 3n-2 steps to complete its computation, the mesh array requires only 2n-1 steps. Symmetries of the mesh array…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…