Related papers: Emulation of Complex Matrix Multiplication based o…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
Artificial intelligence (AI) models are currently driven by a significant upscaling of their complexity, with massive matrix-multiplication workloads representing the major computational bottleneck. In-memory computing (IMC) architectures…
This paper proposes an low power approximate multiplier architecture for deep neural network (DNN) applications. A 4:2 compressor, introducing only a single combination error, is designed and integrated into an 8x8 unsigned multiplier. This…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
Compute-in-memory (CIM) techniques are widely employed in energy-efficient artificial intelligent (AI) processors. They alleviate power and latency bottlenecks caused by extensive data movements between compute and storage units. To extend…
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…
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp.…
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…
With the rapid growth of deep neural networks (DNNs), compute-in-memory (CIM) has emerged as a promising energy-efficient paradigm for accelerating multiply-and-accumulate (MAC) operations. Yet, current CIM architectures are largely limited…
In recent decades, High Performance Computing (HPC) has undergone significant enhancements, particularly in the realm of hardware platforms, aimed at delivering increased processing power while keeping power consumption within reasonable…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
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…
Recently, the demand of low-power deep-learning hardware for industrial applications has been increasing. Most existing artificial intelligence (AI) chips have evolved to rely on new chip technologies rather than on radically new hardware…
Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make…
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
Recent technological developments have led to big data processing, which resulted in significant computational difficulties when solving large-scale linear systems or inverting matrices. As a result, fast approximate iterative matrix…
Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works focus on fully…