Related papers: Modular exponentiation of matrices on FPGA-s

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

FPGA-based hardware accelerators have received increasing attention mainly due to their ability to accelerate deep pipelined applications, thus resulting in higher computational performance and energy efficiency. Nevertheless, the amount of…

Due to the emergence of embedded applications in image and video processing, communication and cryptography, improvement of pictorial information for better human perception like deblurring, denoising in several fields such as satellite…

Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…

Data movement is the dominating factor affecting performance and energy in modern computing systems. Consequently, many algorithms have been developed to minimize the number of I/O operations for common computing patterns. Matrix…

Modern multicore systems are migrating from homogeneous systems to heterogeneous systems with accelerator-based computing in order to overcome the barriers of performance and power walls. In this trend, FPGA-based accelerators are becoming…

We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended…

We present a new efficient OpenCL-based Accelerator for large scale Convolutional Neural Networks called Fast Inference on FPGAs for Convolution Neural Network (FFCNN). FFCNN is based on a deeply pipelined OpenCL kernels architecture. As…

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

In recent years, deep learning has become more and more mature, and as a commonly used algorithm in deep learning, convolutional neural networks have been widely used in various visual tasks. In the past, research based on deep learning…

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 development of in-depth learning, neural network and deep learning algorithms have been widely used in various fields, e.g., image, video and voice processing. However, the neural network model is getting larger and larger,…

Large language models (LLMs) have demonstrated remarkable abilities in natural language processing. However, their deployment on resource-constrained embedded devices remains difficult due to memory and computational demands. In this paper,…

We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…

Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…

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…

Neural networks with a latency requirement on the order of microseconds, like the ones used at the CERN Large Hadron Collider, are typically deployed on FPGAs fully unrolled and pipelined. A bottleneck for the deployment of such neural…

This research introduces an FPGA-based hardware accelerator to optimize the Singular Value Decomposition (SVD) and Fast Fourier transform (FFT) operations in AI models. The proposed design aims to improve processing speed and reduce…