Related papers: Fault-Tolerant Dot-Product Engines
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…
Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
As safety-critical applications increasingly rely on data-parallel floating-point computations, there is an increasing need for flexible and configurable fault tolerance in parallel floating-point accelerators such as tensor engines. While…
Large language models (LLMs) have been massively applied to many tasks, often surpassing state-of-the-art approaches. While their effectiveness in code generation has been extensively studied (e.g., AlphaCode), their potential for code…
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the dot product. The general…
The advent of data-driven real-time applications requires the implementation of Deep Neural Networks (DNNs) on Machine Learning accelerators. Google's Tensor Processing Unit (TPU) is one such neural network accelerator that uses systolic…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation techniques using different…
We present a new approach to fault tolerance for High Performance Computing system. Our approach is based on a careful adaptation of the Algorithmic Based Fault Tolerance technique (Huang and Abraham, 1984) to the need of parallel…
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…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…