Related papers: Fault-Tolerant Dot-Product Engines
The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and matdot codes are generalized by making use of algebraic…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based…
We explore the link between data representation and soft errors in dot products. We present an analytic model for the absolute error introduced should a soft error corrupt a bit in an IEEE-754 floating-point number. We show how this finding…
We present a hardware-based implementation of Linear Program (LP) decoding for binary linear codes. LP decoding frames error-correction as an optimization problem. In contrast, variants of Belief Propagation (BP) decoding frame…
NVIDIA Tensor Cores and AMD Matrix Cores (together called Matrix Accelerators) are of growing interest in high-performance computing and machine learning owing to their high performance. Unfortunately, their numerical behaviors are not…
Error-correcting pairs were introduced independently by Pellikaan and K\"otter as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise products of vectors, and are used for many well-known…
Easy and effective usage of computational resources is crucial for scientific calculations. Following our recent work of machine-learning (ML) assisted scheduling optimization [Ref: J. Comput. Chem. 2023, 44, 1174], we further propose 1)…
Product codes are a concatenated error-correction scheme that has been often considered for applications requiring very low bit-error rates, which demand that the error floor be decreased as much as possible. In this work, we consider…
In-Memory Computing (IMC) introduces a new paradigm of computation that offers high efficiency in terms of latency and power consumption for AI accelerators. However, the non-idealities and defects of emerging technologies used in advanced…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Data transmission from superconducting electronic circuits, such as single flux quantum (SFQ) logic, to room-temperature electronics is susceptible to bit errors, which may result from flux trapping, fabrication defects, and process…
Engineering educational curriculum and standards cover many material and manufacturing options. However, engineers and designers are often unfamiliar with certain composite materials or manufacturing techniques. Large language models (LLMs)…
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…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
The digitisation of industry provides a plethora of novel applications that increase flexibility and reduce setup and maintenance time as well as cost. Furthermore, novel use cases are created by the digitisation of industry, commonly known…
Recent large language models (LLMs) have demonstrated the ability to perform explicit multi-step reasoning such as chain-of-thought prompting. However, their intermediate steps often contain errors that can propagate leading to inaccurate…