Related papers: Fault-Tolerant Dot-Product Engines
When data is stored, compressed, or communicated through a media such as cable or air, sources of noise and other parameters such as EMI, crosstalk, and distance can considerably affect the reliability of these data. Error detection and…
General matrix/matrix multiplication (GEMM) is crucial for scientific computing and machine learning. However, the increased scale of the computing platforms raises concerns about hardware and software reliability. In this poster, we…
In this paper we present a hardware-oriented algorithm for constant matrix-vector product calculating, when the all elements of vector and matrix are complex numbers. The proposed algorithm versus the naive method of analogous calculations…
Industry 4.0 has revolutionized manufacturing by driving digitalization and shifting the paradigm toward additive manufacturing (AM). Fused Deposition Modeling (FDM), a key AM technology, enables the creation of highly customized,…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
The relation between the girth and the error correction capability of column-weight-three LDPC codes is investigated. Specifically, it is shown that the Gallager A algorithm can correct $g/2-1$ errors in $g/2$ iterations on a Tanner graph…
This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It…
In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…
This paper proposes a model validation method that incorporates error due to numerical procedures. Two identified models for Sine Map and Duffing-Ueda Circuit systems have been investigated. The indexes RMSE and MAPE have been applied. We…
Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…
This study investigates the reliability of code generation by Large Language Models (LLMs), focusing on identifying and analyzing defects in the generated code. Despite the advanced capabilities of LLMs in automating code generation,…
A natural desideratum for generative models is self-correction--detecting and revising low-quality tokens at inference. While Masked Diffusion Models (MDMs) have emerged as a promising approach for generative modeling in discrete spaces,…
The goal of this paper is to develop data-driven control design and evaluation strategies based on linear matrix inequalities (LMIs) and dynamic programming. We consider deterministic discrete-time LTI systems, where the system model is…
Given a commutative ring $R$ with identity, a matrix $A\in M_{s\times l}(R)$, and $R$-linear codes $\mathcal{C}_1, \dots, \mathcal{C}_s$ of the same length, this article considers the hull of the matrix-product codes $[\mathcal{C}_1 \dots…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
The need to estimate a positive definite solution to an overdetermined linear system of equations with multiple right hand side vectors arises in several process control contexts. The coefficient and the right hand side matrices are…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
Nowadays refinery optimization utilizes sheer amounts of data, which can be handled with modern Linear Programming (LP) software, but the interpreting and applying the results remains challenging. Large petrochemical companies use massive…