arXiv subjects

Alyson Fox

Publications and source records attributed to Alyson Fox.

7 recordsLinked to original sources

arXiv2026

Skywing: A Platform for Decentralized Mathematical Computing in Unreliable Environments

Emerging edge, autonomous, and cyber-physical systems increasingly require mathematical computation across heterogeneous devices connected by unreliable communication networks. Traditional high-performance computing and distributed data-processing frameworks provide powerful abstractions for managed environments but are less suited to decentralized settings where centralized coordination, reliable communication, and global synchronization cannot be assumed. This paper presents Skywing, an open-source platform for decentralized mathematical computing in unreliable environments. Its programming model consists of three abstractions: agents represent participants in a decentralized computation, processors encapsulate algorithm-specific update rules, and iterations manage distributed execution. Skywing supports asynchronous operation, publish-subscribe communication, managed message handling, and the composition of independent algorithms into complex decentralized workflows. We demonstrate Skywing using representative algorithms from consensus, optimization, and numerical linear algebra. Experiments on the native Skywing runtime include Push Sum and Max Consensus, a composed monitoring and control workflow, resilient Push Sum under delayed communication, and resilient asynchronous Jacobi under malevolent data corruption. These demonstrations show that Skywing supports diverse decentralized algorithms while separating mathematical logic from communication and execution infrastructure. Skywing serves as both a deployment framework for decentralized applications and a research platform for developing resilient mathematical algorithms.

cs.DC↗

arXiv2024

Enhancing ZFP: A Statistical Approach to Understanding and Reducing Error Bias in a Lossy Floating-Point Compression Algorithm

The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression; however, lossless data compression is typically ineffective when applied to floating-point data. Thus, users tend to apply a lossy data compressor, which allows for small deviations from the original data. It is essential to understand how the error from lossy compression impacts the accuracy of the data analytics. Thus, we must analyze not only the compression properties but the error as well. In this paper, we provide a statistical analysis of the error caused by ZFP compression, a state-of-the-art, lossy compression algorithm explicitly designed for floating-point data. We show that the error is indeed biased and propose simple modifications to the algorithm to neutralize the bias and further reduce the resulting error.

math.NA↗

arXiv2022

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in-situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. A linear system with a more dense sparsity pattern is also explored. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

cs.DC↗

arXiv2020

Mixed precision matrix interpolative decompositions for model reduction

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose a mixed-precision algorithm to generate a double-precision accurate matrix interpolative decomposition approximation under a given set of criteria. Though low precision arithmetic suffers from quicker accumulation of round-off error, for many data-rich applications we nevertheless attain viable approximation accuracy, as the error incurred using low precision arithmetic is dominated by the error inherent to low-rank approximation. We then conduct several simulated numerical tests to demonstrate the efficacy of the algorithms and the corresponding error estimates. Finally, we present the application of our algorithms to a problem in model reduction for particle-laden turbulent flow.

math.NA↗

arXiv2020

Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods

Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both inter-node communications and even more-so in on-node data motion. A new approach to address this limitation is to make use of data compression in the form of a compressed data array. Storing data in a compressed data array and converting to standard IEEE-754 types as needed during a computation can reduce the pressure on bandwidth and storage. However, repeated conversions (lossy compression and decompression) introduce additional approximation errors, which need to be shown to not significantly affect the simulation results. We extend recent work [J. Diffenderfer, et al., Error Analysis of ZFP Compression for Floating-Point Data, SIAM Journal on Scientific Computing, 2019] that analyzed the error of a single use of compression and decompression of the ZFP compressed data array representation [P. Lindstrom, Fixed-rate compressed floating-point arrays, IEEE Transactions on Visualization and Computer Graphics, 2014] to the case of time-stepping and iterative schemes, where an advancement operator is repeatedly applied in addition to the conversions. We show that the accumulated error for iterative methods involving fixed-point and time evolving iterations is bounded under standard constraints. An upper bound is established on the number of additional iterations required for the convergence of stationary fixed-point iterations. An additional analysis of traditional forward and backward error of stationary iterative methods using ZFP compressed arrays is also presented. The results of several 1D, 2D, and 3D test problems are provided to demonstrate the correctness of the theoretical bounds.

math.NA↗

arXiv2019

Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We develop mixed precision variants of existing Householder QR algorithms and show error analyses supported by numerical experiments.

math.NA↗

arXiv2018

Error Analysis of ZFP Compression for Floating-Point Data

Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to bound its errors when used to store look-up tables, simulation results, or even the solution state during the computation. \black{In this paper, we analyze the round-off error introduced by ZFP, a %state-of-the-art lossy compression algorithm.} The stopping criteria for ZFP depends on the compression mode specified by the user; either fixed rate, fixed accuracy, or fixed precision [P. Lindstrom, Fixed-rate compressed floating-point arrays, IEEE Transactions on Visualization and Computer Graphics, 2014]. While most of our discussion is focused on the fixed precision mode of ZFP, we establish a bound on the error introduced by all three compression modes. In order to tightly capture the error, we first introduce a vector space that allows us to work with binary representations of components. Under this vector space, we define operators that implement each step of the ZFP compression and decompression to establish a bound on the error caused by ZFP. To conclude, numerical tests are provided to demonstrate the accuracy of the established bounds.

math.NA↗