arXiv subjects

Robert Underwood

Publications and source records attributed to Robert Underwood.

At least 37 records · Page 2Linked to original sources

arXiv2024

LCP: Enhancing Scientific Data Management with Lossy Compression for Particles

Many scientific applications opt for particles instead of meshes as their basic primitives to model complex systems composed of billions of discrete entities. Such applications span a diverse array of scientific domains, including molecular dynamics, cosmology, computational fluid dynamics, and geology. The scale of the particles in those scientific applications increases substantially thanks to the ever-increasing computational power in high-performance computing (HPC) platforms. However, the actual gains from such increases are often undercut by obstacles in data management systems related to data storage, transfer, and processing. Lossy compression has been widely recognized as a promising solution to enhance scientific data management systems regarding such challenges, although most existing compression solutions are tailored for Cartesian grids and thus have sub-optimal results on discrete particle data. In this paper, we introduce LCP, an innovative lossy compressor designed for particle datasets, offering superior compression quality and higher speed than existing compression solutions. Specifically, our contribution is threefold. (1) We propose LCP-S, an error-bound aware block-wise spatial compressor to efficiently reduce particle data size. This approach is universally applicable to particle data across various domains. (2) We develop LCP, a hybrid compression solution for multi-frame particle data, featuring dynamic method selection and parameter optimization. (3) We evaluate our solution alongside eight state-of-the-art alternatives on eight real-world particle datasets from seven distinct domains. The results demonstrate that our solution achieves up to 104% improvement in compression ratios and up to 593% increase in speed compared to the second-best option, under the same error criteria.

cs.DC↗

arXiv2024

cuSZ-$i$: High-Ratio Scientific Lossy Compression on GPUs with Optimized Multi-Level Interpolation

Error-bounded lossy compression is a critical technique for significantly reducing scientific data volumes. Compared to CPU-based compressors, GPU-based compressors exhibit substantially higher throughputs, fitting better for today's HPC applications. However, the critical limitations of existing GPU-based compressors are their low compression ratios and qualities, severely restricting their applicability. To overcome these, we introduce a new GPU-based error-bounded scientific lossy compressor named cuSZ-$i$, with the following contributions: (1) A novel GPU-optimized interpolation-based prediction method significantly improves the compression ratio and decompression data quality. (2) The Huffman encoding module in cuSZ-$i$ is optimized for better efficiency. (3) cuSZ-$i$ is the first to integrate the NVIDIA Bitcomp-lossless as an additional compression-ratio-enhancing module. Evaluations show that cuSZ-$i$ significantly outperforms other latest GPU-based lossy compressors in compression ratio under the same error bound (hence, the desired quality), showcasing a 476% advantage over the second-best. This leads to cuSZ-$i$'s optimized performance in several real-world use cases.

cs.DC↗

arXiv2024

FRSZ2 for In-Register Block Compression Inside GMRES on GPUs

The performance of the GMRES iterative solver on GPUs is limited by the GPU main memory bandwidth. Compressed Basis GMRES outperforms GMRES by storing the Krylov basis in low precision, thereby reducing the memory access. An open question is whether compression techniques that are more sophisticated than casting to low precision can enable large runtime savings while preserving the accuracy of the final results. This paper presents the lightweight in-register compressor FRSZ2 that can decompress at the bandwidth speed of a modern NVIDIA H100 GPU. In an experimental evaluation, we demonstrate using FRSZ2 instead of low precision for compression of the Krylov basis can bring larger runtime benefits without impacting final accuracy.

cs.PF↗

arXiv2024

HoSZp: An Efficient Homomorphic Error-bounded Lossy Compressor for Scientific Data

Error-bounded lossy compression has been a critical technique to significantly reduce the sheer amounts of simulation datasets for high-performance computing (HPC) scientific applications while effectively controlling the data distortion based on user-specified error bound. In many real-world use cases, users must perform computational operations on the compressed data (a.k.a. homomorphic compression). However, none of the existing error-bounded lossy compressors support the homomorphism, inevitably resulting in undesired decompression costs. In this paper, we propose a novel homomorphic error-bounded lossy compressor (called HoSZp), which supports not only error-bounding features but efficient computations (including negation, addition, multiplication, mean, variance, etc.) on the compressed data without the complete decompression step, which is the first attempt to the best of our knowledge. We develop several optimization strategies to maximize the overall compression ratio and execution performance. We evaluate HoSZp compared to other state-of-the-art lossy compressors based on multiple real-world scientific application datasets.

cs.DC↗

arXiv2024

DataStates-LLM: Lazy Asynchronous Checkpointing for Large Language Models

LLMs have seen rapid adoption in all domains. They need to be trained on high-end high-performance computing (HPC) infrastructures and ingest massive amounts of input data. Unsurprisingly, at such a large scale, unexpected events (e.g., failures of components, instability of the software, undesirable learning patterns, etc.), are frequent and typically impact the training in a negative fashion. Thus, LLMs need to be checkpointed frequently so that they can be rolled back to a stable state and subsequently fine-tuned. However, given the large sizes of LLMs, a straightforward checkpointing solution that directly writes the model parameters and optimizer state to persistent storage (e.g., a parallel file system), incurs significant I/O overheads. To address this challenge, in this paper we study how to reduce the I/O overheads for enabling fast and scalable checkpointing for LLMs that can be applied at high frequency (up to the granularity of individual iterations) without significant impact on the training process. Specifically, we introduce a lazy asynchronous multi-level approach that takes advantage of the fact that the tensors making up the model and optimizer state shards remain immutable for extended periods of time, which makes it possible to copy their content in the background with minimal interference during the training process. We evaluate our approach at scales of up to 180 GPUs using different model sizes, parallelism settings, and checkpointing frequencies. The results show up to 48$\times$ faster checkpointing and 2.2$\times$ faster end-to-end training runtime compared with the state-of-art checkpointing approaches.

cs.DC↗

arXiv2024

FedSZ: Leveraging Error-Bounded Lossy Compression for Federated Learning Communications

With the promise of federated learning (FL) to allow for geographically-distributed and highly personalized services, the efficient exchange of model updates between clients and servers becomes crucial. FL, though decentralized, often faces communication bottlenecks, especially in resource-constrained scenarios. Existing data compression techniques like gradient sparsification, quantization, and pruning offer some solutions, but may compromise model performance or necessitate expensive retraining. In this paper, we introduce FedSZ, a specialized lossy-compression algorithm designed to minimize the size of client model updates in FL. FedSZ incorporates a comprehensive compression pipeline featuring data partitioning, lossy and lossless compression of model parameters and metadata, and serialization. We evaluate FedSZ using a suite of error-bounded lossy compressors, ultimately finding SZ2 to be the most effective across various model architectures and datasets including AlexNet, MobileNetV2, ResNet50, CIFAR-10, Caltech101, and Fashion-MNIST. Our study reveals that a relative error bound 1E-2 achieves an optimal tradeoff, compressing model states between 5.55-12.61x while maintaining inference accuracy within <0.5% of uncompressed results. Additionally, the runtime overhead of FedSZ is <4.7% or between of the wall-clock communication-round time, a worthwhile trade-off for reducing network transfer times by an order of magnitude for networks bandwidths <500Mbps. Intriguingly, we also find that the error introduced by FedSZ could potentially serve as a source of differentially private noise, opening up new avenues for privacy-preserving FL.

cs.DC↗

arXiv2024

Understanding The Effectiveness of Lossy Compression in Machine Learning Training Sets

Learning and Artificial Intelligence (ML/AI) techniques have become increasingly prevalent in high performance computing (HPC). However, these methods depend on vast volumes of floating point data for training and validation which need methods to share the data on a wide area network (WAN) or to transfer it from edge devices to data centers. Data compression can be a solution to these problems, but an in-depth understanding of how lossy compression affects model quality is needed. Prior work largely considers a single application or compression method. We designed a systematic methodology for evaluating data reduction techniques for ML/AI, and we use it to perform a very comprehensive evaluation with 17 data reduction methods on 7 ML/AI applications to show modern lossy compression methods can achieve a 50-100x compression ratio improvement for a 1% or less loss in quality. We identify critical insights that guide the future use and design of lossy compressors for ML/AI.

cs.LG↗

arXiv2023

Understanding Patterns of Deep Learning ModelEvolution in Network Architecture Search

Network Architecture Search and specifically Regularized Evolution is a common way to refine the structure of a deep learning model.However, little is known about how models empirically evolve over time which has design implications for designing caching policies, refining the search algorithm for particular applications, and other important use cases.In this work, we algorithmically analyze and quantitatively characterize the patterns of model evolution for a set of models from the Candle project and the Nasbench-201 search space.We show how the evolution of the model structure is influenced by the regularized evolution algorithm. We describe how evolutionary patterns appear in distributed settings and opportunities for caching and improved scheduling. Lastly, we describe the conditions that affect when particular model architectures rise and fall in popularity based on their frequency of acting as a donor in a sliding window.

cs.AI↗

arXiv2023

Black-Box Statistical Prediction of Lossy Compression Ratios for Scientific Data

Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless compression, no theoretical or data-based quantification of lossy compressibility exists for scientific data. Users rely on trial and error to assess lossy compression performance. As a strong data-driven effort toward quantifying lossy compressibility of scientific datasets, we provide a statistical framework to predict compression ratios of lossy compressors. Our method is a two-step framework where (i) compressor-agnostic predictors are computed and (ii) statistical prediction models relying on these predictors are trained on observed compression ratios. Proposed predictors exploit spatial correlations and notions of entropy and lossyness via the quantized entropy. We study 8+ compressors on 6 scientific datasets and achieve a median percentage prediction error less than 12%, which is substantially smaller than that of other methods while achieving at least a 8.8x speedup for searching for a specific compression ratio and 7.8x speedup for determining the best compressor out of a collection.

cs.DC↗

arXiv2022

ROIBIN-SZ: Fast and Science-Preserving Compression for Serial Crystallography

Crystallography is the leading technique to study atomic structures of proteins and produces enormous volumes of information that can place strains on the storage and data transfer capabilities of synchrotron and free-electron laser light sources. Lossy compression has been identified as a possible means to cope with the growing data volumes; however, prior approaches have not produced sufficient quality at a sufficient rate to meet scientific needs. This paper presents Region Of Interest BINning with SZ lossy compression (ROIBIN-SZ) a novel, parallel, and accelerated compression scheme that separates the dynamically selected preservation of key regions with lossy compression of background information. We perform and present an extensive evaluation of the performance and quality results made by the co-design of this compression scheme. We can achieve up to a 196x and 46.44x compression ratio on lysozyme and selenobiotinyl-streptavidin while preserving the data sufficiently to reconstruct the structure at bandwidths and scales that approach the needs of the upcoming light sources

cs.DC↗

arXiv2021

Exploring Lossy Compressibility through Statistical Correlations of Scientific Datasets

Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no known bound for the upper limit on lossy compressibility. Correlation structures in the data, choice of compressor and error bound are factors allowing larger compression ratios and improved quality metrics. Analyzing these three factors provides one direction towards quantifying lossy compressibility. As a first step, we explore statistical methods to characterize the correlation structures present in the data and their relationships, through functional models, to compression ratios. We observed a relationship between compression ratios and statistics summarizing correlation structure of the data, which are a first step towards evaluating the theoretical limits of lossy compressibility used to eventually predict compression performance and adapt compressors to correlation structures present in the data.

stat.AP↗

arXiv2021

SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors

Today's scientific simulations require a significant reduction of data volume because of extremely large amounts of data they produce and the limited I/O bandwidth and storage space. Error-bounded lossy compressor has been considered one of the most effective solutions to the above problem. In practice, however, the best-fit compression method often needs to be customized/optimized in particular because of diverse characteristics in different datasets and various user requirements on the compression quality and performance. In this paper, we develop a novel modular, composable compression framework (namely SZ3), which involves three significant contributions. (1) SZ3 features a modular abstraction for the prediction-based compression framework such that the new compression modules can be plugged in easily. (2) SZ3 supports multialgorithm predictors and can automatically select the best-fit predictor for each data block based on the designed error estimation criterion. (3) SZ3 allows users to easily compose different compression pipelines on demand, such that both compression quality and performance can be significantly improved for their specific datasets and requirements. (4) In addition, we evaluate several lossy compressors composed from SZ3 using the real-world datasets. Specifically, we leverage SZ3 to improve the compression quality and performance for different use-cases, including GAMESS quantum chemistry dataset and Advanced Photon Source (APS) instrument dataset. Experiments show that our customized compression pipelines lead to up to 20% improvement in compression ratios under the same data distortion compared with the state-of-the-art approaches.

cs.DC↗

arXiv2020

Hopf orders in $K[C_p^3]$ in characteristic $p$

Let $p$ be prime, let $K$ be a non-archimedean local field of characteristic $p$ and let $C_p^3$ denote the elementary abelian group of order $p^3$. We give a complete classification of Hopf orders in the $K$-Hopf algebra $(K[C_p^3])^*$ and under a mild condition compute their dual Hopf orders in the group ring $K[C_p^3]$.

math.RA↗

arXiv2020

Hopf Forms and Hopf-Galois Theory

Let $K$ be a finite field extension of $\Q$ and let $N$ be a finite group with automorphism group $F=\Aut(N)$. R. Haggenmüller and B. Pareigis have shown that there is a bijection \[Θ: {\mathcal Gal}(K,F)\rightarrow {\mathcal Hopf}(K[N])\] from the collection of $F$-Galois extensions of $K$ to the collection of Hopf forms of the group ring $K[N]$. For $N=C_n$, $n\ge 1$, $C_p^m$, $p$ prime, $m\ge 1$, and $N=D_3,D_4,Q_8$, we show that $\Q[N]$ admits an absolutely semisimple Hopf form $H$ and find $L$ for which $Θ(L)=H$. Moreover, if $H$ is the Hopf algebra given by a Hopf-Galois structure on a Galois extension $E/K$, we show how to construct the preimage of $H$ under $Θ$ assuming certain conditions.

math.RA↗

arXiv2020

cuSZ: An Efficient GPU-Based Error-Bounded Lossy Compression Framework for Scientific Data

Error-bounded lossy compression is a state-of-the-art data reduction technique for HPC applications because it not only significantly reduces storage overhead but also can retain high fidelity for postanalysis. Because supercomputers and HPC applications are becoming heterogeneous using accelerator-based architectures, in particular GPUs, several development teams have recently released GPU versions of their lossy compressors. However, existing state-of-the-art GPU-based lossy compressors suffer from either low compression and decompression throughput or low compression quality. In this paper, we present an optimized GPU version, cuSZ, for one of the best error-bounded lossy compressors-SZ. To the best of our knowledge, cuSZ is the first error-bounded lossy compressor on GPUs for scientific data. Our contributions are fourfold. (1) We propose a dual-quantization scheme to entirely remove the data dependency in the prediction step of SZ such that this step can be performed very efficiently on GPUs. (2) We develop an efficient customized Huffman coding for the SZ compressor on GPUs. (3) We implement cuSZ using CUDA and optimize its performance by improving the utilization of GPU memory bandwidth. (4) We evaluate our cuSZ on five real-world HPC application datasets from the Scientific Data Reduction Benchmarks and compare it with other state-of-the-art methods on both CPUs and GPUs. Experiments show that our cuSZ improves SZ's compression throughput by up to 370.1x and 13.1x, respectively, over the production version running on single and multiple CPU cores, respectively, while getting the same quality of reconstructed data. It also improves the compression ratio by up to 3.48x on the tested data compared with another state-of-the-art GPU supported lossy compressor.

cs.DC↗

arXiv2020

FRaZ: A Generic High-Fidelity Fixed-Ratio Lossy Compression Framework for Scientific Floating-point Data

With ever-increasing volumes of scientific floating-point data being produced by high-performance computing applications, significantly reducing scientific floating-point data size is critical, and error-controlled lossy compressors have been developed for years. None of the existing scientific floating-point lossy data compressors, however, support effective fixed-ratio lossy compression. Yet fixed-ratio lossy compression for scientific floating-point data not only compresses to the requested ratio but also respects a user-specified error bound with higher fidelity. In this paper, we present FRaZ: a generic fixed-ratio lossy compression framework respecting user-specified error constraints. The contribution is twofold. (1) We develop an efficient iterative approach to accurately determine the appropriate error settings for different lossy compressors based on target compression ratios. (2) We perform a thorough performance and accuracy evaluation for our proposed fixed-ratio compression framework with multiple state-of-the-art error-controlled lossy compressors, using several real-world scientific floating-point datasets from different domains. Experiments show that FRaZ effectively identifies the optimum error setting in the entire error setting space of any given lossy compressor. While fixed-ratio lossy compression is slower than fixed-error compression, it provides an important new lossy compression technique for users of very large scientific floating-point datasets.

cs.DC↗

arXiv2019

The Structure of Hopf Algebras Acting on Dihedral Extensions

We discuss isomorphism questions concerning the Hopf algebras that yield Hopf-Galois structures for a fixed separable field extension $L/K$. We study in detail the case where $L/K$ is Galois with dihedral group $D_p$, $p\ge 3$ prime and give explicit descriptions of the Hopf algebras which act on $L/K$. We also determine when two such Hopf algebras are isomorphic, either as Hopf algebras or as algebras. For the case $p=3$ and a chosen $L/K$, we give the Wedderburn-Artin decompositions of the Hopf algebras.

math.NT↗

arXiv2018

A Class of Automatic Sequences

Let $k\ge 2$. We prove that the characteristic sequence of a regular language over a $k$-letter alphabet is $k$-automatic. More generally, if $t\ge 2$ and $t,k$ are multiplicatively dependent, we show that the characteristic sequence of a regular language over a $t$-letter alphabet is $k$-automatic.

cs.FL↗