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International Conference for High Performance Computing, Networking, Storage and Analysis (HPC)

作者： Cheshmi, Kazem Cetinic, Zachary Dehnavi, Maryam Mehri Univ Toronto Toronto ON Canada

ISBN: (纸本)9781665454445

The compact data structures and irregular computation patterns in sparse matrix computations introduce challenges to vectorizing these codes. Available approaches primarily vectorize strided computation regions of a sparse code. In this work, we propose a locality-based codelet mining (LCM) algorithm that efficiently searches for strided and partially strided regions in sparse matrix computations for vectorization. We also present a classification of partially strided codelets and a differentiation-based approach to generate codelets from memory accesses in the sparse computation. LCM is implemented as an inspector-executor framework called LCM I/E that generates vectorized code for the sparse matrix-vector multiplication (SpMV), sparse matrix times dense matrix (SpMM), and sparse triangular solver (SpTRSV). LCM I/E outperforms the MKL library with an average speedup of 1.67x, 4.1x, and 1.75x for SpMV, SpTRSV, and SpMM, respectively. It is also faster than the state-of-the-art inspector-executor framework Sympiler [1] for the SpTRSV kernel with an average speedup of 1.9x.

关键词： Vectorization Parallel programming Polyhedral analysis sparse matrix computation

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PckGNN: Optimizing Aggregation Operators with Packing Strategies in Graph Neural Networks 38

PckGNN: Optimizing Aggregation Operators with Packing Strate...

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International Parallel and Distributed Processing Symposium (IPDPS)

作者： Hu, Zhengding Sun, Jingwei Li, Zhongyang Sun, Guangzhong Univ Sci & Techonol China Hefei Peoples R China

ISBN: (纸本)9798350387117;9798350387124

Graph Neural Network (GNN) is one of the most prominent machine learning models. It involves a substantial amount of graph-based aggregation operators, which can be abstracted as sparse matrix computation kernels. Due to the irregularity of the graph adjacency matrix, the aggregation has long been the performance bottleneck of GNN. According to our measurements, existing GNN implementations fall short of achieving optimal performance due to their insufficient consideration of load balancing and data locality. To bridge these performance gaps, we propose PckGNN, which aims to accelerate GNN aggregation operators on GPUs with packing strategies. PckGNN categorizes graph matrices into two types based on different sparsity levels and conducts two packing strategies respectively. For sparser matrices, Neighbor Packing enhances load balancing through a moderate-grained non-zero grouping approach. For denser matrices, Bin Packing exposes more potentials of cache data reuse by bin partitioning, non-zero extracting, format converting and two-level scheduling. Experimental results on SpMM and SDDMM show that PckGNN achieves speedups of 1.46x similar to 6.14x over existing implementations. When applied GNN inference of three typical models, it achieves speedups of more than 1.29x over the state-of-the-art frameworks.

关键词： Graph Neural Network sparse matrix computation GPU

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Scalable Node Embedding Algorithms using Distributed sparse matrix Operations

Scalable Node Embedding Algorithms using Distributed Sparse ...

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1st International Conference on Smart Energy Systems and Artificial Intelligence (SESAI)

作者： Ranawaka, Isuru Azad, Ariful Indiana Univ Bloomington IN 47405 USA

ISBN: (纸本)9798350364613;9798350364606

We introduce a distributed memory parallel algorithm for force-directed node embedding that places vertices of a graph into a low-dimensional vector space based on the interplay of attraction among neighboring vertices and repulsion among distant vertices. We develop our algorithms using two sparse matrix operations, SDDMM and SpMM. We propose a configurable pull -push -based communication strategy that optimizes memory usage and data transfers based on computing resources and asynchronous MPI communication to overlap communication and computation. Our algorithm scales up to 256 nodes on distributed supercomputers by surpassing the performance of state-of-the-art algorithms

关键词： Embedding SDDMM sparse matrix computation SpMM

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PrSpMV: An Efficient Predictable Kernel for SpMV 41

PrSpMV: An Efficient Predictable Kernel for SpMV

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41st IEEE International Conference on Computer Design (ICCD)

作者： Fu, Gelin Xia, Tian Qu, Shaoru Luo, Zhongpei Li, Shuyu Cheng, Pengyu Guo, Runfan Ding, Yitong Ren, Pengju Xi An Jiao Tong Univ Xian Peoples R China

ISBN: (纸本)9798350342918

sparse matrix-Vector Multiplication (SpMV) has been widely applied in scientific computation, industry simulation, and intelligent computation domains, which is the critical algorithm in all these applications. Due to the poor data locality, low cache usage, and extremely irregular branch patterns caused by the highly sparse and random distributions, SpMV optimization has become one of the most challenging problems for modern high-performance processors. In this paper, we study the bottlenecks of SpMV on current out-of-order CPUs and propose a novel SpMV kernel named PrSpMV to improve its performance by pursuing high predictability. Specifically, we improve the memory access regularity and locality by creating serialized access patterns so that the data prefetching efficiency and cache usage are optimized. We also improve pipeline efficiency by creating regular branch patterns to make branch prediction more accurate. Experiment results show that using the above optimization approaches, PrSpMV can eliminate nearly all branch mispredictions. Moreover, it can also significantly reduce the average L2 cache miss rate from 57% to 20% via efficiently leveraging hardware prefetchers. By using PrSpMV, stride prefetcher can be boosted with 1.31x speedup and dedicated irregular prefetcher can be improved with 1.40x speedup. Meanwhile, on commercial high-end Intel processors, it achieves 1.32x speedup against some state-of-the-art SpMV kernels.

关键词： sparse matrix computation Data Prefetching Branch Prediction

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Vectorizing sparse matrix computations with partially-strided codelets 22

Vectorizing sparse matrix computations with partially-stride...

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Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

作者： Kazem Cheshmi Zachary Cetinic Maryam Mehri Dehnavi University of Toronto Toronto Canada

The compact data structures and irregular computation patterns in sparse matrix computations introduce challenges to vectorizing these codes. Available approaches primarily vectorize strided computation regions of a sparse code. In this work, we propose a locality-based codelet mining (LCM) algorithm that efficiently searches for strided and partially strided regions in sparse matrix computations for vectorization. We also present a classification of partially strided codelets and a differentiation-based approach to generate codelets from memory accesses in the sparse computation. LCM is implemented as an inspector-executor framework called LCM I/E that generates vectorized code for the sparse matrix-vector multiplication (SpMV), sparse matrix times dense matrix (SpMM), and sparse triangular solver (SpTRSV). LCM I/E outperforms the MKL library with an average speedup of 1.67×, 4.1×, and 1.75× for SpMV, SpTRSV, and SpMM, respectively. It is also faster than the state-of-the-art inspector-executor framework Sympiler [1] for the SpTRSV kernel with an average speedup of 1.9×.

关键词： parallel programming vectorization sparse matrix computation polyhedral analysis

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A NEW CLASS OF AMG INTERPOLATION METHODS BASED ON matrix-matrix MULTIPLICATIONS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2021年第5期43卷 S540-S564页

作者： LI, Ruipeng Sjogreen, Bjorn Yang, Ulrike Meier Ctr Appl Sci Comp Lawrence Livermore Natl Lab Livermore CA 94551 USA

A new class of distance-two interpolation methods for algebraic multigrid (AMG) that can be formulated in terms of sparse matrix-matrix multiplications is presented and analyzed. Compared with similar distance-two prolongation operators [H. De Sterck et al., Numer. Linear Algebra Appl., 15 (2008), pp. 115-139], the proposed algorithms exhibit improved efficiency and portability to various computing platforms, since they allow one to easily exploit existing high-performance sparse matrix kernels. The new interpolation methods have been implemented in hypre [R. D. Falgout and U. M. Yang, hypre: A library of high performance preconditioners, in computational Science - ICCS 2002, P. M. A. Sloot et al., eds., Springer, Berlin, Heidelberg, 2002, pp. 632-641], a widely used parallel multigrid solver library. With the proposed interpolations, the overall time of hypre's BoomerAMG setup can be considerably reduced, while sustaining equivalent, sometimes improved, convergence rates. Numerical results for a variety of test problems on parallel machines are presented that support the superiority of the proposed interpolation operators over the existing ones in hypre.

关键词： AMG interpolation sparse matrix computation parallel and distributed computing

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Machine Learning to Design an Auto-tuning System for the Best Compressed Format Detection for Parallel sparse computations

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PARALLEL PROCESSING LETTERS 2021年第4期31卷 p1-37页

作者： Hamdi-Larbi, Olfa Mehrez, Ichrak Dufaud, Thomas Univ Tunis El Manar Fac Sci Tunis URAPOP Tunis 2092 Tunisia Taibah Univ MIS Dept Coll Business Madinah Saudi Arabia Univ Paris Saclay Univ Versailles St Quentin Lab Li Parad F-78280 Guyancourt France CEA Saclay Maison Simulat F-91191 Gif Sur Yvette France

Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning.

关键词： Design and optimization for HPC systems smart system grid and cluster computing multi-core architectures and support large scale scientific computing data parallel model sparse matrix computation

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Enabling and Scaling the HPCG Benchmark on the Newest Generation Sunway Supercomputer with 42 Million Heterogeneous Cores 21

Enabling and Scaling the HPCG Benchmark on the Newest Genera...

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International Conference for High Performance Computing, Networking, Storage and Analysis (SC21)

作者： Zhu, Qianchao Luo, Hao Yang, Chao Ding, Mingshuo Yin, Wanwang Yuan, Xinhui Peking Univ Ctr Data Sci Beijing 100871 Peoples R China Peking Univ Sch Math Sci Beijing 100871 Peoples R China Peking Univ Natl Engn Lab Big Data Anal & Applicat Beijing 100871 Peoples R China Peking Univ Sch Elect Engn & Comp Sci Beijing 100871 Peoples R China Natl Res Ctr Parallel Comp Engn & Technol Beijing 100190 Peoples R China

ISBN: (纸本)9781450384421

We study and evaluate performance optimization techniques for the HPCG benchmark on the newest generation Sunway supercomputer. Specifically, a two -level blocking scheme is proposed to expose adequate parallelism in the symmetric Gauss-Seidel kernel while keeping a fast convergence rate, a fine-grained kernel fusion technique is developed to alleviate the bandwidth load on local storage with small capacity, and a low overhead thread collaboration method is presented to efficiently move data between threads and hide its cost with data transfer operations. Test results show that the optimized HPCG code is able to exploit 73.0% of the theoretical memory bandwidth, and scale to over 42 million heterogeneous cores with 95.5% weak-scaling efficiency and 5.91 Pflop/s performance. We also study how the performance can be improved if the specific rules of HPCG are not fully obeyed, and design dependency preserving parallelization and vectorization methods, further boosting performance to 27.6 Pflop/s.

关键词： HPCG sparse matrix computation the newest generation Sunway supercomputer

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ReservoirPy: An Efficient and User-Friendly Library to Design Echo State Networks 29th

ReservoirPy: An Efficient and User-Friendly Library to Desig...

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29th International Conference on Artificial Neural Networks (ICANN)

作者： Trouvain, Nathan Pedrelli, Luca Dinh, Thanh Trung Hinaut, Xavier INRIA Bordeaux Sud Ouest Talence France Bordeaux INP CNRS LaBRI UMR 5800 Talence France Univ Bordeaux Inst Malad Neurodegenerat CNRS UMR 5293 Bordeaux France

ISBN: (纸本)9783030616168;9783030616151

We present a simple user-friendly library called ReservoirPy based on Python scientific modules. It provides a flexible interface to implement efficient Reservoir Computing (RC) architectures with a particular focus on Echo State Networks (ESN). Advanced features of ReservoirPy allow to improve up to 87.9% of computation time efficiency on a simple laptop compared to basic Python implementation. Overall, we provide tutorials for hyperparameters tuning, offline and online training, fast spectral initialization, parallel and sparse matrix computation on various tasks (MackeyGlass and audio recognition tasks). In particular, we provide graphical tools to easily explore hyperparameters using random search with the help of the hyperopt library.

关键词： Reservoir Computing Echo State Networks Offline learning Online learning Hyperparameter optimization Parallel computing sparse matrix computation Toolbox

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Performance evaluation and analysis of sparse matrix and graph kernels on heterogeneous processors

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CCF TRANSACTIONS ON HIGH PERFORMANCE COMPUTING 2019年第2期1卷 131-143页

作者： Zhang, Feng Liu, Weifeng Feng, Ningxuan Zhai, Jidong Du, Xiaoyong Renmin Univ China Key Lab Data Engn & Knowledge Engn MOE Beijing Peoples R China Renmin Univ China Sch Informat Beijing Peoples R China China Univ Petr Dept Comp Sci & Technol Beijing Peoples R China Tsinghua Univ Dept Comp Sci & Technol Beijing Peoples R China

Heterogeneous processors integrate very distinct compute resources such as CPUs and GPUs into the same chip, thus can exploit the advantages and avoid disadvantages of those compute units. We in this work evaluate and analyze eight sparse matrix and graph kernels on an AMD CPU-GPU heterogeneous processor by using 956 sparse matrices. Five characteristics, i.e., load balancing, indirect addressing, memory reallocation, atomic operations, and dynamic characteristics are our major considerations. The experimental results show that although the CPU and GPU parts access the same DRAM, very different performance behaviors are observed. For example, though the GPU part in general outperforms the CPU part, it cannot achieve the best performance in all cases given by the CPU part. Moreover, the bandwidth utilization of atomic operations on heterogeneous processors can be much higher than a high-end discrete GPU.

关键词： Heterogeneous processor Performance analysis sparse matrix computation

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