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Optimizing SpMV for Diagonal Sparse Matrices on GPU

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Optimizing SpMV for Diagonal Sparse Matrices on GPU

International Conference on parallel Processing (ICPP)

作者： Xiangzheng Sun Yunquan Zhang Ting Wang Xianyi Zhang Liang Yuan Li Rao Graduate University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences (CAS) Beijing China Chinese Academy of Sciences Beijing Beijing CN Laboratory of Parallel Software and Computational Science Institute of Software Chinese Academy of Sciences (CAS) Beijing China

Sparse Matrix-Vector multiplication (SpMV) is an important computational kernel in scientific applications. Its performance highly depends on the nonzero distribution of sparse matrices. In this paper, we propose a new storage format for diagonal sparse matrices, defined as Compressed Row Segment with Diagonal-pattern (CRSD). In CRSD, we design diagonal patterns to represent the diagonal distribution. As the Graphics Processing Units (GPUs) have tremendous computation power and OpenCL makes them more suitable for the scientific computing, we implement the SpMV for CRSD format on the GPUs using OpenCL. Since the OpenCL kernels are complied at runtime, we design the code generator to produce the codelets for all diagonal patterns after storing matrices into CRSD format. Specifically, the generated codelets already contain the index information of nonzeros, which reduces the memory pressure during the SpMV operation. Furthermore, the code generator also utilizes property of memory architecture and thread schedule on the GPUs to improve the performance. In the evaluation, we select four storage formats from prior state-of-the-art implementations (Bell and Garland, 2009) on GPU. Experimental results demonstrate that the speedups reach up to 1.52 and 1.94 in comparison with the optimal implementation of the four formats for the double and single precision respectively. We also evaluate on a two-socket quad-core Intel Xeon system. The speedups reach up to 11.93 and 12.79 in comparison with CSR format under 8 threads for the double and single precision respectively.

关键词： Sparse matrices Indexes Graphics processing unit Kernel Arrays Copper Instruction sets

Suggesting variable order for cylindrical algebraic decomposition via reinforcement learning 23

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Suggesting variable order for cylindrical algebraic decompos...

Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Fuqi Jia Yuhang Dong Minghao Liu Pei Huang Feifei Ma Jian Zhang State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China Laboratory of Parallel Software and Computational Science Institute of Software Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China Stanford University Stanford

Cylindrical Algebraic Decomposition (CAD) is one of the pillar algorithms of symbolic computation, and its worst-case complexity is double exponential to the number of variables. Researchers found that variable order dramatically affects efficiency and proposed various heuristics. The existing learning-based methods are all supervised learning methods that cannot cope with diverse polynomial sets. This paper proposes two Reinforcement Learning (RL) approaches combined with Graph Neural Networks (GNN) for Suggesting Variable Order (SVO). One is GRL-SVO(UP), a branching heuristic integrated with CAD. The other is GRL-SVO(NUP), a fast heuristic providing a total order directly. We generate a random dataset and collect a real-world dataset from SMT-LIB. The experiments show that our approaches outperform state-of-the-art learning-based heuristics and are competitive with the best expert-based heuristics. Interestingly, our models show a strong generalization ability, working well on various datasets even if they are only trained on a 3-var random dataset. The source code and data are available at https://***/dongyuhang22/GRL-SVO.

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Performance Evaluation of Service Orchestration with Dynarric Latency Simulation

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China Communications 2012年第12期9卷 68-79页

作者： Zhang Changyou Zhu Dongfeng Hu Jingjing Jin Haifei Laboratory of Parallel Software and Computational Science Institute of Sottware Chinese Academy of Science Beijing 100190 P. R. China HOST Key Laboratory School of Electrical Engineering and Computer Science Peking University Beijing 100085 P. R. China School of Computer Beijing Institute of Technology Beijing 100081 P. R. China School of Computer Beijing University of Posts and Telecommunications Beijing 100082 P. R. China

Dynamic latency over the Intemet is an Important parameter for evaluating the performance of Web service orchestration. In this paper, we propose a performance analyzing and correctness checking method for service orchestration with dynamic latency simulated in Colored PetriNets （CPNs）. First, we extend the CPN to Web Service Composition Orchestration Network System （WS-CONS） for the description of dynamic latency in service orchestration. Secondly, with simulated dynamic latency, a buffer-limited policy and admittance-control policy are designed in WS- CONS and implemented on CPN Tools. In the buffer-limited policy, the passing messages would be discarded if the node capacity is not adequate. In the admittance-control policy, the ability of a message entering the system depends on the number of messages concurrently flowing in the system. This helps to enhance the success rate of message passing. Finally, the system performance is evaluated through running models in CPN Tools. Simulated results show that the dynamic latency plays an important role in the system throughput and response latency. This simulation helps system designers to quickly make proper compromises at low cost.

关键词： service orchestration CPN dynamic latency simulation

Teracluster LSSC-II--Its designing principles and applications in large scale numerical simulations

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中国科学A辑（英文版） 2004年第z1期47卷 53-68页

作者： Zhang Linbo Chen Shiyi LI Xinliang CAO Jianwen ZHANG Wensheng GONG Xingao State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mechanical Engineering The Johns Hopkins University and Center for Computational Science and Engineering Peking University Beijing 100875 China Institute of Mechanics Chinese Academy of SciencesBeijing 100080 China Parallel Computing Laboratory Institute of Software Chinese Academy of Sciences Beijing 100080 China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Surface Physics Laboratory National Key Laboratory Fudan University Shanghai 200433 Institute of Solid State Physics Chinese Academy of Sciences Hefei 230031 China

The teracluster LSSC-II installed at the State Key laboratory of Scientific and Engineering Computing, Chinese Academy of sciences is one of the most powerful PC clusters in China. It has a peek performance of 2Tflops. With a Linpack performance of 1.04Tflops, it is ranked at the 43rd place in the 20th TOP500 List (November 2002), 51st place in the 21st TOP500 List (June 2003), and the 82nd place in the 22nd TOP500 List (November 2003) with a new Linpack performance of 1.3Tflops. In this paper, we present some design principles of this cluster, as well as its applications in some large-scale numerical simulations.

关键词： high performance computing PC cluster large scale numerical simulations

Physically based parallel ray tracer for the Metropolis light transport algorithm on the Tianhe-2 supercomputer

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Physically based parallel ray tracer for the Metropolis ligh...

International Conference on parallel and Distributed Systems (ICPADS)

作者： Changmao Wu Yunquan Zhang Congli Yang Yutong Lu University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Architecture CAS Beijing China Laboratory of Parallel Software & Computational Science CAS Beijing China Department of Computer Science & Technology National University of Defense Technology Changsha Hunan China

Developing an efficient and highly scalable ray tracer for the Metropolis light transport algorithm is becoming increasingly important as the request for photorealistic images becomes a common trend. Although the Metropolis light transport algorithm has produced some of the most realistic images to date, it usually takes a great amount of time to render an image. The development of an efficient and highly scalable ray tracer for the Metropolis light transport algorithm is hard due in large part to the irregular memory access patterns, the imbalanced workload of light-carrying paths and the complicated mathematical model and complex physical processes. In this paper, we present a highly scalable physically based parallel ray tracer for the Metropolis light transport algorithm. Firstly, we present the idea of snapshot and sub-snapshot, then propose a novel assignment partitioning algorithm for compute nodes and CPU cores since the demand-driven assignment partitioning algorithms don't work. Secondly, we propose a physically based parallel ray racing framework for the Metropolis light transport algorithm, which is based on a master-worker architecture. Finally, we discuss the issue of granularity of the assignment partitioning and some optimization strategies for improving overall performance, then a hybrid scheduling strategy combining a static and dynamic scheduling strategy is described. Experiments show that our physically based ray tracer almost reaches linear speedup by using 26,400 CPU cores on the Tianhe-2 supercomputer. Our ray tracer is more efficient and highly scalable.

关键词： Partitioning algorithms EMTP

Sparse spectral-galerkin method on an arbitrary tetrahedron using generalized koornwinder polynomials

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arXiv 2021年

作者： Jia, Lueling Li, Huiyuan Zhang, Zhimin Beijing Computational Science Research Center Beijing100193 China State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China Department of Mathematics Wayne State University DetroitMI48202 United States

In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koornwinder polynomials are introduced on the reference tetrahedron as basis functions with their various recurrence relations and differentiation properties being explored. The method leads to well-conditioned and sparse linear systems whose entries can either be calculated directly by the orthogonality of the generalized Koornwinder polynomials for differential equations with constant coefficients or be evaluated efficiently via our recurrence algorithm for problems with variable coefficients. Clenshaw algorithms for the evaluation of any polynomial in an expansion of the generalized Koornwinder basis are also designed to boost the efficiency of the method. Finally, numerical experiments are carried out to illustrate the effectiveness of the proposed Koornwinder spectral *** Codes 65N25, 65N35 © 2021, CC0.

关键词： Polynomials

H(curl2)-conforming quadrilateral spectral element method for quad-curl problems

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arXiv 2021年

作者： Wang, Lixiu Shan, Weikun Li, Huiyuan Zhang, Zhimin Beijing Computational Science Research Center Beijing100193 China School of Science Henan University of Technology Zhengzhou Henan450001 China State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China Department of Mathematics Wayne State University MI48202 United States

In this paper, we propose an H(curl2)-conforming quadrilateral spectral element method to solve quad- curl problems. Starting with generalized Jacobi polynomials, we first introduce quasi-orthogonal poly- nomial systems for vector fields over rectangles. H(curl2)-conforming elements over arbitrary convex quadrilaterals are then constructed explicitly in a hierarchical pattern using the contravariant transform together with the bilinear mapping from the reference square onto each quadrilateral. It is astonishing that both the simplest rectangular and quadrilateral spectral elements possess only 8 degrees of freedom on each physical element. In the sequel, we propose our H(curl2)-conforming quadrilateral spectral element approximation based on the mixed weak formulation to solve the quad-curl equation and its eigenvalue problem. Numerical results show the effectiveness and efficiency of our method. Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Jacobi-galerkin spectral method for eigenvalue problems of riesz fractional differential equations

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arXiv 2018年

作者： Chen, Lizhen Mao, Zhiping Li, Huiyuan Beijing Computational Sciences and Research Center Beijing100193 China Division of Applied Mathematics Brown University 182 George St ProvidenceRI02912 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

An effcient Jacobi-Galerkin spectral method for calculating eigenvalues of Riesz fractional partial diferential equations with homogeneous Dirichlet boundary values is proposed in this paper. In order to retain the symmetry and positive defniteness of the discrete linear system, we introduce some properly defned Sobolev spaces and approximate the eigenvalue problem in a standard Galerkin weak formulation instead of the Petrov-Galerkin one as in literature. Poincaré and inverse inequalities are proved for the proposed Galerkin formulation which finally help us establishing a sharp estimate on the algebraic system's condition number. Rigorous error estimates of the eigenvalues and eigenvectors are then readily obtained by using Babuška and Osborn's approximation theory on self-adjoint and positive-defnite eigenvalue problems. Numerical results are presented to demonstrate the accuracy and effciency, and to validate the asymptotically exponential oder of convergence. Moreover, the Weyl-type asymptotic law λn = O(n2α) for the n-th eigenvalue λn of the Riesz fractional differential operator of order 2α, and the condition number N4αof its algebraic system with respect to the polynomial degree N are observed.35R11, 65N25, 65N35, 74S25 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

A Prompting-based Approach for Adversarial Example Generation and Robustness Enhancement

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arXiv 2022年

作者： Yang, Yuting Huang, Pei Cao, Juan Li, Jintao Lin, Yun Dong, Jin Song Ma, Feifei Zhang, Jian Key Lab of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China Beijing China National University of Singapore Singapore Laboratory of Parallel Software and Computational Science ISCAS Beijing China

Recent years have seen the wide application of NLP models in crucial areas such as finance, medical treatment, and news media, raising concerns of the model robustness and vulnerabilities. In this paper, we propose a novel prompt-based adversarial attack to compromise NLP models and robustness enhancement technique. We first construct malicious prompts for each instance and generate adversarial examples via mask-and-filling under the effect of a malicious purpose. Our attack technique targets the inherent vulnerabilities of NLP models, allowing us to generate samples even without interacting with the victim NLP model, as long as it is based on pre-trained language models (PLMs). Furthermore, we design a prompt-based adversarial training method to improve the robustness of PLMs. As our training method does not actually generate adversarial samples, it can be applied to large-scale training sets efficiently. The experimental results show that our attack method can achieve a high attack success rate with more diverse, fluent and natural adversarial examples. In addition, our robustness enhancement method can significantly improve the robustness of models to resist adversarial attacks. Our work indicates that prompting paradigm has great potential in probing some fundamental flaws of PLMs and fine-tuning them for downstream tasks. Copyright © 2022, The Authors. All rights reserved.

关键词： Natural language processing systems