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1. Scalability of Hybrid SpMV with Hypergraph Partitioning and Vertex Delegation for Communication Avoidance

   Page, Brian A ; Kogge, Peter M ( March 2021 , International Conference on High Performance Computing & Simulation (HPCS 2020))

   null (Ed.)

   Communication overhead has been identified as the primary factor in overall performance degradation for sparse and irregular problems such as SpMV. Many works have shown significant communication reductions, but only for matrices with specific characteristics and by dramatically reworking the computations. This study develops and evaluates a communication avoiding distributed heterogeneous implementation for strong scaling of SpMV on the Sierra supercomputer architecture. To address the far bigger matrices characteristic of real problems, we utilize a hypergraph partitioning package HYPE to determine workload distribution and reduce inter-node communication. Additionally we investigated the performance impact of performing hypergraph partitioning on scale free graphs which had undergone a vertex delegation pre-processing step. We achieved up to 97% reduction in average message size per process at scale when using the HYPE partitioner. Despite this we show how optimizing SpMV on existing GPU architectures does provide increased computational performance, yet does not address the dominant communication overhead factor at scale despite attempts to avoid communication where possible. 

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2. WISE: Predicting the Performance of Sparse Matrix Vector Multiplication with Machine Learning

   https://doi.org/10.1145/3572848.3577506  

   Yesil, Serif ; Heidarshenas, Azin ; Morrison, Adam ; Torrellas, Josep ( February 2023 , Proceedings of the 28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming)

   Sparse Matrix-Vector Multiplication (SpMV) is an essential sparse kernel. Numerous methods have been developed to accelerate SpMV. However, no single method consistently gives the highest performance across a wide range of matrices. For this reason, a performance prediction model is needed to predict the best SpMV method for a given sparse matrix. Unfortunately, predicting SpMV’s performance is challenging due to the diversity of factors that impact it. In this work, we develop a machine learning framework called WISE that accurately predicts the magnitude of the speedups of different SpMV methods over a baseline method for a given sparse matrix. WISE relies on a novel feature set that summarizes a matrix’s size, skew, and locality traits. WISE can then select the best SpMV method for each specific matrix. With a set of nearly 1,500 matrices, we show that using WISE delivers an average speedup of 2.4× over using Intel’s MKL in a 24-core server. 

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3. Hardware accelerator thread for unstructured sparse data processing

   Pranathi Vasireddy, Krishna Kavi ( October 2022 , International Conference on Computer Aided Design)

   Sparse matrix-dense vector (SpMV) multiplication is inherent in most scientific, neural networks and machine learning algorithms. To efficiently exploit sparsity of data in the SpMV computations, several compressed data representations have been used. However, the compressed data representations of sparse date can result in overheads for locating nonzero values, requiring indirect memory accesses and increased instruction count and memory access delays. We call these translations of compressed representations as metadata processing. We propose a memory-side accelerator for metadata (or indexing) computations and supplying only the required nonzero values to the processor, additionally permitting an overlap of indexing with core computations on nonzero elements. In this contribution, we target our accelerator for low-end microcontrollers with very limited memory and processing capabilities. In this paper we will explore two dedicated ASIC designs of the proposed accelerator that handles the indexed memory accesses for compressed sparse row (CSR) format working alongside a simple RISC-like programmable core. One version of the the accelerator supplies only vector values corresponding to nonzero matrix values and the second version supplies both nonzero matrix and matching vector values for SpMV computations. Our experiments show speedups ranging between 1.3 and 2.1 times for SpMV for different levels of sparsities. Our accelerator also results in energy savings ranging between 15.8% and 52.7% over different matrix sizes, when compared to the baseline system with primary RISC-V core performing all computations. We use smaller synthetic matrices with different sparsities and larger real-world matrices with higher sparsities (below 1% non-zeros) in our experimental evaluations. 

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4. Scalability of Sparse Matrix Dense Vector Multiply (SpMV) on a Migrating Thread Architecture

   https://doi.org/10.1109/IPDPSW50202.2020.00088  

   Page, Brian A. ; Kogge, Peter M. ( May 2020 , 2020 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW))

   null (Ed.)

   Sparse matrix dense vector multiplication (SpMV), exhibits the memory bandwidth and communication driven nature of many sparse linear algebra operations. Irregular memory accesses from the non-zero structure within a sparse matrix wreak havoc on performance. This paper presents strong scaling for communication avoiding SpMV implementations on a migrating thread system intended to address the lack of locality in sparse problems. We developed communication avoiding SpMV code to attempt to reduce off-node thread migration by using the hypergraph partitioning package HYPE to determine workload distribution. Additionally, we investigate the performance impact of overlapping communication and computation through the use of remote memory operations supported by the architecture. Incorporating remote memory operations with hypergraph partitioning we achieved 6.18X speedup for overall performance. 

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5. Scalability of Hybrid SpMV on Intel Xeon Phi Knights Landing

   Page, Brian A. ; Kogge, Peter M. ( July 2019 , Int. Conf. on High Performance Computing and Simulation)

   null (Ed.)

   SpMV, the product of a sparse matrix and a dense vector, is emblematic of a new class of applications that are memory bandwidth and communication, not flop, driven. Sparsity and randomness in such computations play havoc with performance, especially when strong, instead of weak, scaling is attempted. In this study we develop and evaluate a hybrid implementation for strong scaling of the Compressed Vectorization-oriented sparse Row (CVR) approach to SpMV on a cluster of Intel Xeon Phi Knights Landing (KNL) processors. We show how our hybrid SpMV implementation achieves increased computational performance, yet does not address the dominant communication overhead factor at extreme scale. Issues with workload distribution, data placement, and remote reductions are assessed over a range of matrix characteristics. Our results indicate that as P 􀀀! 1 communication overhead is by far the dominant factor despite improved computational performance. 

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