Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userProver efficient public verification of dense or sparse/structured matrix-vector multiplication
62
0
0.0
(
0
)
Added by
Jean-Guillaume Dumas
Publication date
2017
fields
Informatics Engineering
and research's language is
English
Authors
Jean-Guillaume Dumas
Ask ChatGPT about the research
No Arabic abstract
With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing it. This verification can be private, between the Client and the Server, or public, when the result can be verified by any third party. We here present protocols for the verification of matrix-vector multiplications, that are secure against malicious Servers. The obtained algorithms are essentially optimal in the amortized model: the overhead for the Server is limited to a very small constant factor, even in the sparse or structured matrix case; and the computational time for the public Verifier is linear in the dimension. Our protocols combine probabilistic checks and cryptographic operations, but minimize the latter to preserve practical efficiency. Therefore our protocols are overall more than two orders of magnitude faster than existing ones.
rate research
Read More
Group membership verification checks if a biometric trait corresponds to one member of a group without revealing the identity of that member. Recent contributions provide privacy for group membership protocols through the joint use of two mechanisms: quantizing templates into discrete embeddings and aggregating several templates into one group representation. However, this scheme has one drawback: the data structure representing the group has a limited size and cannot recognize noisy queries when many templates are aggregated. Moreover, the sparsity of the embeddings seemingly plays a crucial role on the performance verification. This paper proposes a mathematical model for group membership verification allowing to reveal the impact of sparsity on both security, compactness, and verification performances. This model bridges the gap towards a Bloom filter robust to noisy queries. It shows that a dense solution is more competitive unless the queries are almost noiseless.
Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms including CPUs, GPUs and Xeon Phi. First, the CSR5 format is insensitive to the sparsity structure of the input matrix. Thus the single format can support an SpMV algorithm that is efficient both for regular matrices and for irregular matrices. Furthermore, we show that the overhead of the format conversion from the CSR to the CSR5 can be as low as the cost of a few SpMV operations. We compare the CSR5-based SpMV algorithm with 11 state-of-the-art formats and algorithms on four mainstream processors using 14 regular and 10 irregular matrices as a benchmark suite. For the 14 regular matrices in the suite, we achieve comparable or better performance over the previous work. For the 10 irregular matrices, the CSR5 obtains average performance improvement of 17.6%, 28.5%, 173.0% and 293.3% (up to 213.3%, 153.6%, 405.1% and 943.3%) over the best existing work on dual-socket Intel CPUs, an nVidia GPU, an AMD GPU and an Intel Xeon Phi, respectively. For real-world applications such as a solver with only tens of iterations, the CSR5 format can be more practical because of its low-overhead for format conversion. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSR5
Generalized Sparse Matrix-Matrix Multiplication (SpGEMM) is a ubiquitous task in various engineering and scientific applications. However, inner product based SpGENN introduces redundant input fetches for mismatched nonzero operands, while outer product based approach suffers from poor output locality due to numerous partial product matrices. Inefficiency in the reuse of either inputs or outputs data leads to extensive and expensive DRAM access. To address this problem, this paper proposes an efficient sparse matrix multiplication accelerator architecture, SpArch, which jointly optimizes the data locality for both input and output matrices. We first design a highly parallelized streaming-based merger to pipeline the multiply and merge stage of partial matrices so that partial matrices are merged on chip immediately after produced. We then propose a condensed matrix representation that reduces the number of partial matrices by three orders of magnitude and thus reduces DRAM access by 5.4x. We further develop a Huffman tree scheduler to improve the scalability of the merger for larger sparse matrices, which reduces the DRAM access by another 1.8x. We also resolve the increased input matrix read induced by the new representation using a row prefetcher with near-optimal buffer replacement policy, further reducing the DRAM access by 1.5x. Evaluated on 20 benchmarks, SpArch reduces the total DRAM access by 2.8x over previous state-of-the-art. On average, SpArch achieves 4x, 19x, 18x, 17x, 1285x speedup and 6x, 164x, 435x, 307x, 62x energy savings over OuterSPACE, MKL, cuSPARSE, CUSP, and ARM Armadillo, respectively.
The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for many numerical linear algebra kernel operations or graph traversal applications. Parallelizing SymmSpMV on todays multicore platforms with up to 100 cores is difficult due to the need to manage conflicting updates on the result vector. Coloring approaches can be used to solve this problem without data duplication, but existing coloring algorithms do not take load balancing and deep memory hierarchies into account, hampering scalability and full-chip performance. In this work, we propose the recursive algebraic coloring engine (RACE), a novel coloring algorithm and open-source library implementation, which eliminates the shortcomings of previous coloring methods in terms of hardware efficiency and parallelization overhead. We describe the level construction, distance-k coloring, and load balancing steps in RACE, use it to parallelize SymmSpMV, and compare its performance on 31 sparse matrices with other state-of-the-art coloring techniques and Intel MKL on two modern multicore processors. RACE outperforms all other approaches substantially and behaves in accordance with the Roofline model. Outliers are discussed and analyzed in detail. While we focus on SymmSpMV in this paper, our algorithm and software is applicable to any sparse matrix operation with data dependencies that can be resolved by distance-k coloring.
Sparse matrix vector multiplication (SpMV) is an important kernel in scientific and engineering applications. The previous optimizations are sparse matrix format specific and expose the choice of the best format to application programmers. In this work we develop an auto-tuning framework to bridge gap between the specific optimized kernels and their general-purpose use. We propose an SpMV auto-tuner (SMAT) that provides an unified interface based on compressed sparse row (CSR) to programmers by implicitly choosing the best format and the fastest implementation of any input sparse matrix in runtime. SMAT leverage a data mining model, which is formulated based on a set of performance parameters extracted from 2373 matrices in UF sparse matrix collection, to fast search the best combination. The experiments show that SMAT achieves the maximum performance of 75 GFLOP/s in single-precision and 33 GFLOP/s in double-precision on Intel, and 41 GFLOP/s in single-precision and 34 GFLOP/s in double-precision on AMD. Compared with the sparse functions in MKL library, SMAT runs faster by more than 3 times.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
