OuterSPACE: An Outer Product Based Sparse Matrix Multiplication Accelerator

2018 ◽  
Author(s):  
Subhankar Pal ◽  
Jonathan Beaumont ◽  
Dong-Hyeon Park ◽  
Aporva Amarnath ◽  
Siying Feng ◽  
...  
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Outer Product

Fast Bilinear Algorithms for Symmetric Tensor Contractions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Edgar Solomonik ◽  
James Demmel
Keyword(s):  
Symmetric Matrix ◽  
Matrix Multiplication ◽  
Computational Cost ◽  
Symmetric Tensor ◽  
Partial Sums ◽  
Symmetric Tensors ◽  
Outer Product ◽  
Bilinear Complexity ◽  
Special Cases ◽  
Tensor Contractions

AbstractIn matrix-vector multiplication, matrix symmetry does not permit a straightforward reduction in computational cost. More generally, in contractions of symmetric tensors, the symmetries are not preserved in the usual algebraic form of contraction algorithms. We introduce an algorithm that reduces the bilinear complexity (number of computed elementwise products) for most types of symmetric tensor contractions. In particular, it lowers the bilinear complexity of symmetrized contractions of symmetric tensors of order {s+v} and {v+t} by a factor of {\frac{(s+t+v)!}{s!t!v!}} to leading order. The algorithm computes a symmetric tensor of bilinear products, then subtracts unwanted parts of its partial sums. Special cases of this algorithm provide improvements to the bilinear complexity of the multiplication of a symmetric matrix and a vector, the symmetrized vector outer product, and the symmetrized product of symmetric matrices. While the algorithm requires more additions for each elementwise product, the total number of operations is in some cases less than classical algorithms, for tensors of any size. We provide a round-off error analysis of the algorithm and demonstrate that the error is not too large in practice. Finally, we provide an optimized implementation for one variant of the symmetry-preserving algorithm, which achieves speedups of up to 4.58\times for a particular tensor contraction, relative to a classical approach that casts the problem as a matrix-matrix multiplication.

scholarly journals Sparse matrix multiplication: The distributed block-compressed sparse row library

2014 ◽  
Vol 40 (5-6) ◽  
pp. 47-58 ◽  
Author(s):  
Urban Borštnik ◽  
Joost VandeVondele ◽  
Valéry Weber ◽  
Jürg Hutter
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Compressed Sparse Row

Unleashing the performance of bmSparse for the sparse matrix multiplication in GPUs

2021 ◽  
Author(s):  
Gonzalo Berger ◽  
Manuel Freire ◽  
Renzo Marini ◽  
Ernesto Dufrechou ◽  
Pablo Ezzatti
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication

Optimization of GPU-based Sparse Matrix Multiplication for Large Sparse Networks

2020 ◽  
Author(s):  
Jeongmyung Lee ◽  
Seokwon Kang ◽  
Yongseung Yu ◽  
Yong-Yeon Jo ◽  
Sang-Wook Kim ◽  
...  
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication ◽  
Sparse Networks

A 7.3 M Output Non-Zeros/J Sparse Matrix-Matrix Multiplication Accelerator using Memory Reconfiguration in 40 nm

2019 ◽  
Author(s):  
Subhankar Pal ◽  
Dong-hyeon Park ◽  
Siying Feng ◽  
Paul Gao ◽  
Jielun Tan ◽  
...  
Keyword(s):  
Sparse Matrix ◽  
Matrix Multiplication
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