Effective Machine Learning Based Format Selection and Performance Modeling for SpMV on GPUs

58 Pages·2017·2.66 MB·English

Effective Machine Learning Based Format
Selection and Performance Modeling for SpMV on
GPUs
Israt Nisa*, Charles Siegel+, Aravind Sukumaran
Rajam*, Abhinav Vishnu+, P. Sadayappan*
*The Ohio State University
+Pacific Northwest National Laboratory
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Sparse Matrix-Vector Multiplication
Ax = y
x y
1 1
x x x
x y
x 2 2
x y
x x x X 3 = 3
x … …
x x
…. ….
x x x y
N N
Input Matrix A(MxN) Vector x (Nx1) Vector y(Mx1)
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Applications of SpMV
Linear Algebra
Fluid Dynamics
Graph Analytics
Deep Learning eigenvalue
problems
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Recent Formats of SpMV
Yet, no absolute
lightspmv-2015 winner!
yaSpMV-2014
Liu et al.
Yan et al.
CSR5-2015
clSpMV-2012 Liu et al.
Su et al.
Adaptive-2016
Zardoshti et al.
merge-spmv-2012
Duanet al.
HolaSpMV-2017
Adaptive-CSR-2015
Steinberger et al. Mayanket al.
CSR, ELL-2009
Bell et al.
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Recent Works on Format Selection and
Performance Modeling
Classification
• Decision Tree – Li et al. (PLDI-2013), Sedaghati et al. (ICS 2015)
• Support Vector Machine (SVM )– Benatial et al. (ICPP 2016)
• Deep learning – Zhao et al. (PPoPP 2018), Cui et al. (MCSoC 2016)
Performance modeling
• Analytical modeling – Zhao et al. (HPCA 2011), Zardoshti et al. (J-SC 2016), Guo et
al. (CC 2015)
• Multi Layer Perceptron (MLP) – Benatia et al. (ICPADS 2016)
• Support Vector Regression (SVR) – Benatia et al. (ICPADS 2016)
Problems addressed
1. A model to efficiently predict the best-performing format for a
unseen sparse matrix for GPU
2. Can the SpMV execution time for an unseen sparse matrix be
effectively predicted for various representation formats?
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Performance Variation across formats on GPU
P100
25
20
S 15
P
O
L
F
G 10
5
0
COO ELL CSR HYB merged- based CSR CSR5_time
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Performance Variation across formats
25 2.85x
20
S 15
P
O
L
F
G 10
1x
5
0
COO ELL CSR HYB merged- based CSR CSR5_time
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Performance Variation across formats
25
1.6x
20
S 15
P
O
L
F
G 10
1x
5
0
COO ELL CSR HYB merged- based CSR CSR5_time
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Performance Variation across formats
2.35x
25
20
S 15
P
O
L
F
G 10
1x
5
0
COO ELL CSR HYB merged- based CSR CSR5_time
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