Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Linear Algebra at Large Scale
Search
Elizabeth Ramirez
April 27, 2018
Science
7
900
Linear Algebra at Large Scale
Elizabeth Ramirez
April 27, 2018
Tweet
Share
More Decks by Elizabeth Ramirez
See All by Elizabeth Ramirez
Maritime Transportation from Space: The most important industry you know nothing about.
eramirem
0
18
LADL-Code Mesh V
eramirem
0
180
Transition Matrix Estimation in High Dimensional Time Series.
eramirem
0
240
The Linear Algebra of Deep Learning
eramirem
2
700
Linear Algebra for FE Developers
eramirem
1
610
Top 10: Los mejores algoritmos del Siglo XX
eramirem
0
410
Numerical Analysis for Orbit Propagation
eramirem
0
210
A New Approach to Linear Filtering and Prediction Problems
eramirem
0
1.5k
Kalman Filters for non-rocket science - PyCon 2016
eramirem
2
380
Other Decks in Science
See All in Science
拡散モデルの概要 −§2. スコアベースモデルについて−
nearme_tech
PRO
0
510
機械学習による確率推定とカリブレーション/probabilistic-calibration-on-classification-model
ktgrstsh
2
220
Machine Learning for Materials (Lecture 6)
aronwalsh
0
500
The thin line between reconstruction, classification, and hallucination in brain decoding
ykamit
1
880
多次元展開法を用いた 多値バイクラスタリング モデルの提案
kosugitti
0
190
大規模言語モデルの開発
chokkan
PRO
84
32k
Mechanistic Interpretability の紹介
sohtakahashi
0
320
Machine Learning for Materials (Lecture 9)
aronwalsh
0
210
Iniciativas independentes de divulgação científica: o caso do Movimento #CiteMulheresNegras
taisso
0
140
Direct Preference Optimization
zchenry
0
270
Introduction to Graph Neural Networks
joisino
PRO
4
2k
科学で迫る勝敗の法則(名城大学公開講座.2024年10月) / The principle of victory discovered by science (Open lecture in Meijo Univ. 2024)
konakalab
0
190
Featured
See All Featured
Keith and Marios Guide to Fast Websites
keithpitt
408
22k
The Power of CSS Pseudo Elements
geoffreycrofte
72
5.3k
Sharpening the Axe: The Primacy of Toolmaking
bcantrill
37
1.8k
Building Adaptive Systems
keathley
38
2.2k
"I'm Feeling Lucky" - Building Great Search Experiences for Today's Users (#IAC19)
danielanewman
226
22k
Speed Design
sergeychernyshev
24
570
How GitHub (no longer) Works
holman
311
140k
Bash Introduction
62gerente
608
210k
How to Think Like a Performance Engineer
csswizardry
19
1.1k
BBQ
matthewcrist
85
9.3k
I Don’t Have Time: Getting Over the Fear to Launch Your Podcast
jcasabona
27
1.9k
Bootstrapping a Software Product
garrettdimon
PRO
305
110k
Transcript
Linear Algebra at Large Scale Elizabeth Ramirez @eramirem
Computational Engineer We model complex systems on the planet, like
forestry and agriculture using satellite imagery.
None
Top 10 Algorithms of the 20th Century
Often the most expensive computations in large-scale codes. Curse of
Dimensionality
Linear Systems Nonlinear Systems Machine Learning Deep Learning
Most ubiquitous problem in Scientific Computing and Data Analysis
What solves? Systems of Equations Polynomial Interpolation Linear Least-Squares
What we know? Gaussian Elimination Complexity
HPC Alternative: Iterative Methods General Form
Jacobi Gauss-Seidel
Convergence of Basic Iterative Methods Spectral radius
Krylov Subspaces
Conjugate Gradient Method (CG) i) ii)
Conjugate Gradient (CG)
Bi-conjugate gradient (BiCG) Any linear system
Deep Learning Primitives Weights, inputs, outputs stored in tensors Matrix
Multiplication Convolution Inner Product Transposition Rectified Linear Unit (ReLu)
Matrix Multiplication Fundamental task Naive: Strassen:
Low-Rank Approximation Accelerates matrix multiplication, therefore, accelerates convolution. Requires SVD:
Low-Rank Multiplication:
Single Instruction Multiple Data (SIMD) Data-level parallelism Incompatible with code
designed for sequential processors Instruction set available in commercial CPUs and GPGPUs
Intel® Math Kernel Library (Intel® MKL) Improved Matrix Multiplication Performance
in LAPACK LU decomposition and inverse without pivoting Take advantage of SIMD instruction set In summary: High Performance Linear Algebra
None
References http://www.siam.org/pdf/news/637.pdf https://software.intel.com/en-us/mkl https://software.intel.com/en-us/articles/t ensorflow-optimizations-on-modern-intel-arc hitecture