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
20
LADL-Code Mesh V
eramirem
0
190
Transition Matrix Estimation in High Dimensional Time Series.
eramirem
0
250
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
230
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
マテリアルズ・インフォマティクスの先端で起きていること / What's Happening at the Cutting Edge of Materials Informatics
snhryt
1
190
化学におけるAI・シミュレーション活用のトレンドと 汎用原子レベルシミュレーター: Matlantisを使った素材開発
matlantis
0
470
Tensor Representations in Signal Processing and Machine Learning (Tutorial at APSIPA-ASC 2020)
yokotatsuya
0
120
機械学習を支える連続最適化
nearme_tech
PRO
1
260
Cross-Media Information Spaces and Architectures (CISA)
signer
PRO
3
31k
事業会社における 機械学習・推薦システム技術の活用事例と必要な能力 / ml-recsys-in-layerx-wantedly-2024
yuya4
4
300
Design of three-dimensional binary manipulators for pick-and-place task avoiding obstacles (IECON2024)
konakalab
0
130
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
240
ベイズ最適化をゼロから
brainpadpr
2
1.1k
生成AI による論文執筆サポートの手引き(ワークショップ) / A guide to supporting dissertation writing with generative AI (workshop)
ks91
PRO
0
400
(論文読み)贈り物の交換による地位の競争と社会構造の変化 - 文化人類学への統計物理学的アプローチ -
__ymgc__
1
180
山形とさくらんぼに関するレクチャー(YG-900)
07jp27
1
270
Featured
See All Featured
The Cult of Friendly URLs
andyhume
78
6.2k
A Tale of Four Properties
chriscoyier
158
23k
The Myth of the Modular Monolith - Day 2 Keynote - Rails World 2024
eileencodes
21
2.5k
RailsConf & Balkan Ruby 2019: The Past, Present, and Future of Rails at GitHub
eileencodes
134
33k
The Psychology of Web Performance [Beyond Tellerrand 2023]
tammyeverts
46
2.4k
Designing for humans not robots
tammielis
250
25k
Faster Mobile Websites
deanohume
306
31k
KATA
mclloyd
29
14k
What’s in a name? Adding method to the madness
productmarketing
PRO
22
3.3k
Measuring & Analyzing Core Web Vitals
bluesmoon
6
260
Statistics for Hackers
jakevdp
797
220k
How to train your dragon (web standard)
notwaldorf
91
5.9k
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