In multilinear algebra, a tensor decomposition is any scheme for expressing a tensor as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions. The main tensor decompositions are: * tensor rank decomposition; * higher-order singular value decomposition; * Tucker decomposition; * matrix product states, and operators or tensor trains; * ; and * . (Wikipedia).
Nick Vannieuwenhoven: "Sensitivity of tensor decompositions"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Sensitivity of tensor decompositions" Nick Vannieuwenhoven - KU Leuven Abstract: Tensor decompositions such as the tensor rank de
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
What is a Tensor? Lesson 30: Transformation of forms - formal study (Part I)
What is a Tensor? Lesson 30: Transformation of forms - formal study (Part I)
From playlist What is a Tensor?
Lek-Heng Lim: "What is a tensor? (Part 1/2)"
Watch part 2/2 here: https://youtu.be/Lkpmd5-mpHY Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "What is a tensor? (Part 1/2)" Lek-Heng Lim - University of Chicago, Statistics Abstract: We discuss the three best-known definitions of a tensor:
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Ankur Moitra: "Tensor Decompositions and their Applications (Part 1/2)"
Watch part 2/2 here: https://youtu.be/npPaMknLJWQ Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensor Decompositions and their Applications (Part 1/2)" Ankur Moitra - Massachusetts Institute of Technology Abstract: Tensor decompositions play
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Review of Decomposition by the Dot Product
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
What is a Tensor? Lesson 31: Tensor Densities (Part 2 of Tensor Transformations)
This video is about What is a Lesson 31: Tensor Densities (Part 2 of Tensor Transformations) We introduce the *classical* definition of a tensor density and connect that definition to our more robust approach associated with vector spaces and their associated bases. I will demonstrate som
From playlist What is a Tensor?
What is a Tensor? Lesson 29: Transformations of tensors and p-forms (part review)
What is a Tensor? Lesson 29: Tensor and N-form Transformations This long lesson begins with a review of tensor product spaces and the relationship between coordinate transformations on spacetime and basis transformations of tensor fields. Then we do a full example to introduce the idea th
From playlist What is a Tensor?
Solve a System of Linear Equations Using LU Decomposition
This video explains how to use LU Decomposition to solve a system of linear equations. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Matrix Equations
Ankur Moitra: "Tensor Decompositions and their Applications (Part 2/2)"
Watch part 1/2 here: https://youtu.be/UyO4igyyYQA Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensor Decompositions and their Applications (Part 2/2)" Ankur Moitra - Massachusetts Institute of Technology Abstract: Tensor decompositions play
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Tensor Decomposition Definitions of Neural Net Architectures
This paper describes complexity theory of neural networks, defined by tensor decompositions, with a review of simplification of the tensor decomposition for simpler neural network architectures. The concept of Z-completeness for a network N is defined in the existence of a tensor decomposi
From playlist Wolfram Technology Conference 2021
Singular Values of Tensors
From playlist Spring 2019 Symbolic-Numeric Computing
Aravindan Vijayaraghavan: "Smoothed Analysis for Tensor Decompositions and Unsupervised Learning"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Smoothed Analysis for Tensor Decompositions and Unsupervised Learning" Aravindan Vijayaraghavan - Northwestern University Abstrac
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Anna Seigal: "From Linear Algebra to Multi-Linear Algebra"
Watch part 2/2 here: https://youtu.be/f5MiPayz_e8 Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "From Linear Algebra to Multi-Linear Algebra" Anna Seigal - University of Oxford Abstract: Linear algebra is the foundation to methods for finding
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Jean Kossaifi: "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch" Jean Kossaifi - Nvidia Corporation Abstrac
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
On Expressiveness and Optimization in Deep Learning - Nadav Cohen
Members' Seminar Topic: On Expressiveness and Optimization in Deep Learning Speaker: Nadav Cohen Affiliation: Member, School of Mathematics Date: April 2, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Rong Ge: "Beyond Lazy Training for Over-parameterized Tensor Decomposition"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Beyond Lazy Training for Over-parameterized Tensor Decomposition" Rong Ge - Duke University Abstract: Over-parametrization is an
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
This is a game changer! (AlphaTensor by DeepMind explained)
#alphatensor #deepmind #ai Matrix multiplication is the most used mathematical operation in all of science and engineering. Speeding this up has massive consequences. Thus, over the years, this operation has become more and more optimized. A fascinating discovery was made when it was sho
From playlist Papers Explained
Ankur Moitra : Tensor Decompositions and their Applications
Recording during the thematic meeting: «Nexus of Information and Computation Theories » theJanuary 27, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Nexus Trimester - 2016 -Tutorial Week at CIRM
Linear Algebra 18a: Introduction to the Eigenvalue Decomposition
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations