Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties. The wave function is encoded as a tensor contraction of a network of individual tensors. The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network. This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems. (Wikipedia).
Calculus 3: Tensors (1 of 28) What is a Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t
From playlist CALCULUS 3 CH 10 TENSORS
Miles Stoudenmire: "Tensor Networks for Machine Learning and Applications"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Tensor Networks for Machine Learning and Applications" Miles Stoudenmire - Flatiron Institute Abstract: Tensor networks are
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Toronto Deep Learning Series, 11-Feb-2019 https://tdls.a-i.science/events/2019-02-11 TENSOR FIELD NETWORKS: ROTATION- AND TRANSLATION-EQUIVARIANT NEURAL NETWORKS FOR 3D POINT CLOUDS We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, a
From playlist Math and Foundations
What Is A Tensor Lesson #1: Elementary vector spaces
We define a vector space and lay the foundation of a solid understanding of tensors.
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Crash Course on TensorFlow Tensors and their Applications
We discuss the most important features of tensors in TensorFlow, useful tensor methods you should know, and where you would use them in your Deep Learning projects. Notebook Link: https://colab.research.google.com/drive/1Zcrw257e9XjInjTwz-pHtrJ_YuEsR45u?usp=sharing TIMESTAMPS: 0:00 Int
From playlist Math for Machine Learning
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
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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
Glen Evenbly: "Using tensor networks to design improved wavelets for image compression"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "Using tensor networks to design improved wavelets for image compression" Glen Evenbly - Georgia Institute of Technology, Physics Abstract: Tensor networks
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
What is a Tensor 10: Metric spaces
What is a Tensor 10: Metric spaces
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Anthony Nouy: Approximation and learning with tree tensor networks - Lecture 1
Recorded during the meeting "Data Assimilation and Model Reduction in High Dimensional Problems" the July 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone A kinetic description of a plasma in external and self-consistent fiel
From playlist Numerical Analysis and Scientific Computing
Anthony Nouy: "Approximation and learning with tree tensor networks"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Approximation and learning with tree tensor networks" Anthony Nouy - Université de Nantes Abstract: Tree tensor networks (T
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Tensors for Neural Networks, Clearly Explained!!!
Tensors are super important for neural networks, but can be confusing because different people use the word "Tensor" differently. In this StatQuest, we clear this up and tell you what the big deal is. BAM! NOTE: If you are not already familiar with Neural Networks, check out the Neural Ne
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Johnnie Gray: "Hyper-optimized tensor network contraction - simplifications, applications & appr..."
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Hyper-optimized tensor network contraction - simplifications, applications and approximations" Johnnie Gray - California Ins
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Lei Wang: "Tropical Tensor Networks"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Tropical Tensor Networks" Lei Wang - Chinese Academy of Sciences Abstract: I will present a unified exact tensor network ap
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
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Garnet Chan - Arithmetic tensor networks and integration - IPAM at UCLA
Recorded 26 January 2022. Garnet Chan of the California Institute of Technology presents "Arithmetic tensor networks and integration" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: I will discuss how to perform arithmetic with tensor networks and the consequences for the in
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
An invitation to tensor networks - Michael Walter
Computer Science/Discrete Mathematics Seminar II Topic: An invitation to tensor networks Speaker: Michael Walter Affiliation: University of Amsterdam Date: December 11, 2018 For more video please visit http://video.ias.edu
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Furong Huang: "Understanding, Interpreting & Designing NN Models Through Tensor Representations"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Understanding, Interpreting and Designing Neural Network Models Through Tensor Representations" Furong Huang - Universit
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras We complete our survey of the basic algebraic structures that appear in the study of general relativity. Also, we develop the important example of the tensor algebra.
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Joseph Landsberg: "Geometry associated to tensor network states"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "Geometry associated to tensor network states" Joseph Landsberg (Clay Scholar) - Texas A&M University - College Station Abstract: I will discuss geometric i
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021