Essays about: "tensor rank"

Showing result 1 - 5 of 7 essays containing the words tensor rank.

  1. 1. A Hierarchical Tucker Solver for the Vlasov-Maxwell System

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : Oskar Tegby; [2023]
    Keywords : ;

    Abstract : The Vlasov-Maxwell equations is a common model to describe the behavior of a plasma, but come at the cost of their dimensionality since both spatial and veloocity data is stored in three dimensions. This causes a significant obstacle to be able solve them numerically since the size of the data is N^6, which yields a data size of 8. READ MORE

  3. 2. Tensor rank and support rank in the context of algebraic complexity theory

    University essay from KTH/Matematik (Avd.)

    Author : Pelle Andersson; [2023]
    Keywords : linear algebra; tensor product; tensor rank; matrix multiplication; complexity; linjär algebra; tensorprodukt; tensorrang; matrismultiplikation; komplexitet;

    Abstract : Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. READ MORE

  4. 3. An Investigation of Low-Rank Decomposition for Increasing Inference Speed in Deep Neural Networks With Limited Training Data

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Victor Wikén; [2018]
    Keywords : deep neural networks; convolutional neural networks; AlexNet; inference speed; optimization; low-rank tensor decomposition; fine-grained classification problem; dog breed classification; transfer learning;

    Abstract : In this study, to increase inference speed of convolutional neural networks, the optimization technique low-rank tensor decomposition has been implemented and applied to AlexNet which had been trained to classify dog breeds. Due to a small training set, transfer learning was used in order to be able to classify dog breeds. READ MORE

  5. 4. Speeding up PARAFAC : Approximation of tensor rank using the Tucker core

    University essay from Uppsala universitet/Statistiska institutionen

    Author : Lukas Arnroth; [2018]
    Keywords : Tucker decomposition; PARAFAC; tensor rank; split-half analysis;

    Abstract : In this paper, the approach of utilizing the core tensor from the Tucker decomposition, in place of theuncompressed tensor, for nding a valid tensor rank for the PARAFAC decomposition is considered.Validity of the proposed method is investigated in terms of error and time consumption. READ MORE

  6. 5. The Square-Root Isometry of Coupled Quadratic Spaces : On the relation between vielbein and metric formulations of spin-2 interactions

    University essay from Stockholms universitet/Fysikum; Stockholms universitet/Oskar Klein-centrum för kosmopartikelfysik (OKC)

    Author : Kocic Mikica B.; [2014]
    Keywords : modified gravity; bigravity; bimetric theory; square-root isometry;

    Abstract : Bimetric theory is an extension to general relativity that introduces a secondary symmetric rank-two tensor field. This secondary spin-2 field is also dynamical, and to avoid the Boulware-Deser ghost issue, the interaction between the two fields is obtained through a potential that involes the matrix square-root of the tensors. READ MORE