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Rank-Adaptive Time Integration Of Tree Tensor Networks

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Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

STREAMING TENSOR TRAIN APPROXIMATION

Daniel Kressner

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

Philadelphia2023

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Lausanne2023

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Liang Xu

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

A new method for lattice reduction using directional and hyperplanar shearing

Cyril Cayron

A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called 'basis rhombicity' which is the sum of the absolute val ...

INT UNION CRYSTALLOGRAPHY2022

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

OXFORD UNIV PRESS2021

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

WILEY2020

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We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

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We propose a graph signal processing framework to overcome the computational burden of Tensor Robust PCA (TRPCA). Our framework also serves as a convex alternative to graph regularized tensor factorization methods. Our method is based on projecting a tenso ...

IEEE2019

HOTmix: characterizing hindered diffusion using a mixture of generalized higher order tensors

Jean-Philippe Thiran, Erick Jorge Canales Rodriguez, Gabriel Girard, David Paul Roger Romascano, Marco Pizzolato, Jonathan Rafael Patino Lopez, Alessandro Daducci, Muhamed Barakovic, Gaëtan Olivier D Rensonnet, Tim Bjørn Dyrby

We present HOTmix, a new model to describe the diffusion MRI signal for molecules undergoing hindered diffusion. HOTmix is based on a mixture of generalized higher order tensors, explicitly incorporating the diffusion sequence’s time-dependent parameters. ...

2019