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Backpropagation-Friendly Eigendecomposition

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Daniel Kressner, Alice Cortinovis

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Randomized flexible GMRES with deflated restarting

Laura Grigori, Emeric Martin

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...

Springer2024

Explainable Face Verification via Feature-Guided Gradient Backpropagation

Touradj Ebrahimi, Yuhang Lu, Zewei Xu

Recent years have witnessed significant advance- ment in face recognition (FR) techniques, with their applications widely spread in people’s lives and security-sensitive areas. There is a growing need for reliable interpretations of decisions of such syste ...

2024

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Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...

Wien2023

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Designing self-tracking experiences: A qualitative study of the perceptions of barriers and facilitators to adopting digital health technology for automatic urine analysis at home

Delphine Ribes Lemay, Nicolas Henchoz, Emily Clare Groves, Margherita Motta, Andrea Regula Schneider

Self-tracking technologies open new doors to previously unimaginable scenarios. The diagnosis of diseases years in advance, or supporting the health of astronauts on missions to Mars are just some of many example applications. During the COVID-19 pandemic, ...

2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

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We propose a physics-informed neural network (PINN) as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the scattered field ...

SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Efficient algorithms for wave problems

Boris Bonev

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...

EPFL2021