Publications associées à Application linéaire par morceaux

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

PROBING INTRACELLULAR ELASTICITY WITH MINIMAL-HESSIAN REGISTRATION

Michaël Unser

We propose an image-based elastography method to measure the heterogeneous stiffness inside a cell and its nucleus. It uses a widely accessible setup consisting of plate compression imaged with fluorescence microscopy. Our framework recovers a spatial map ...

IEEE2023

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Hubbard U through polaronic defect states

Alfredo Pasquarello, Stefano Falletta

Since the preliminary work of Anisimov and co-workers, the Hubbard corrected DFT+U functional has been used for predicting properties of correlated materials by applying on-site effective Coulomb interactions to specific orbitals. However, the determinatio ...

NATURE PORTFOLIO2022

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Iurii Timrov

Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, densit ...

2021

An adaptive algorithm for the transport equation with time dependent velocity

Marco Picasso, Samuel Dubuis

An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

2020

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...

HEBREW UNIV MAGNES PRESS2020

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Michaël Unser, Shayan Aziznejad, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

2020

Koopmans-Compliant Functionals and Potentials and Their Application to the GW100 Test Set

Nicola Marzari, Nicola Colonna, Ngoc Linh Nguyen, Andrea Ferretti

Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piecewise linearity of the total energy as a function of the fractional addition/removal of an electron to/from any orbital. We a ...

AMER CHEMICAL SOC2019

Deep Spline Networks With Control Of Lipschitz Regularity

Michaël Unser, Shayan Aziznejad

The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite-dimensional optimization problem, we resolve the ambiguity by search ...

IEEE2019

Relative Effects of the Hospital Readmissions Reduction Program on Hospitals That Serve Poorer Patients

Yun Wang, Christine Choirat

Importance: Hospitals that serve poorer populations have higher readmission rates. It is unknown whether these hospitals effectively lowered readmission rates in response to the Hospital Readmissions Reduction Program (HRRP). Objective: To compare pre-post ...

2019

Range-based underwater target localization using an autonomous surface vehicle: Observability analysis

In the field of marine robotics, the problem of range based underwater target localization can be defined as that of localizing an unknown - fixed or moving - target from a surface vehicle called the tracker, using range information available about the tar ...

2018

A wrist sensor and algorithm to determine instantaneous walking cadence and speed in daily life walking

Kamiar Aminian, Pierre-André Farine, Benedikt Fasel, Cyntia Duc, Flavien Bardyn, Farzin Dadashi, Martin Savary

In daily life, a person’s gait—an important marker for his/her health status—is usually assessed using inertial sensors fixed to lower limbs or trunk. Such sensor locations are not well suited for continuous and long duration measurements. A better locatio ...

Springer Heidelberg2017

Superresolution Reconstruction for Magnetic Resonance Spectroscopic Imaging Exploiting Low-Rank Spatio-Spectral Structure

Jeffrey Adam Kasten

Magnetic resonance spectroscopic imaging (MRSI) is a rapidly developing medical imaging modality, capable of conferring both spatial and spectral information content, and has become a powerful clinical tool. The ability to non-invasively observe spatial ma ...

EPFL2015

Investigating empirical implications of hysteresis in day-to-day travel time variability

Nikolaos Geroliminis, Mehmet Yildirimoglu, Ypatia Stefania Limniati

Day-to-day travel time variability plays a significant role in travel time reliability. Nowadays, travelers not only seek to minimize their travel time on average, but also value its variation. The variation in the mean and the variance of travel time (acr ...

Pergamon-Elsevier Science Ltd2015

A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems

Sami Driss Karkar

The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) [1] and extended by Karkar et al. (2013) [2] now allows to follow the periodic solutions of regularized non-smooth systems (stiff systems). This pap ...

Elsevier2014

A Multi-Dimensional Analysis of Hard Shoulder Running Systems

André-Gilles Dumont, Dimitrios Efthymiou, Sofia Samoili

The use of Hard Shoulder Running (HSR) systems is a relatively recent control policy aiming to ameliorate traffic conditions in recurrent congested networks. This ITS strategy attracts researchers and practitioners interest, in an attempt to assess its imp ...

2014

Fast Partitioning of Vector-Valued Images

Martin Kurt Storath

We propose a fast splitting approach to the classical variational formulation of the image partitioning problem, which is frequently referred to as the Potts or piecewise constant Mumford-Shah model. For vector-valued images, our approach is significantly ...

Siam Publications2014