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Concept

Piecewise

Related publications (25)

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

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

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

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

Polaron hopping through piecewise-linear functionals

Alfredo Pasquarello, Stefano Falletta

We use piecewise-linear functionals to study the polaron energy landscape and hopping rates in beta-Ga2O3, which we adopt as an example of an anisotropic material hosting multiple polaronic states. We illustrate various functionals for polaron localization ...

AMER PHYSICAL SOC2023

Region Extraction in Mesh Intersection

Annalisa Buffa, Pablo Antolin Sanchez, Emiliano Cirillo

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special ...

2023

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

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

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

Random extrapolation for primal-dual coordinate descent

Volkan Cevher, Ahmet Alacaoglu

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, an ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

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

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

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

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

Nicola Marzari, Nicola Colonna, Ngoc Linh Nguyen

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

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

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

Pumps running as turbines for energy recovery in water supply systems

João Nuno Gomes Borga Delgado

Pressurised water supply systems are infrastructures that offer a potential for energy recovery in locations where these systems operate with an excessive pressure. The integration of micro hydropower plants for energy recovery is a challenge, as these sys ...

EPFL2018

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, Farzin Dadashi, Martin Savary, Flavien Bardyn

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

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

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