Publications associées à Théorème de convergence dominée

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

LDP and CLT for SPDEs with transport noise

Lucio Galeati

In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...

SPRINGER2023

Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

Ali H. Sayed, Kun Yuan, Sulaiman A S A E Alghunaim

This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framewor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Analytical and Machine Learning Methods for the Complete Safe Coordination of Astrobot Swarms

Matin Macktoobian

The recent generations of massive spectroscopic surveys aim at the ray collection from a multitude of cosmological targets in the course of observations. For this purpose, astrobots are used to change the configuration of optical fibers from one observatio ...

EPFL2021

Over-the-Air Computation via Reconfigurable Intelligent Surface

Yuning Jiang, Wei Chen

Over-the-air computation (AirComp) is a disruptive technique for fast wireless data aggregation in Internet of Things (IoT) networks via exploiting the waveform superposition property of multiple-access channels. However, the performance of AirComp is bott ...

2021

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

Variance-Reduced Stochastic Learning Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform d ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Disorder‐Induced Signal Filtering with Topological Metamaterials

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Disorder, ubiquitously present in realistic structures, is generally thought to disturb the performance of analog wave devices, as it often causes strong multiple scattering effects that largely arrest wave transportation. Contrary to this general view, he ...

Wiley2020

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Marc Gillioz

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a dist ...

Springer Nature2020

Axiomatic scale theory

Martin Alois Rohrmeier, Daniel Harasim

Scales are a fundamental concept of musical practice around the world. They commonly exhibit symmetry properties that are formally studied using cyclic groups in the field of mathematical scale theory. This paper proposes an axiomatic framework for mathema ...

TAYLOR & FRANCIS LTD2020

The asymmetric multitype contact process

Thomas Mountford, Daniel Rodrigues Valesin

We study the multitype contact process on Z(d) under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, ...

ELSEVIER SCIENCE BV2019

Dynamic Average Diffusion With Randomized Coordinate Updates

Ali H. Sayed, Bicheng Ying, Kun Yuan

This work derives and analyzes an online learning strategy for tracking the average of time-varying distributed signals by relying on randomized coordinate-descent updates. During each iteration, each agent selects or observes a random entry of the observa ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

Assyr Abdulle, Andrea Di Blasio

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

SIAM PUBLICATIONS2019

A Linearly Convergent Proximal Gradient Algorithm for Decentralized Optimization

Ali H. Sayed, Kun Yuan, Sulaiman A S A E Alghunaim

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based proximal decent ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Penalization and Bayesian numerical methods for multiscale inverse problems

Andrea Di Blasio

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...

EPFL2019

Convergence Of Variance-Reduced Learning Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...

IEEE2018

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Convergence Analysis and Criterion for Data Assimilation with Sensitivities from Monte Carlo Neutron Transport Codes

Andreas Pautz, Daniel Jerôme Siefman, Mathieu Hursin

Sensitivity coefficients calculated with Monte Carlo neutron transport codes are subject to statistical fluctuations. The fluctuations affect parameters that are calculated with the sensitivity coefficients. The convergence study presented here describes t ...

ANS2018

Real-Time Optimization Based on Adaptation of Surrogate Models

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti, Martand Singhal

Recently, different real-time optimization (RTO) schemes that guarantee feasibility of all RTO iterates and monotonic convergence to the optimal plant operating point have been proposed. However, simulations reveal that these schemes converge very slowly t ...

Elsevier Science Bv2016

Two subtle convex nonlocal approximations of the BV-norm

Hoài-Minh Nguyên

Inspired by the BBM formula and by work of G. Leoni and D. Spector, we analyze the asymptotic behavior of two sequences of convex nonlocal functionals (Psi(n)(u)) and (Phi(n)(u)) which converge formally to the BV-norm of u. We show that pointwise convergen ...

Elsevier2016