Publications related to Differentiable function

Scalable constrained optimization

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Joao Pedro Gonçalves Ramos

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Springer Heidelberg2024

Graphical solutions to one-phase free boundary problems

Xavier Fernandez-Real Girona, Hui Yu

We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...

Walter De Gruyter Gmbh2023

The statistical complexity of early-stopped mirror descent

Tomas Vaskevicius, Varun Kanade

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrain ...

Oxford Univ Press2023

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery

Jonathan Paul Sauder

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and of ...

2022

Regularized Diffusion Adaptation via Conjugate Smoothing

Ali H. Sayed, Stefan Vlaski

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Martin Peter Stoller, Joao Pedro Gonçalves Ramos

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

2021

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

IEEE2020

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Ali H. Sayed, Sulaiman A S A E Alghunaim, Ming Yan

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...

IEEE2020

Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Federico Alberto Alfredo Felici, Cristian Galperti

This paper introduces a recent innovation in dealing with non-periodic behavior often referred to as transients in perturbative experiments. These transients can be the result from the unforced response due to the initial condition and other slow trends in ...

2020

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which ...

2019

Geometric ergodicity for some space-time max-stable Markov chains

Erwan Fabrice Koch

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of cont ...

ELSEVIER SCIENCE BV2019

Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

Maria-Alexandra Paun

In the framework of Fractal Theory of Motion for the Scale Relativity Theory with arbitrary and constant fractal dimensions, dynamics in complex systems associated to the fractal-non-fractal transition are analyzed. Working with the assumption that these d ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2019

Tits Buildings And K-Stability

Giulio Codogni

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits ...

CAMBRIDGE UNIV PRESS2019

Backpropagation-Friendly Eigendecomposition

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

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matri ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Calculus of variations: A differential form approach

Swarnendu Sil

We study integrals of the form integral(Omega) f(d omega(1), ..., d omega(m)), where m >= 1 is a given integer, 1

WALTER DE GRUYTER GMBH2019

Reparameterizing Discontinuous Integrands for Differentiable Rendering

Wenzel Alban Jakob, Guillaume Rémi Bruno Loubet

Differentiable rendering has recently opened the door to a number of challenging inverse problems involving photorealistic images, such as computational material design and scattering-aware reconstruction of geometry and materials from photographs. Differe ...

ASSOC COMPUTING MACHINERY2019