Edouard Pauwels | DeepAI

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∙ 05/23/2023

One-step differentiation of iterative algorithms

In appropriate frameworks, automatic differentiation is transparent to t...

0 Jérôme Bolte, et al. ∙

∙ 12/15/2022

Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems

We leverage path differentiability and a recent result on nonsmooth impl...

0 Jérôme Bolte, et al. ∙

∙ 07/26/2022

The derivatives of Sinkhorn-Knopp converge

We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterati...

0 Edouard Pauwels, et al. ∙

∙ 06/01/2022

Nonsmooth automatic differentiation: a cheap gradient principle and other complexity results

We provide a simple model to estimate the computational costs of the bac...

0 Jérôme Bolte, et al. ∙

∙ 05/31/2022

Automatic differentiation of nonsmooth iterative algorithms

Differentiation along algorithms, i.e., piggyback propagation of derivat...

0 Jérôme Bolte, et al. ∙

∙ 01/11/2022

Path differentiability of ODE flows

We consider flows of ordinary differential equations (ODEs) driven by pa...

0 Swann Marx, et al. ∙

∙ 06/23/2021

Numerical influence of ReLU'(0) on backpropagation

In theory, the choice of ReLU'(0) in [0, 1] for a neural network has a n...

0 David Bertoin, et al. ∙

∙ 06/08/2021

Nonsmooth Implicit Differentiation for Machine Learning and Optimization

In view of training increasingly complex learning architectures, we esta...

0 Jérôme Bolte, et al. ∙

∙ 03/05/2021

Second-order step-size tuning of SGD for non-convex optimization

In view of a direct and simple improvement of vanilla SGD, this paper pr...

0 Camille Castera, et al. ∙

∙ 11/24/2020

Sequential convergence of AdaGrad algorithm for smooth convex optimization

We prove that the iterates produced by, either the scalar step size vari...

0 Cheik Traoré, et al. ∙

∙ 07/17/2020

A Hölderian backtracking method for min-max and min-min problems

We present a new algorithm to solve min-max or min-min problems out of t...

0 Jérôme Bolte, et al. ∙

∙ 07/15/2020

Incremental Without Replacement Sampling in Nonconvex Optimization

Minibatch decomposition methods for empirical risk minimization are comm...

0 Edouard Pauwels, et al. ∙

∙ 06/03/2020

A mathematical model for automatic differentiation in machine learning

Automatic differentiation, as implemented today, does not have a simple ...

0 Jérôme Bolte, et al. ∙

∙ 05/29/2020

Long term dynamics of the subgradient method for Lipschitz path differentiable functions

We consider the long-term dynamics of the vanishing stepsize subgradient...

0 Jérôme Bolte, et al. ∙

∙ 02/10/2020

Polynomial Optimization for Bounding Lipschitz Constants of Deep Networks

The Lipschitz constant of a network plays an important role in many appl...

0 Tong Chen, et al. ∙

∙ 10/31/2019

Rate of convergence for geometric inference based on the empirical Christoffel function

We consider the problem of estimating the support of a measure from a fi...

0 Mai Trang Vu, et al. ∙

∙ 09/23/2019

Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learning

The Clarke subdifferential is not suited to tackle nonsmooth deep learni...

0 Jérôme Bolte, et al. ∙

∙ 05/29/2019

An Inertial Newton Algorithm for Deep Learning

We devise a learning algorithm for possibly nonsmooth deep neural networ...

0 Camille Castera, et al. ∙

∙ 10/19/2018

Data analysis from empirical moments and the Christoffel function

Spectral features of the empirical moment matrix constitute a resourcefu...

0 Edouard Pauwels, et al. ∙

∙ 05/21/2018

Relating Leverage Scores and Density using Regularized Christoffel Functions

Statistical leverage scores emerged as a fundamental tool for matrix ske...

0 Edouard Pauwels, et al. ∙

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