Nicolas Henri Bernard Flammarion

Publications associées (18)

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Is there an analog of Nesterov acceleration for gradient-based MCMC?

Nicolas Henri Bernard Flammarion, Xiang Cheng

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm perfor ...

2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Nicolas Henri Bernard Flammarion, Aditya Vardhan Varre, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

Advances in Neural Information Processing Systems 20212021

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Understanding and Improving Fast Adversarial Training

Nicolas Henri Bernard Flammarion, Maksym Andriushchenko

A recent line of work focused on making adversarial training computationally efficient for deep learning models. In particular, Wong et al. (2020) showed that ℓ∞-adversarial training with fast gradient sign method (FGSM) can fail due to a phenomenon called ...

2020

Square Attack: a query-efficient black-box adversarial attack via random search

Nicolas Henri Bernard Flammarion, Maksym Andriushchenko, Francesco Croce

We propose the Square Attack, a new score-based black-box

l_2

and

l_\infty

adversarial attack that does not rely on local gradient information and thus is not affected by gradient masking. The Square Attack is based on a randomized search scheme where ...

2020

Online Robust Regression via SGD on the l1 loss

Nicolas Henri Bernard Flammarion, Scott William Pesme

We consider the robust linear regression problem in the online setting where we have access to the data in a streaming manner, one data point after the other. More specifically, for a true parameter , we consider the corrupted Gaussian linear model $ y=\la ...

2020

On Convergence-Diagnostic based Step Sizes for Stochastic Gradient Descent

Nicolas Henri Bernard Flammarion, Scott William Pesme, Aymeric Daphnis Kévin Dieuleveut

Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In this paper, we s ...

2020

Sparse-RS: a versatile framework for query-efficient sparse black-box adversarial attacks

Nicolas Henri Bernard Flammarion, Maksym Andriushchenko, Francesco Croce

A large body of research has focused on adversarial attacks which require to modify all input features with small l2- or l∞-norms. In this paper we instead focus on query-efficient sparse attacks in the black-box setting. Our versatile framework, Sparse-RS ...

2020

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l_2

and

l_\infty

adversarial attack that does not rely on local gradient information and thus is not affected by gradient masking. The Square Attack is based on a randomized search scheme where ...

2020