Concept

Méthode du gradient conjugué

Publications associées (392)

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Daniel Kressner, Alice Cortinovis

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Fabio Nobile, Tommaso Vanzan

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Randomized flexible GMRES with deflated restarting

Laura Grigori, Emeric Martin

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...

Springer2024

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

EPFL2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Domain adaptation via alignment of operation profile for Remaining Useful Lifetime prediction

Olga Fink, Ismail Nejjar, Mengjie Zhao

Effective Prognostics and Health Management (PHM) relies on accurate prediction of the Remaining Useful Life (RUL). Data-driven RUL prediction techniques rely heavily on the representativeness of the available time-to-failure trajectories. Therefore, these ...

2024

Discovering Lobby-Parliamentarian Alignments through NLP

Matthias Grossglauser, Victor Kristof, Aswin Suresh

We discover alignments of views between interest groups (lobbies) and members of the European Parliament (MEPs) by automatically analyzing their texts. Specifically, we do so by collecting novel datasets of lobbies’ position papers and MEPs’ speeches, and ...

2024

, , , , ,

While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of recent works to ...

Piscataway2023

Efficient and Accurate Handling of Periodic Flows in Time-Sensitive Networks

Jean-Yves Le Boudec, Seyed Mohammadhossein Tabatabaee

Total Flow Analysis (TFA) is a method for the worst-case analysis of time-sensitive networks. It uses service curve characterizations of the network nodes and arrival curves of flows at their sources; for tractability, the latter are often taken to be line ...

2023

, ,

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

\gamma

and momentum parameter

\beta

that allows u ...

2024

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

EPFL2024