Výsledky vyhledávání - "Hernández Martin"

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Deep Neural Networks: Multi-Classification and Universal Approximation

Autor: Hernández, Martín, Zuazua, Enrique

We demonstrate that a ReLU deep neural network with a width of $2$ and a depth of $2N+4M-1$ layers can achieve finite sample memorization for any dataset comprising $N$ elements in $\mathbb{R}^d$, where $d\ge1,$ and $M$ classes, thereby ensuring accu

Externí odkaz: http://arxiv.org/abs/2409.06555

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Mini-batch descent in semiflows

Autor: Corella, Alberto Domínguez, Hernández, Martín

This paper investigates the application of mini-batch gradient descent to semiflows. Given a loss function, we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow

Externí odkaz: http://arxiv.org/abs/2407.07556

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Averaged observations and turnpike phenomenon for parameter-dependent systems

Autor: Hernández, Martín, Lazar, Martin, Zamorano, Sebastián

Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions with respect

Externí odkaz: http://arxiv.org/abs/2404.17455

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Laser-driven ion and electron acceleration from near-critical density gas targets: towards high-repetition rate operation in the 1 PW, sub-100 fs laser interaction regime

Ion acceleration from gaseous targets driven by relativistic-intensity lasers was demonstrated as early as the late 90s, yet most of the experiments conducted to date have involved picosecond-duration, Nd:glass lasers operating at low repetition rate

Externí odkaz: http://arxiv.org/abs/2311.04187

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Uniform Turnpike Property and Singular Limits

Autor: Hernandez, Martin, Zuazua, Enrique

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and u

Externí odkaz: http://arxiv.org/abs/2308.15257

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