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stat.ML2024
Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks
Martín Hernández, Enrique Zuazua
We present a fully constructive analysis of deep ReLU neural networks for classification and function approximation tasks. First, we prove that any dataset with distinct points…
math.OC2024
Mini-batch descent in semiflows
Alberto Domínguez Corella, Martín Hernández
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-b…
math.OC2024
Averaged observations and turnpike phenomenon for parameter-dependent systems
Martín Hernández, Martin Lazar, Sebastián Zamorano
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 i…