Sobre o Evento
In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning, Universal Approximation and Normalizing flows.
We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control. We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics.
Texto informado pelo autor.
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Apoiadores / Parceiros / Patrocinadores
Enrique Zuazua Iriondo holds a Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at the Department of Mathematics at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany). He is the Director of Deusto CCM – Chair of Computational Mathematics at Deusto Foundation, University of Deusto – Bilbao (Basque Country, Spain) where he led the ERC “DyCon: Dynamic Control” project (2016-2022). Since 2001 he is a Professor of Applied Mathematics of the Department of Mathematics at UAM – Autonomous University of Madrid.
His fields of expertise in the area of Applied Mathematics cover topics related with Partial Differential Equations, Systems Control and Machine Learning, led to some fruitful collaboration in different industrial sectors such as the optimal shape design in aeronautics and the management of electrical and water distribution networks.
With an important high impact on his work (h-index = 73), he has mentored a significant number of postdoctoral researchers and coached a wide network of Science managers.
He holds a degree in Mathematics from the University of the Basque Country, and a dual PhD degree from the same university (1987) and the Université Pierre et Marie Curie, Paris (1988). In 1990 he became Professor of Applied Mathematics at the Complutense University of Madrid, to later move to UAM in 2001.