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- Journal Article
In this article, we develop a framework for showing that neural networks can overcome the curse of dimensionality in different high-dimensional approximation problems. Our approach is based on the notion of a catalog network, which is a generalization of a standard neural network in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of functions. As such, catalog networks constitute a rich family of continuous functions. We show that under appropriate conditions on the catalog, catalog networks can efficiently be approximated with rectified linear unit-type networks and provide precise estimates on the number of parameters needed for a given approximation accuracy. As special cases of the general results, we obtain different classes of functions that can be approximated with recitifed linear unit networks without the curse of dimensionality. Show more
Journal / seriesIEEE Transactions on Neural Networks and Learning Systems
Organisational unit09557 - Cheridito, Patrick / Cheridito, Patrick
02204 - RiskLab / RiskLab
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