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Transdisciplinary Research Institute for Advancing Data Science

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Now showing 1 - 5 of 5
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    Lecture 5: Mathematics for Deep Neural Networks: Energy landscape and open problems
    ( 2019-03-18) Schmidt-Hieber, Johannes
    To derive a theory for gradient descent methods, it is important to have some understanding of the energy landscape. In this lecture, an overview of existing results is given. The second part of the lecture is devoted to future challenges in the field. We describe important future steps needed for the future development of the statistical theory of deep networks.
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    Lecture 4: Mathematics for Deep Neural Networks: Statistical theory for deep ReLU networks
    ( 2019-03-15) Schmidt-Hieber, Johannes
    We outline the theory underlying the recent bounds on the estimation risk of deep ReLU networks. In the lecture, we discuss specific properties of the ReLU activation function that relate to skipping connections and efficient approximation of polynomials. Based on this, we show how risk bounds can be obtained for sparsely connected networks.
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    Lecture 3: Mathematics for Deep Neural Networks: Advantages of Additional Layers
    ( 2019-03-13) Schmidt-Hieber, Johannes
    Why are deep networks better than shallow networks? We provide a survey of the existing ideas in the literature. In particular, we discuss localization of deep networks, functions that can be easily approximated by deep networks and finally discuss the Kolmogorov-Arnold representation theorem.
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    Lecture 2: Mathematics for Deep Neural Networks: Theory for shallow networks
    ( 2019-03-08) Schmidt-Hieber, Johannes
    We start with the universal approximation theorem and discuss several proof strategies that provide some insights into functions that can be easily approximated by shallow networks. Based on this, a survey on approximation rates for shallow networks is given. It is shown how this leads to estimation rates. In the lecture, we also discuss methods that fit shallow networks to data.
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    Lecture 1: Mathematics for Deep Neural Networks
    ( 2019-03-06) Schmidt-Hieber, Johannes
    There are many different types of neural networks that differ in complexity and the data types that can be processed. This lecture provides an overview and surveys the algorithms used to fit deep networks to data. We discuss different ideas that underly the existing approaches for a mathematical theory of deep networks.