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Computer Science > Machine Learning

arXiv:2310.20360 (cs)
[Submitted on 31 Oct 2023]

Title:Mathematical Introduction to Deep Learning: Methods,
Implementations, and Theory

Authors:Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
Download a PDF of the paper titled Mathematical Introduction to Deep
Learning: Methods, Implementations, and Theory, by Arnulf Jentzen and
2 other authors
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    Abstract:This book aims to provide an introduction to the topic
    of deep learning algorithms. We review essential components of
    deep learning algorithms in full mathematical detail including
    different artificial neural network (ANN) architectures (such as
    fully-connected feedforward ANNs, convolutional ANNs, recurrent
    ANNs, residual ANNs, and ANNs with batch normalization) and
    different optimization algorithms (such as the basic stochastic
    gradient descent (SGD) method, accelerated methods, and adaptive
    methods). We also cover several theoretical aspects of deep
    learning algorithms such as approximation capacities of ANNs
    (including a calculus for ANNs), optimization theory (including
    Kurdyka-Lojasiewicz inequalities), and generalization errors. In
    the last part of the book some deep learning approximation
    methods for PDEs are reviewed including physics-informed neural
    networks (PINNs) and deep Galerkin methods. We hope that this
    book will be useful for students and scientists who do not yet
    have any background in deep learning at all and would like to
    gain a solid foundation as well as for practitioners who would
    like to obtain a firmer mathematical understanding of the objects
    and methods considered in deep learning.

Comments: 601 pages, 36 figures, 45 source codes
          Machine Learning (cs.LG); Artificial Intelligence (cs.AI);
Subjects: Numerical Analysis (math.NA); Probability (math.PR);
          Machine Learning (stat.ML)
MSC       68T07
classes:
Cite as:  arXiv:2310.20360 [cs.LG]
          (or arXiv:2310.20360v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2310.20360
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Benno Kuckuck [view email]
[v1] Tue, 31 Oct 2023 11:01:23 UTC (2,327 KB)
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