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Computer Science > Machine Learning

arXiv:2105.04026 (cs)
[Submitted on 9 May 2021]

Title:The Modern Mathematics of Deep Learning

Authors:Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp
Petersen
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    Abstract: We describe the new field of mathematical analysis of
    deep learning. This field emerged around a list of research
    questions that were not answered within the classical framework
    of learning theory. These questions concern: the outstanding
    generalization power of overparametrized neural networks, the
    role of depth in deep architectures, the apparent absence of the
    curse of dimensionality, the surprisingly successful optimization
    performance despite the non-convexity of the problem,
    understanding what features are learned, why deep architectures
    perform exceptionally well in physical problems, and which fine
    aspects of an architecture affect the behavior of a learning task
    in which way. We present an overview of modern approaches that
    yield partial answers to these questions. For selected
    approaches, we describe the main ideas in more detail.

Comments: This review paper will appear as a book chapter in the book
          "Theory of Deep Learning" by Cambridge University Press
Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as:  arXiv:2105.04026 [cs.LG]
          (or arXiv:2105.04026v1 [cs.LG] for this version)

Submission history

From: Julius Berner [view email]
[v1] Sun, 9 May 2021 21:30:42 UTC (2,534 KB)
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Philipp Petersen
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