Mathematical Aspects of Deep Learning (eBook, PDF)

Redaktion: Grohs, Philipp; Kutyniok, Gitta

• Format: PDF

Produktbeschreibung

In recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 22. Dezember 2022
• Englisch
• ISBN-13: 9781009035682
• Artikelnr.: 70911809

Inhaltsangabe

1. The modern mathematics of deep learning Julius Berner, Philipp Grohs,
Gitta Kutyniok and Philipp Petersen; 2. Generalization in deep learning
Kenji Kawaguchi, Leslie Pack Kaelbling, and Yoshua Bengio; 3. Expressivity
of deep neural networks Ingo Gühring, Mones Raslan and Gitta Kutyniok; 4.
Optimization landscape of neural networks René Vidal, Zhihui Zhu and
Benjamin D. Haeffele; 5. Explaining the decisions of convolutional and
recurrent neural networks Wojciech Samek, Leila Arras, Ahmed Osman,
Grégoire Montavon and Klaus-Robert Müller; 6. Stochastic feedforward neural
networks: universal approximation Thomas Merkh and Guido Montúfar; 7. Deep
learning as sparsity enforcing algorithms A. Aberdam and J. Sulam; 8. The
scattering transform Joan Bruna; 9. Deep generative models and inverse
problems Alexandros G. Dimakis; 10. A dynamical systems and optimal control
approach to deep learning Weinan E, Jiequn Han and Qianxiao Li; 11.
Bridging many-body quantum physics and deep learning via tensor networks
Yoav Levine, Or Sharir, Nadav Cohen and Amnon Shashua.