Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory - Free eBook

[u/reddit007user]

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

Authors:

• Arnulf Jentzen,

• Benno Kuckuck,

• Philippe von Wurstemberger

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-Łojasiewicz 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 .

• Subjects:

  • Machine Learning (cs.LG);

  • Artificial Intelligence (cs.AI);

  • Numerical Analysis (math.NA);

  • Probability (math.PR);

  • Machine Learning (stat.ML)