Mathematical Foundations of Deep Learning Models and Algorithms

Konstantinos Spiliopoulos, Richard B. Sowers, Justin Sirignano (Autoren)

Buch | Hardcover

550 Seiten

2025
American Mathematical Society (Verlag)
978-1-4704-8108-7 (ISBN)

Noch nicht erschienen (ca. Dezember 2025)
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Deep learning uses multi-layer neural networks to model complex data patterns. Large models-with millions or even billions of parameters-are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine. This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included. The book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning. Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.

Konstantinos Spiliopoulos, Boston University, MA. Richard B. Sowers, University of Illinois at Urbana Champaign, Illinois. Justin Sirignano, University of Oxford, United Kingdom

Erscheint lt. Verlag	25.12.2025
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-4704-8108-1 / 1470481081
ISBN-13	978-1-4704-8108-7 / 9781470481087
Zustand	Neuware