Mathematical Foundations of Deep Learning Models and Algorithms

Konstantinos Spiliopoulos, Richard B. Sowers, Justin Sirignano

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English

American Mathematical Society
31 December 2025

Calculus & mathematical analysis; Applied mathematics

Series: Graduate Studies in Mathematics

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.

By: Konstantinos Spiliopoulos, Richard B. Sowers, Justin Sirignano
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470483999
ISBN 10: 1470483998
Series: Graduate Studies in Mathematics
Pages: 550
Publication Date: 31 December 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

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