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petersen p mathematical theory deep learning 2025

Type:: E-books
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Uploaded On:: Aug. 12, 2025, 11:09 a.m.
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Textbook in PDF format This book serves as an introduction to the key ideas in the mathematical analysis of deep learning. It is designed to help students and researchers to quickly familiarize themselves with the area and to provide a foundation for the development of university courses on the mathematics of deep learning. Our main goal in the composition of this book was to present various rigorous, but easy to grasp, results that help to build an understanding of fundamental mathematical concepts in deep learning. To achieve this, we prioritize simplicity over generality. As a mathematical introduction to deep learning, this book does not aim to give an exhaustive survey of the entire (and rapidly growing) field, and some important research directions are missing. In particular, we have favored mathematical results over empirical research, even though an accurate account of the theory of deep learning requires both. The book is intended for students and researchers in mathematics and related areas. While we believe that every diligent researcher or student will be able to work through this manuscript, it should be emphasized that a familiarity with analysis, linear algebra, probability theory, and basic functional analysis is recommended for an optimal reading experience. To assist readers, a review of key concepts in probability theory and functional analysis is provided in the appendix. The material is structured around the three main pillars of deep learning theory: Approximation theory, Optimization theory, and Statistical Learning theory. This structure, which corresponds to the three error terms typically occuring in the theoretical analysis of deep learning models, is inspired by other recent texts on the topic following the same outline. More specifically, Chapter 1 provides an overview and introduces key questions for understand deep learning. Chapters 2 - 9 explore results in approximation theory, Chapters 10 - 13 discuss optimization theory for deep learning, and the remaining Chapters 14 - 16 address the statistical aspects of deep learning

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petersen p mathematical theory deep learning 2025

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