Mathematical theory of deep learning

TL;DR

This book offers a comprehensive mathematical foundation for deep learning, covering approximation, optimization, and statistical theories to help students and researchers understand the core principles.

Contribution

It synthesizes fundamental mathematical theories relevant to deep learning, providing accessible and rigorous insights into its theoretical underpinnings.

Findings

Provides foundational mathematical analysis of deep neural networks

Bridges approximation, optimization, and statistical learning theories

Serves as an educational resource for researchers and students

Abstract

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural network theory. Serving as a guide for students and researchers in mathematics and related fields, the book aims to equip readers with foundational knowledge on the topic. It prioritizes simplicity over generality, and presents rigorous yet accessible results to help build an understanding of the essential mathematical concepts underpinning deep learning.