Mathematical Foundations of Deep Learning

TL;DR

This book provides a thorough and rigorous mathematical foundation for deep learning, covering theoretical aspects, control and reinforcement learning, and generative models that are central to current AI advancements.

Contribution

It offers a comprehensive, mathematically rigorous treatment of deep learning principles, integrating control, reinforcement learning, and generative models.

Findings

Deep neural networks have strong approximation capabilities.

Optimal control and reinforcement learning are integrated with deep learning.

Contemporary generative models are explained within a rigorous mathematical framework.

Abstract

This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory and algorithms of optimal control and reinforcement learning integrated with deep learning techniques, to contemporary generative models that drive today's advances in artificial intelligence.