Mathematical Foundations of Deep Learning
Machine Learning
2026-03-20 v1 Optimization and Control
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.
Cite
@article{arxiv.2603.18387,
title = {Mathematical Foundations of Deep Learning},
author = {Xiaojing Ye},
journal= {arXiv preprint arXiv:2603.18387},
year = {2026}
}
Comments
Draft version. Final version is published in "Chapman & Hall/CRC Mathematics and Artificial Intelligence Series" by Taylor & Francis in 2026