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Mathematical Foundations of Deep Learning

arXiv cs.LG / 3/20/2026

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Key Points

  • The article announces a new arXiv draft book titled "Mathematical Foundations of Deep Learning" that provides a rigorous mathematical treatment of foundational ideas in deep learning.
  • It covers core theoretical topics including the approximation capabilities of deep neural networks.
  • It explores the theory and algorithms of optimal control and reinforcement learning integrated with deep learning techniques.
  • It discusses contemporary generative models that are driving today's advances in artificial intelligence.
  • Being a draft on arXiv, the work is released as v1 and invites feedback from the research community.

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.