Mathematical Foundations of Deep Learning

Xiaojing Ye

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arXiv · 2603.18387

Mathematical Foundations of Deep Learning

Xiaojing Ye

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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.

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Xiaojing Ye. 2026-03-19. Mathematical Foundations of Deep Learning. https://arxiv.org/abs/2603.18387

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