生成式AI数学基础小书

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Abstract:This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence. Rather than surveying every recent architecture or implementation detail, it develops a coherent route through the ideas connecting major families of generative models, from PCA, probabilistic PCA, variational autoencoders, and diffusion models to normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. The aim is to make the structure of generative modelling more accessible without removing the mathematical substance needed to understand how these models are derived and related. The book is intended as a foundation-building primer for mathematically curious researchers, practitioners, and students.

Comments:	Revised preprint version, 195 pages. Added visual explanations throughout. Comments and corrections are welcome
Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:	arXiv:2605.29713 [cs.LG]
	(or arXiv:2605.29713v2 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2605.29713 arXiv-issued DOI via DataCite

Submission history

From: Tianhua Chen [view email]
[v1] Thu, 28 May 2026 10:12:00 UTC (125 KB)
[v2] Tue, 8 Sep 2026 07:17:36 UTC (1,168 KB)