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《The Little Book of Generative AI Foundations》：生成式 AI 数学基础导引书
The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer
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《The Little Book of Generative AI Foundations》是一本面向研究人员、从业者和学生的 195 页预印本数学基础导引书。该书系统介绍了现代生成式 AI 的数学原理，涵盖从 PCA、变分自编码器、扩散模型到 GAN、自回归因果分解等主流模型家族。修订后的版本增加了贯穿全书的图解说明，旨在使生成式建模的结构更易于理解。
正文 · 原文
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)
来源：Hacker News-首页 · arxiv.org