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《生成式人工智能基礎小書：直觀的數學入門指南》介紹生成模型數學基礎
《生成式人工智能基础小书：直观的数学入门指南》
AI 導讀
《生成式人工智能基礎小書》以推導為主線，精簡介紹現代生成式人工智能的數學基礎。內容涵蓋 PCA、probabilistic PCA、變分自編碼器、擴散模型、正規化流、自回歸分解、GAN、Wasserstein GAN 和基於能量的模型。這份 195 頁的 v2 預印本加入全書視覺化解説。
正文
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)
來源：Hacker News 熱門（buzzing.cc 中文翻譯） · arxiv.org