一本讲透生成AI数学原理的入门书，帮你理解各种模型怎么来的。
The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer
- 从PCA到扩散模型，系统推导主流生成模型的数学脉络。
- 聚焦核心思想而非具体实现，强调模型间的内在联系。
- 适合想深入理解生成模型原理的科研人员和学生。
本书提供了一本紧凑且以推导为导向的现代生成式人工智能数学基础入门。不泛泛而谈各类最新架构或实现细节，而是构建一条连贯路径，贯穿从主成分分析（PCA）、概率主成分分析（probabilistic PCA）、变分自编码器（VAE）、扩散模型到归一化流（normalising flows）、自回归因子分解、生成对抗网络（GAN）、Wasserstein GAN 和能量模型等主要生成模型家族的核心思想。目标是使生成建模的整体结构更易理解，同时保留理解模型推导与关联所必需的数学实质。本书旨在为数学兴趣浓厚的研究者、从业者和学生打下坚实基础。
原文摘要 · Abstract (English)
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.
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