A 195-Page Math Primer on How Generative AI Works, Now on arXiv

Tianhua Chen of the University of Huddersfield in the UK has published an introductory book on the mathematical foundations of generative AI on arXiv. It is titled “The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer.” The first version went up on May 28, 2026, and the revised edition (v2), posted on September 8, runs 195 pages.

The intended readers are people who research AI or use it in their work, along with students. The author structured the book to draw out, step by step, the mathematical principles behind generative AI and the relationships between models. It is worth a look for readers who want to move beyond simply trying AI out and study what sits underneath it.

What principles does it cover?

The book starts with principal component analysis (PCA) and probabilistic principal component analysis, techniques for compressing the key features of a dataset onto a handful of axes. Rather than immediately listing off a series of models, it establishes a starting point first and builds the explanation from there. The structure follows the mathematics of each individual model while also examining how it relates to the others.

The scope includes variational autoencoders and the diffusion models widely used for image generation. From there it moves on to normalizing flows, autoregressive models, generative adversarial networks (GANs), and energy-based models. It gathers generative AI models that readers may have encountered under separate names into a single volume and explains the mathematics needed to understand each one.

The author notes that this is not a book that covers the full landscape of the latest models or implementation details. Rather than comparing which model comes out ahead on benchmarks or walking through the steps of building a service, it is aimed at studying the underlying principles of various models and the connections between them.

What changed in the revised edition?

The revised edition adds illustrated explanations. The update brings visual material to a text that develops mathematical principles in stages. The arXiv page retains the submission records for both the initial release and the revision, and the 195-page count refers to the revised edition.

The book can be read on arXiv as a PDF or as a web document. The news also reached Hacker News on November 3 local time, where it drew 351 points and 55 comments.

That makes one more learning resource for tracing the various generative AI models back to their mathematical foundations. For readers who use AI, it is another option for studying how it works at a deeper level.