The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer
A compact, derivation-oriented book on the mathematical foundations of generative AI.
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- Primary sourcearXiv
- Discovery linkHacker News
- Linked in sourceView PDF
- Linked in sourcearXiv:2605.29713v2
- Linked in source[v1]
- Linked in sourcecs.AI
- Linked in sourceLearn more about arXivLabs
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A compact, derivation-oriented book on the mathematical foundations of generative AI. Instead of surveying recent architectures, it builds a route connecting PCA, probabilistic PCA, variational autoencoders, diffusion models, normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. The stated aim is to make generative modelling structure more accessible while keeping the mathematical substance needed for derivations. The revised version is a 195-page preprint with added visual explanations.
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Source claims not independently checked; this is a self-described preprint, and the abstract describes intent rather than evaluated learning outcomes.
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The book connects PCA, probabilistic PCA, VAEs, and diffusion models within one derivation-oriented route.
Source: arXiv ↗Stored source-based brief · key point 1 · AINewsIQ paraphraseIt also covers normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models.
Source: arXiv ↗Stored source-based brief · key point 2 · AINewsIQ paraphraseIt deliberately omits surveying every recent architecture or implementation detail.
Source: arXiv ↗Stored source-based brief · key point 3 · AINewsIQ paraphraseVersion 2 is a 195-page revised preprint that adds visual explanations throughout.
Source: arXiv ↗Stored source-based brief · key point 4 · AINewsIQ paraphraseLimits from the stored brief
Source claims not independently checked; this is a self-described preprint, and the abstract describes intent rather than evaluated learning outcomes.
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- Version 1 · published
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Why this may matter
A structured primer tying major generative model families together through their derivations can help students and practitioners understand how these models relate, rather than treating each as an isolated method.
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Source claims not independently checked; this is a self-described preprint, and the abstract describes intent rather than evaluated learning outcomes.
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