Alice's Adventures in a Differentiable Wonderland, Volume I: A Tour of the Land
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A modern textbook on how neural networks really work, from tensors and gradients to transformers. The first three chapters lay the ground: what the book is about, the linear algebra and calculus a network runs on, gradient descent, and what a dataset and a loss function are.
This is a sample: 3 of 13 chapters.
The first part of the book, called Compass and Needle, chapters two to six, sets up exactly this machinery. Seeing a network as a chain of differentiable building blocks raises two questions, and the book's second figure illustrates them. First, what kinds of data can go in and come out?
Most of the models in the book are built from very plain ingredients: sums, multiplications, and a few bent functions such as the exponential, sines and cosines, and square roots. Vectors, the tensors with one direction, have their own arithmetic, which mathematicians call a vector space.
For the second kind, the book gives a generalised dot product. Take two tensors of the same shape, with three directions, multiply them position by position, and add up every single product. It is nothing but the ordinary dot product of the two tensors flattened into long lists.
Now to gradient descent. Suppose we want the input that makes a function of many numbers as small as possible, its minimum.
The chapter's opening figure looks ahead to something remarkable. A differentiable model transforms its input step by step with operations from linear algebra.
How is such a model trained? Because the examples are assumed independent and drawn from the same distribution, the probability a model assigns to the whole dataset is the product of the probabilities it assigns to each example's true output. That product is called the likelihood of the dataset.
Examples for: a curious adult with school maths who uses AI apps every day; add one modern instance per idea, such as how a chat assistant or a phone's photo app is trained
The lectures retell the English text of arXiv 2404.17625 (version 3, 2025) by Simone Scardapane, published under an open licence that allows retelling and translation. The retelling, the drawings and the voice are made by AI and checked against the book by a second model. How AI is used.
The lectures adapt the original and are released under the same licence, free to share and adapt with credit to the author and a link to this page: CC BY-SA 4.0
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