---
title: "Learn"
url: "/learn"
---

The library is organised two ways, and both are worth knowing about.

**By taxonomy.** Every post sits in exactly one category and one subcategory,
which is where its URL comes from. If you know roughly what you are looking for,
this is the faster route.

**By series.** A series is an ordered arc that cuts across the taxonomy — the
maths, then the models, then the networks — and reads front to back. If you are
learning something rather than looking something up, start with a series.

Posts that are written but not yet released appear here as cards without links.
That is deliberate: the plan is public before the prose is finished.

## Categories

- [Essential Maths](/learn/essential-maths.md): Machine learning rests on four pieces of mathematics: linear algebra, calculus and optimisation, probability and statistics, and information theory. This category derives each one from the ground up, in the notation papers actually use, and stops at the point where the maths starts earning its keep.
- [Machine Learning](/learn/machine-learning.md): The classical models, taken seriously. Each post derives a model rather than importing it, states the assumptions it makes about the data, shows the loss it minimises and how that loss is optimised, and ends with the failure modes that send practitioners reaching for something more complicated.
- [Deep Learning](/learn/deep-learning.md): Deep learning is what happens when you stack the models from the previous category and find a way to train the stack. This category starts at the single unit, builds to a network, and treats backpropagation as the idea that makes the whole enterprise computationally tractable.
- [AI Systems](/learn/ai-systems.md): A model is the smallest part of an AI system — the rest is retrieval, evaluation, and the operational discipline that decides whether the thing survives contact with real data and real users. These posts are about that surrounding engineering, not the model of the month.

## Series

- [From Matrices to Neural Networks](/learn/series/from-matrices-to-neural-networks.md): Eight posts across three categories, read in dependency order. Linear algebra and calculus give the space and the gradient, linear and logistic regression introduce the vocabulary of fitting, and neurons and backpropagation generalise all of it into a network you can train.
- [The Loss Function Toolkit](/learn/series/the-loss-function-toolkit.md): Maximum likelihood estimation shows where a loss function comes from statistically; entropy and cross-entropy show where the same loss comes from informationally. This series puts both derivations side by side and ends at the specific case every classifier relies on — why cross-entropy is the natural loss for classification, not merely the conventional one.
- [From One Model to Many: The Ensemble Story](/learn/series/the-ensemble-story.md): The bias-variance tradeoff explains why a single model is stuck choosing what to get wrong. Decision trees give a model simple enough to combine cheaply, forests and boosting show the two structurally different ways of combining it, and cross-validation supplies the honest measurement that tells you whether the combination actually helped.
- [Anatomy of a Modern Neural Network](/learn/series/anatomy-of-a-modern-neural-network.md): An architecture on paper and a network that trains are separated by five practical decisions this series takes in turn — the non-linearity, the starting weights, the normalisation that keeps activations workable, the regularisation that fights memorisation, and the optimiser doing the updating. Each is a fix to a specific, nameable failure.
- [The Road to Transformers](/learn/series/the-road-to-transformers.md): Recurrent networks were the obvious way to handle sequences until their own architecture — weight sharing across time — turned into the vanishing gradient problem. This series follows that failure directly to its resolution, attention, and ends with the transformer built from attention block by block.