---
title: "From Matrices to Neural Networks"
url: "/learn/series/from-matrices-to-neural-networks"
---

Most paths into deep learning start at the framework and work backwards,
picking up the mathematics only when something breaks. This one runs the other
way, and the payoff is that nothing later in the arc arrives unexplained.

## The four movements

**The space** — vectors and matrices. What a vector is, what a map does to
one, and why the arithmetic is shaped the way it is.

**The slope** — derivatives and gradients. The geometric fact that makes
"train a model" mean something concrete: move against the gradient.

**The fit** — what learning means, then linear and logistic regression. Where
loss functions come from, and the full anatomy of a supervised model at the
smallest size where it is still complete.

**The network** — neurons and backpropagation. Stacking the fitted model,
discovering what that costs, and the algorithm that makes the cost affordable.

## How to read it

In order, if you are learning this for the first time. Each part assumes the
ones before it and nothing else, and the dependencies are stated in every post
so you can rejoin the arc partway if you already have the earlier material.

Parts still in draft are listed here anyway — the arc is declared in full, so
the shape of the whole is visible before the last part is written.

## Parts

- [What Are Neurons?](/learn/deep-learning/foundations/what-are-neurons.md): An artificial neuron is a weighted sum followed by a non-linearity, which makes it a logistic regression that has stopped claiming to model a probability. This post explains what the non-linearity is actually for, why stacking linear units gains nothing, and how a layer becomes a matrix multiply.