Stage 1 · Beginner · F1
Numbers That Learn
A photo is a single point in a space with three million dimensions.
12 lessons · 105 minEasy
About this chapter
Every model you will ever build touches only lists of numbers. Here those lists become arrows you can drag, and matrices become machines that bend the space the arrows live in. You will feel why a dot product is a similarity score, why length matters, and what one layer can and cannot reach. Then the chapter turns the lights on in a space with twelve thousand dimensions, where everything is far from everything and almost every pair of directions is square to the other. No formula is needed to follow any of it.
What you will be able to do
- 18 min
A Photo Is One Point
Read a picture as one long list of numbers, and that list as a single point.
- 28 min
Arrows and Lists
Switch between a vector as a list of numbers and a vector as an arrow.
- 38 min
Adding and Stretching
Add two vectors and scale one, and say what each does to the picture.
- 48 min
How Long, How Far
Measure the size of a vector and the distance between two of them.
- 59 min
One Number for Agreement
Read the sign and rough size of a dot product straight off a picture.
- 69 min
Agreement Without Volume
Score two vectors on direction alone, and say when that beats a dot product.
- 79 min
A Matrix Moves Space
Read a two by two matrix as a stretch, a turn, or a squash of the whole plane.
- 89 min
Doing It By Hand
Multiply a matrix by a vector yourself, and predict the shape of the result.
- 99 min
Doing It Twice
Combine two moves into one matrix, and say why a stack of them needs a bend.
- 109 min
Two Arrows Are Enough
Say which points a set of arrows can reach, and what the dimension of that reach is.
- 1110 min
A Strange Place to Live
Name two things that stop being true when a space has thousands of dimensions.
- 129 min
Where Each Idea Lands
Point at the place inside a neural network where each idea from this chapter is used.
Before you start
Nothing to learn first. You can start here.