Stage 1 · Beginner · F2
The Slope of Everything
Every AI model is a machine for taking one derivative.
12 lessons · 101 minEasy
About this chapter
Learning is one question asked over and over: if I nudge this number, does the error go up or down? This chapter builds that question from a picture rather than a definition. You will zoom in on a curve until it turns into a straight road, meet the chain rule as a row of gears, and read a gradient as an arrow that points uphill. By the end you can say what a model is doing when it trains, check a gradient by hand, and tell a real bottom from a saddle.
What you will be able to do
- 17 min
The Question Every Model Asks
State learning as a search for the direction that lowers the error.
- 27 min
How Fast, Not How Much
Turn two readings into a rate, and read that rate off a curve.
- 38 min
Zoom In Until It Is Straight
Say why a smooth curve looks like a line up close, and read the tilt there.
- 49 min
The Derivative Is a Slope at a Point
Read the tangent anywhere on a curve and say what the sign of the derivative means there.
- 58 min
The Rules You Will Actually Use
Differentiate powers and sums without looking anything up.
- 610 min
The Chain Rule Is the Whole Game
Send a rate through a chain of boxes by multiplying one link at a time.
- 78 min
One Knob at a Time
Take a partial derivative and name the numbers you froze to get it.
- 89 min
The Gradient Points Uphill
Read a gradient as an arrow: a direction to climb and a steepness.
- 99 min
Bottoms, Tops and Saddles
Tell a bottom, a top and a saddle apart when the ground is flat.
- 109 min
Every Model Is a Derivative Machine
Explain why one derivative of one number is all a model ever needs.
- 119 min
Measure It Both Ways
Measure a derivative by nudging, pick a sensible step, and use it to check the rules.
- 128 min
A Taste of Area
Add up thin slices to get the area under a curve, and say why probability needs it.