What you will be able to see
The step below is Lesson 3’s home still. The valley is Lesson 6’s ravine. Both numbers are numpy-locked. Unit 0 teaches that language; P1–P5 are live in Learn (quizzes stay on paper). Lessons 1–22 are all live — the Optimisation track spine is complete.
Start at w = 4, height 8. Home eta 0.5 lands at w = 2, height 8 → 2. Eta 2 bounces 4 and −4.
Live step: w 4.00 → 2.00, height 8.00 → 2.00. Home step. Height 8 → 2.
Start at (1, 0.1), height 1. Slope (1, 10). Conditioning κ = 100. The 3D y-axis is stretched so the trench is visible; height is true f.
Honest η = 1/κ = 0.01 moves to (0.99, 0.00). Lesson 3’s η = 0.5 on this valley flies to (0.5, -4.9), height 1200.6. One learning rate cannot serve both axes. That is why Adam exists.
Locked still f = ½(x² + 100y²) · home 1, 0.1
The path
The language of the hill → landscape → unconstrained walking → the modern trainer → walls → prices → product constraints.
A lesson links once its video, notes, quiz, and interactive ship. Lesson 1 is linked; the rest of the titles below stay unlinked until their media ships.
Live
Unit P. The language of the hill
Lists, slopes, uphill arrows, ravine algebra, and a chord test — the words the 22-lesson walk will use without stopping to define them.
Live
Unit A. The landscape
A loss is a hill. The gradient points uphill. A step walks the other way.
Live
Unit B. Unconstrained walking
Ravines, noisy batches, memory, and a local bowl. Same downhill, better compasses.
Live
Unit C. The modern trainer
Per-coordinate trust, AdamW as the LLM recipe, saddles that look like arrival.
Live
Unit D. Walls
A feasible set is a wall. Project. Or hide the nonsmooth piece in a prox.
Live
Unit E. Prices
A multiplier is a price. KKT is stationarity on the wall. The gap certifies arrival.
Live
Unit F. Product constraints
KL balls, LoRA subspaces, and barriers. The constraints products actually ship.