Plate II
The Halftime Show: An Artificial Brain on the Football Field (Understanding this means understanding the Great 2033 Race)
Picture halftime. The marching band fills the field in rank after rank: drums, trombones, trumpets, sousaphones. Suddenly the scoreboard lights up a number. The whole band stops and looks. Each band member is a helper, one artificial neuron. The drummers nearest the scoreboard read its lights and pass the word to the trombones, who pass it to the trumpets, who pass it to the sousaphones. At the far end stand ten sousaphone players, one for each digit 0 through 9. Whoever plays loudest is the band's answer.
DrumsInput layer. Each drummer reads one row of scoreboard lights.
TrombonesFirst hidden layer. They notice little strokes and edges.
TrumpetsSecond hidden layer. They notice bigger pieces: loops and long lines.
SousaphonesOutput layer. Ten players, one for each digit 0–9.
This band is a small picture of the idea. The real network in the 3Blue1Brown videos reads a 28 × 28 picture, so its first rank has 784 helpers, followed by two ranks of 16 and a final rank of 10.
Plate III
Rehearsal: Why the Band Needs Thousands and Thousands of Sevens
A brand-new band does not know any numbers. Every player's listening knobs start out set at random, so the first time the scoreboard shows a 7, the band might shout “3!” Before it can perform, the band has to rehearse, and rehearse, and rehearse.
At rehearsal we show the band picture after picture of handwritten numbers. Each picture comes with the right answer attached, like an answer key. No two sevens look alike. Some lean, some have a line through the middle, some are sloppy.
777777̶7
If the band sees enough different sevens, it slowly learns what all sevens have in common: a line across the top and a slant coming down. Eventually, whenever any 7 appears, the sousaphone player for 7 plays loudest.
And when the band gets it wrong, there is a way to work backward from the last row to make it right. Start at the sousaphones, measure how wrong the answer was, and walk back rank by rank, telling every player how to adjust their listening. This is called backpropagation. Taking those small corrections one step at a time is called gradient descent. Doing it over and over, picture after picture, is called training.
One rehearsal, repeated many thousands of times
- Step 1Show a pictureA handwritten 7, with the answer key that says “seven.”
- Step 2The band guessesThe message passes up the ranks. The band answers “3.”
- Step 3Score the mistakeHow wrong was it? That number is the cost.
- Step 4Work backwardBackpropagation walks back from the sousaphones, and every knob turns a tiny bit.
Then the next picture, and the next, and the next…
How much practice?
60,000practice pictures in the famous handwritten-digit collection used in the 3Blue1Brown videos, about 6,000 of each digit.
10,000more pictures kept hidden until the end, as a final test. They show whether the band truly learned sevens or only memorized the practice pictures.
Trillionsof words read by large language models like GPT. The bigger the band, the more rehearsal it needs.
The band does not see each picture only once. It goes through the whole stack again and again, getting a little better each time.
- Training data
- All the practice examples the network learns from.
- Label
- The right answer attached to each example, like an answer key.
- Training
- Showing examples, scoring mistakes, and turning the knobs, over and over.
- Epoch
- One full trip through all the practice examples.
- Test set
- Examples kept hidden during practice, used at the end to check what was really learned.