Beat 1 · Concrete
A line learns to divide
Two groups of dots. A straight line nudges itself until it cleanly splits them.
Two groups of dots — circles and squares — sit in the plane. The perceptron’s learning rule tilts and shifts a single straight line, one mistake at a time, until every circle is on one side and every square on the other: a clean dividing boundary, found from examples alone.
misclassified dot correctly placed clean boundary found ○ group A · □ group B
Beat 2 · Abstract
The unit, stripped bare
Inputs times weights, summed, then a threshold fires. The weights are the boundary.
A perceptron unit: each input x is multiplied by a weight w, the products are summed with a bias, and a threshold (step) decides whether the unit “fires”. Adjusting the weights is exactly the same act as tilting the dividing line from Beat 1 — the weights are the boundary.
weights w₁, w₂ (adjusting) boundary they define output fires
Beat 3 · Interactive
Then it hits a wall
Switch the dots to XOR — diagonal pairs. One straight line can never split them.
The same line, but now the dots form an XOR pattern: each group occupies two opposite corners. No single straight line can place all four corners correctly — at least two dots stay misclassified, forever. This is the wall Minsky & Papert proved in 1969, and it set up the first AI winter.
still wrong (the wall) correctly placed line, still trying