The Training Run

Trained by hand from all-zero knobs, a perceptron learns to sort melons in four passes — every step checkable arithmetic, nothing arriving from outside.

The task: sort melons as ripe or not from thump-sound and skin-yellow, each rated 0 to 3. Six training melons: ripe at three-two, two-two, and one-three; unripe at zero-one, one-zero, and two-zero. Start in total ignorance — balance zero, both weights zero — and cycle the examples with the nudging rule. Pass one: the first ripe melon scores zero, reads unripe, wrong — add its features to the knobs. Three more errors follow — each unripe melon scoring positive, each subtracting its features — and the pass ends with the balance driven negative and the yellow weight ahead of sound. Pass two: four errors again, same characters — the stubborn three-two melon scoring exactly zero, the serial offender two-zero dragged down again. Pass three: only three errors; the quiet spread between ripe and unripe scores is widening. Pass four: six melons, six correct verdicts, no nudges — converged, after eleven corrections in all. The final knobs: balance minus five, sound one, yellow three. Read them as a sentence: ripe when sound plus three times yellow beats five. The machine decided yellowness matters three times as much as thump — not because anyone told it, but because that was the opinion the errors sculpted. And run the boundary check that closes every training story: each ripe melon now scores positive — four, three, and five — and each unripe scores negative — minus two, minus four, minus three. A straight line through melon-space, tilted three-to-one toward yellow, drawn by mistakes alone.