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Follow one weight past all four bottles, and the whole thing becomes clear.
Press next bottle to step through the four wines. Nothing trains here. The weights are frozen at the place training gave up, all four sitting near 12 and a half, having started at 20 and drifted together until they stopped moving. All you are doing is looking at what each bottle would ask of them.
Take the cabernet weight, and watch what the four bottles ask of it.
The plummy cabernet arrives. It costs 40 and the model guesses too low. The error is positive, cabernet's unit is 1, so the rule pushes the cabernet weight up.
The apricotty cabernet arrives. It costs 10 and the model guesses too high. The error is negative, cabernet's unit is 1 again, so the rule pushes the cabernet weight down.
Same weight. Same size of push, because the two errors are the same size. Opposite directions.
The two bottles cancel. Not approximately, exactly, and the cabernet weight ends the pair where it started.
Now do it for viognier. The plummy viognier is cheap, pushing it down. The apricotty viognier is expensive, pushing it up. Cancelled.
Plummy? Up on the cabernet, down on the viognier. Cancelled.
Apricotty? Down on the cabernet, up on the viognier. Cancelled.
All four weights, cancelled by their own training set.
And notice this is not the model being stupid. Each of those corrections was correct. Every one of them made the guess better for the bottle in front of it. It is only when you put them together that they annihilate.
Here is the sentence worth carrying out of this chapter:
The cabernet weight is being asked to be two different numbers, and it can only be one.
A high number, because plummy cabernets are expensive. A low number, because apricotty cabernets are cheap. There is no single value that is both, so the rule averages the demands and lands in the middle, which satisfies neither.
Every weight in this machine is in the same position. That is why the model settles on 25 dollars for everything and stops.
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