The error goes the other way

Bottle six is worth stopping on, because something happens there that has not happened once in this entire chapter.

It is a plain viognier. No plum, no apricot, nothing but the grape. It costs 6 dollars, and it is the cheapest wine in the set.

By the time it arrives in that first round, five bottles have already pushed the weights around. Viognier is sitting at 11.66.

The guess is 11 dollars 66. The wine costs 6.

The guess is too high.

Every previous bottle was underpriced, and every correction so far has pushed weights up. This one is different, and the difference shows up in the very first step.

The error has always been worked out the same way: the real price minus the guess.

On bottle one that was 22 - 12, which is 10. A positive number, because the guess fell short. Here the same subtraction gives:

6 - 11.66 = -5.66

Below zero, for the first time. Not because anything new was introduced, but because the guess overshot, and subtracting a bigger number from a smaller one lands underneath zero. A price 5 dollars 66 too high and a price 5 dollars 66 too low are the same distance from correct. The minus sign is only recording which side it fell on.

Now push that through the rule.

weight change = error x unit x learning rate

That is the whole event. A negative times a positive gives a negative, so the change is negative, and adding a negative number takes the weight down instead of up. Viognier drops from 11.66 to 11.09.

Nothing special was added to make any of this happen. There is no second rule for guesses that come out too high. It is the same multiplication that raised weights on the first five bottles, running unchanged, and the sign of the error is the only thing that differs.

Which is worth noticing, because it is what makes the whole thing self-correcting. The weights are not being pushed in some predetermined direction. They are being pushed toward whatever the bottles say, and when a bottle says too much, they come back down.