They did not speak equally loudly

So how could this be fixed?

The problem was never that the corrections were wrong. Each one hit its bottle exactly. The problem was that each one went all the way, and in going all the way it wiped out whatever the last bottle had established.

Which suggests something almost annoyingly simple. What if the corrections just did not go all the way?

Start again from the beginning, with all four weights back at 8. This time, do not try to fix the bottle completely. Move the weights only a little way toward being right, and let the next bottle move them a little further.

One part of the earlier fix still holds. Only move the weights whose inputs spoke up.

Back to the first bottle, then. The guess was 10 dollars too low. Look at what actually happened when the bottle was priced.

The same rule still applies. Viognier and apricotty are both 0, so this bottle gives us no reason to change their weights.

That leaves cabernet and plummy. Both affected the guess, but they did not speak equally loudly. Cabernet's input was 1, so it contributed 8 dollars. Plummy's input was 0.5, so it contributed 4 dollars.

That gap carries over to any change we make. Add 1 to cabernet's weight and the guess rises by a whole dollar, because its unit of 1 passes the change through untouched. Add the same 1 to plummy's weight and the guess rises by only 50 cents, because its unit of 0.5 halves the change on its way to the total.

That is how much the guess responds to each weight. The question the learning rule has to answer is the one next to it: how far should each weight actually move?

When we make this small correction, should we add the same number to both weights? Or should plummy's weight change less because its input was only half as strong?