Backpropagation

That backward trace is called .

Think of checking a long calculation after finding that its answer is wrong. You do not start again from the beginning. You start at the end and work backward, and at each step you can see how much that step contributed to the final total.

Backpropagation does this through the network. The prediction moved forward through the connections. The calculation now runs backward through those steps and measures how sensitive the final error is to each weight.

That is the same number you would get by nudging one weight and running the mushroom through again, except it arrives for every weight at once, from a single backward pass, without rerunning the network once per weight.

The smooth calculations make that sensitivity measurable. "Share of the blame" is only an analogy. Backpropagation does not divide one error into pieces. It calculates how a small change to each weight would change the error.

Backpropagation does not move any weight. It calculates the sensitivities that an optimizer can use.