Assign Blame from Output to Input

Which parameter contributed to the error?

Backpropagation efficiently calculates how much each parameter contributed to the final loss. After a forward pass stores intermediate values, the process moves backward from loss through output and hidden layers, applying the calculus chain rule to connect local changes.

input -> hidden score -> activation -> output -> loss
              backward: loss blame flows <-------

Think of each operation reporting two things: what it received during the forward pass and how sensitive its output is to its input. The backward pass multiplies those local sensitivities along each path. The result for a parameter is its gradient, the direction and rate at which a small parameter change would affect loss.

Analogy: A final bill is wrong. Auditing backward asks how much each subtotal, quantity, and price contributed to the discrepancy. The chain rule connects responsibility through nested calculations.

Warning: Backpropagation computes gradients; it does not update parameters. An optimizer uses those gradients to choose the actual update.