Change one parameter

Compare a derivative’s local prediction with the actual change in loss.

Fixed observations: x = 2, y = 5. Model: ŷ = wx + b. Loss: L = ½(ŷ − y)².

Prediction ŷ3
Error ŷ − y−2
Loss L2

Loss derivatives: ∂L/∂w = −4; ∂L/∂b = −2

Use a small change to test what the derivative predicts.