Everyone learns backpropagation as "apply the chain rule." Almost nobody explains why it's fast — and that "why" is the whole reason deep learning is computationally possible at all.
So I animated one full training step to show the part most explanations skip.
What you're actually seeing
Forward pass: a single signal travels through 3 weights → a prediction → compared to the target = the loss.
Backward pass: the error (δ) flows back through the network. δ₃ is computed at the output, then reused to get δ₂, which is reused to get δ₁ — never recalculated from scratch.
