Backpropagation Is Just Dynamic Programming (I Animated It to Prove It)

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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.

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