TL;DRBackpropagation efficiently computes the gradient for every weight via the chain rule.
To do gradient descent in a deep net, you need each weight's gradient. Backprop computes them in one backward pass: run the input forward to get the loss, then propagate the error backward layer by layer using the chain rule, reusing intermediate results. It's what makes training deep networks computationally feasible — the algorithm that powers all modern deep learning.
Key points
Forward pass → loss; backward pass → gradients
Chain rule, layer by layer
Reuses intermediates (efficient)
Makes deep-net training feasible
Common mistakes
Thinking gradients are computed per-weight separately
Confusing the forward and backward passes
Vanishing/exploding gradients in very deep nets
Try it: Describe the forward-then-backward flow of one training step.
Example code
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<body style="background:#06040d;color:#e6e0ff;font-family:monospace;padding:20px"><pre>forward: input → layers → prediction → loss
backward: loss → gradients back through layers (chain rule)
update weights → repeat</pre></body></html>