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Backpropagation: graphs, shapes and stability

Backpropagation: chain rule across the whole graph in one pass

A neural network is a chain of functions. To train it you need to know how each weight affects the error. Backpropagation computes this efficiently: it goes from output to input, applying the chain rule at each node. PyTorch does this automatically — but understanding the mechanics matters for diagnosing vanishing gradients, explosions, and dead neurons.

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