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act VI

The Connectionist Turn

Backpropagation let networks with hidden layers learn. Almost everything modern rests on it.

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Learning from Blame

before this →Feedback: The Other Tree
1986Backpropagation — Rumelhart, Hinton and Williams show networks can learn their own hidden features.
2006Deep belief nets — Hinton's greedy layer-wise training restarts the neural-network field.

A single neuron can only draw a straight line. Stack neurons in layers and the network can bend, curve, and carve out any shape. But for thirty years, nobody could work out how to train the hidden layers — the neurons in the middle, whose correct outputs nobody knows.

inputhiddenoutputa boundary no line can make
hidden layers turn straight lines into curves

The algorithm

Backpropagation (popularised in 1986 by Rumelhart, Hinton, and Williams) solves the credit-assignment problem. Make a prediction, measure the error, then send the blame backward through the network using the chain rule. Each weight learns how much it contributed to the mistake, and moves to reduce it.

A multilayer perceptron — an input layer, one or more hidden layers, an output layer — is the result. With enough hidden units it can approximate essentially any function. The universal approximation theorem made it official.

What went wrong anyway

the vanishing gradient

Blame weakens as it travels backward. In a deep network, the signal shrinks at every layer until early layers learn almost nothing — the vanishing gradient problem. This is why “deep” learning had to wait: it took better activations (ReLU), better initialisation, and later skip connections to let the gradient flow.

the connectionRemember this when we reach ResNets and transformers. Both are, at heart, careful answers to the vanishing gradient.
PREDICTforward pass through every layer
BLAMEchain rule, backward through the stack
FIXnudge weights; repeat a million times
introduces →hidden layermultilayer perceptronvanishing gradient
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